Talk:Global Positioning System/Archive 6

Figures on demodulation, decoding, and position calculation
There are problems with the figure in the file, Gps_ca_gold.svg depicted in the section, Demodulation and decoding, of the 00:51, 6 January 2010 version. The problems are
 * (1) The figure makes it appear that there are only two channels corresponding to satellite n1 and satellite n2. There should be channels corresponding to satellite n1, satellite n2, satellite n3 ... . and
 * (2) Some of the text is shown with a black font on a blue background making it difficult to read.

There is certainly no objection to improving on the art in the original figure in the file, Image:Ca gold.jpg, but please make sure you take care of the problems (1) and (2) above.

There is a problem with the figure in the file, Lat_2spheres_2.svg‎ depicted in the section, Position calculation advanced, of the 00:51, 6 January 2010 version.. This figure is not compatible with the text, "A figure, Two Sphere Surfaces Intersecting in a Circle, is shown below depicting this which hopefully will aid the reader in visualizing this intersection. Two points at which the surfaces of the spheres intersect are clearly marked on the figure. The distance between these two points is the diameter of the circle of intersection. If you are not convinced of this, consider how a side view of the intersecting spheres would look. This view would look exactly the same as the figure because of the symmetry of the spheres. And in fact a view from any horizontal direction would look exactly the same. This should make it clear to the reader that the surfaces of the two spheres actually do intersect in a circle."

In order to be compatible with the text, it is necessary that the polar axis of each sphere be vertical and that they are both along the same vertical line. There is no objection to improving the art work of the figure in the file, Lat_2spheres_2.jpg‎, but any improved version must be fully compatible with the text, just looking pretty is not sufficient. —Preceding unsigned comment added by RHB100 (talk • contribs) 21:33, 6 January 2010 (UTC)


 * Isn't Ca gold.jpg wrong anyway, though? I mean, don't most modern receivers modulate the broadcast signal down to an intermediate frequency, digitise it, then track each individual satellite with a separate costas loop? That's the impression I got, from the books I've read. I mean, every satellite's signal is doppler shifted, so the carrier frequencies are actually spread over a few kHz; surely trying to demodulate them all with the same carrier signal wouldn't work? Of course, I realise some simplifications to make the article accessible to its audience Mike1024 (t/c) 11:12, 7 January 2010 (UTC)

There are some simplifications in Ca gold.jpg. However, as you point out some simplifications to make the article accessible to its audience are necessary. RHB100 (talk) 20:40, 15 January 2010 (UTC)

NUDET/nuclear detonation detection payload needs love?
IMO a section of the article should be devoted to info on the nuclear detonation detection payload aboard GPS satellites. Since it seems that the article on the satellites themselves has been largely merged into this article on GPS, their alternate use should be mentioned here. This is something that almost no one with user level knowledge about GPS knows, but a use that is probably just as important to the US military as GPS location. I always thought it was clever that they found a way to build a watchful eye on the world that no one would want to destroy :). If someone wants to find for references to this usage, you could start with looking up the suspected nuclear detonation off the coast of Africa years ago, I think that's how I had learned about it. these 2 pages are a start: http://www.rand.org/pubs/monograph_reports/MR614/MR614.appb.pdf http://www.decodesystems.com/gps.html —Preceding unsigned comment added by 67.172.0.150 (talk) 13:41, 11 January 2010 (UTC)

inaccurate
The hidden comment, "The wikipedia article does describe trilateration, but not how an iterative version for the problem at hand would work. The algoritm which is mentioned in this article only does not always converge towards a solution" is vague, ambigous, and apparently self contradictory depending on how you resolve the vagueness and ambiguity. The Wikipedia article on GPS certainly does describe how an iterative approach using one dimensional root finding with the aid of trilateration would work along with a description of how a multi-dimensional approach not using trilateration would work. RHB100 (talk) 21:42, 22 February 2010 (UTC)

The error analysis which has been added to the GPS article is based on [http://books.google.com/books?id=lvI1a5J_4ewC&printsec=frontcover&source=gbs_navlinks_s#v=onepage&q=&f=false The global positioning system: theory and applications By Bradford W. Parkinson, James J. Spilker], which is a highly respected source. RHB100 (talk) 21:42, 22 February 2010 (UTC)

''The receiver utilizes the messages it receives to determine thetransit time of each message and computes the distances to eachsatellite. These distances along with the satellites' locations areused with the possible aid of trilaterationto compute the position of the receiver. This position is thendisplayed, perhaps with a moving map display or latitude and longitude;elevation information may be included. Many GPS units also show derivedinformation such as direction and speed, calculated from positionchanges.''
 * This is not true. For this, the receiver would need a very precise clock. It doesn't have one. In fact, it measures the differences between the times of the messages, and from those differences, it calculates the differences between the distances, and then it calculates the location. I will fix this, feel free to change my wordings and so. --Gerrit CUTEDH 22:34, 11 February 2010 (UTC)


 * The statement "This is not true. For this, the receiver would need a very precise clock" is an invalid conclusion. Just because you don't know how to get around the problem of receiver clock inaccuracy does not mean that other people cannot solve the problem. RHB100 (talk) 20:47, 22 February 2010 (UTC)


 * Unfortunately this error is very common. One website that gets it right is, otherwise one would probably have to look in scientific literature and technical reports and patents, and I'm not sure how accessible and public those are. --Gerrit CUTEDH 22:45, 11 February 2010 (UTC)
 * An accurate clock is not required to get the distances to each satellite. The clock just needs to be "in the ball park" and the distance to the fourth satellite along with some very clever math will provide the clock correction. --  Denelson83  09:02, 12 February 2010 (UTC)
 * I do agree with Gerrit. If a simplified model is used to explain the principle, keep it simple and do not try to use the simple model to explain the complex calculations. It's nice that the next paragraaf explains the clock correction. But the "Correcting a GPS receiver's clock" is flawed (as well). The suggested algoritm sometimes converges towards a solution, sometimes 'overcompensates' and then does not converge to a solution and sometimes does not even go towards the solution. The $$\scriptstyle b \,=\, da / c\ $$ does not indicate in which direction and by how much the clock should be corrected for. In general the trilateration solution is not a good solution, problems with it are: It does not always converge, if it does converge it converges 'slow', it can not be used to discern between the two points. Compared to the pseudoalgoritm published on several places on the internet it uses a hugh amount of operations.


 * I think the statement regarding $$\scriptstyle b \,=\, da / c\ $$ is untrue since it is specifically stated that the GPS receiver clock can be advanced if $$ \scriptstyle  b $$ is positive or delayed if $$ \scriptstyle b $$ is negative.  It also says by how much since b is in units of time. RHB100 (talk) 20:47, 22 February 2010 (UTC)
 * With the information of one single constellation of 4 satellites and one receiver and one starting error, the $$\scriptstyle b \,=\, da / c\ $$ gives different results depending on which satellite is used as the 4th satellite. With the same constellation, b can be positive and can be negative, also the value does vary to some extend, some values becoming so large that if used for correction the error becomes larger.
 * With positive and negative values for one single constellation, there is no indication that b should be added or subtracted to correct the error, with the different sizes the size is no real indication for the size of the error.
 * I do agree with you that you stated how to add or subtract b from the 'time'. But by 'correction' I expect that after the correction the error is smaller than before. With B being negative and positive for the same constellation and 'time', it can not be that in both situations the endresult is an improvement.
 * The algoritm I used was constructed from the information in the 'trilateration' article and from the information given in the GPS article. Because the used formulas where derived from the texts it is difficult to see where the actual problem lies. This is not the only objection to iteration using trilateration, but one of the objections to iteration with trilateration. So if the complete algoritm was given in formulas or in programming code (pseudo code for example) it would be easier to point out the shortcommings of the method.
 * Crazy Software Productions (talk) 21:11, 24 February 2010 (UTC)


 * The pseudorangealgoritm works far superior compared to trilatertion. In general the pseudorange algoritm needs only one iteration for each solution and needs far fewer operations than trilateration for each cycle. Pseudorange calculation can be used to correct the clocktime, but does not need the clock time, only the relative distances (pseudoranges) are needed. The pseudo algoritm does not use spheres (and is not based on spheres).


 * I have implemented the pseudo range algoritm and the trilateration algoritm. With the trilateration algoritm I have showed with examples that it does not always converge. I came to the conclusion that the author did not try the trilateration algoritm on enough examples to see that there are plenty of examples where it does not converge well or at all.
 * The pseudo range algoritm always performs well, but it needs a starting estimate for were the receiver is. This starting estimate can be hundreds of miles off, even with hundreds of miles off, 5 iterations are enough to get a solution which is matematically correct within mm (milimeters). (With almost all satellite configurations even the middle of the earth can be choosen as a starting estimate and still only 5 iterations are needed to get within a mm solution).Crazy Software Productions (talk) 16:39, 20 February 2010 (UTC)


 * The paragraph right after that explains clock accuracy. Your explanation needlessly introduces a complex topic "differences in distance".  The idea is that this section oversimplifies in order to communicate the concept.  That it is not rigorous is a feature, not an inaccuracy.  Despite that, it was reasonably faithful to the technical material, but I might be biased.  (I wrote the text which largely remained there.)  —EncMstr (talk) 23:38, 11 February 2010 (UTC)

In a paragraph above, Gerrit says "One website that gets it right is ". However if you read this article you will find that it says, "The position is determined based on triangulation". But GPS is not based on triangulation as defined at triangulation. RHB100 (talk) 21:15, 17 February 2010 (UTC)

Move

 * The following discussion is an archived discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section. 

The result of the move request was: page not moved after 18 days. Anthony Appleyard (talk) 15:52, 21 March 2010 (UTC)

Global Positioning System → GPS — Latter redirects here, WP:COMMONNAME, Category:GPS and this discussion. —Justin (koavf)❤T☮C☺M☯ 23:03, 4 March 2010 (UTC)


 * Oppose. Our usual titling standards tend to support expanding acronyms, unless the expanded version is never used at all. For instance, we have an article at Federal Bureau of Investigation for the entity universally known as the FBI. "Global Positioning System" is much more frequently used than that example, even if it is frequently abbreviated. — Gavia immer (talk) 12:39, 21 March 2010 (UTC)
 * The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

Relativity - correction
The effect of gravitational frequency shift on the GPS system due to general relativity is that a clock closer to a massive object will be slower than a clock farther away. Applied to the GPS system, the receivers are much closer to Earth than the satellites, causing the GPS clocks to be faster by a factor of 5×10^(-10), or about 45.9 μs/day. This gravitational frequency shift is also a noticeable effect.

There is a mistake. Yes, it is true, that the clock father away will be faster due to the weaker gravitional field. However, in case of orbiting satellites the effective gravitational field is completely canceled by the acceleration (remember totaly weightless astronauts in the orbit). According of the postulate of the general relativity theory an steady acceleration is equivalent to a homogenuos gravitational field - the satellite is in the effective zero-field. Thus, the factor 45.9 μs/day must correspond to zero-field time dilatation, not somewhat-weaker-field time dilatation.

--Huncut (talk) 13:30, 18 March 2010 (UTC)

GPS2, is there such a thing?
I heard a guy talking about GPS2. According to him, it wasn't a new system, not even new satellites. Instead it was a new way of sending signals, so that the receiver would be able to tell whether, and maybe even how, a signal had reflected on buildings or other obstacles, before reaching the receiver.

There is a wikipedia page "GPS2" that redirects to the GPS article, but no information on it here.

Does anyone know about this?

Velle (talk) 23:25, 24 March 2010 (UTC)


 * Perhaps you're thinking of GPS modernization, which is (according to that article) sometimes called GPS III, and involves the launch of so-called 'block 3' satellites? The GPS satellites have a designed life of 10 to 15 years, so as they gradually get replaced, new satellites are launched with some new capabilities, to get the benefits of technologies developed since the 1985 launch of the first GPS satellites. The new signals will be easier for receivers to track reliably, and they'll be broadcast alongside the existing signals so older receivers will keep on working. For more information, see GPS modernization.


 * Block 1 GPS satellites were the demonstration satellites launched in the 1970s and early 1980s prior to the launch of the main GPS constellation; Block 2 satellites are the current main satellites; Block 3 satellites are the modernised satellites with new signals. I've never heard the expression "GPS 2" used before, but perhaps it would refer to the block 2 satellites, i.e. the satellites currently in operation, while "GPS 1" would refer to the block 1 satellites? Mike1024 (t/c) 09:20, 25 March 2010 (UTC)

Iteration using Trilateraton
''

Note 1.

In the trilateration / gps article this algoritm is described.

What root finding algorithm was used? RHB100 (talk) 21:17, 12 April 2010 (UTC)

A trilateration point is calculated. (Trilat point TP X,Y,Z)

The distance to the fourth satellite (X4,Y4,Z4) R4 is calculated.

R4= SQRT( (X - X4)^2 + (Y - Y4)^2 + (Z - Z4)^2  )

P4 is the measured pseudorange to the fourth satellite.

DA = R4 - P4 This is supposidly used for the clock correction.

''

''

Note 2.

All numbers are represented in meters except for da/c which is meters/(meters/sec) = seconds.

The trilateraton points can easely be verified by recalculating the distance to the satellites,

this will give the exact measured pseudoranges.

R4 can easely be verified by recalculationg the distance from the trilateration point to the fourth satellite.

P4 is the measured pseudorange distance to the satellite which is used as the fourth satellite.

DA and DA/c can easely be calculated.

''

The Example. The satellite constellation is from an example on the web. Satellite (SV) coordinates in ECEF XYZ Ephemeris Parameters and SV time for satellites SV15 SV27 SV7 and SV31.

The example

The above constellation is used four times, each time a different satellite is used as the fourth satellite. Three satellites are used to calculate the trilateration point X,Y,Z. The fourth satellite is used to calculate the distance (R4) from the trilateration point to the 4th sphere.

X, Y, and Z as used above and below are first estimates of receiver position based on intersection of sphere surfaces. RHB100 (talk) 20:20, 14 April 2010 (UTC)

The corrections are shown in Red. ( -1488.179383,  -176.3092095,   +148.8429348,   -269.6591897 )

Off the above numbers only two of the corrections converge towards a solution, two others diverge from a solution. The example shows that the calculated corrections can be in the wrong direction (plus and minus) and the corrections do vary in 'size'. Because the direction of the error and the size of the error is unknown, a correction can not be evaluated to being correct or not. This example shows that iteration using trilateration using the algoritme as given in both articles can not work.

'''You should not have used da/c. You should have used, the correction from one of the root finding methods in Numerical Recipes.''' RHB100 (talk) 20:38, 13 April 2010 (UTC)

It is a regrettable that the author(s) of these parts of the articles have not checked for this.

This is not the only problem for this supposed method of positional calculation.

Conclusion: Iterating using trilateration as described in the article and in the trilateration article is not suitable for positional calculations.

'''There is no description of the iterative algorithm using trilateration to use in the GPS article. Therefore your conclusion refers to something which does not exist. Most important, there is no description of the function of da for choosing the value of b for the next iteration. Reference is made to the chapter on root finding in the book on Numerical Recipes but the choice of which root finding method to use is the responsibility of the algorithm developer. I have not found any statement of what root finding method you used. If you simply used da/c to estimate the time correction, it is not at all surprising that your algorithm did not converge. You need to thoroughly understand the chapter on root finding in numerical recipes.''' RHB100 (talk) 21:17, 12 April 2010 (UTC)

Crazy Software Productions (talk) 12:02, 7 April 2010 (UTC)


 * If this is not original research and if it can be properly sourced (with preferably secondary sources), perhaps you can incorporate it into the article. DVdm (talk) 12:09, 7 April 2010 (UTC)
 * The article mentions trilateration eleven times and discusses solving for position and clock offset separately - but I can't see a citation supporting that. For example, where article says "The receiver can solve by trilateration followed by one dimensional numerical root finding. [48]" citing Numerical Recipes - but google book search tells me that numerical recipes does not contain the word "trilateration" or "GPS" - in other words, that citation doesn't really seem to support the assertion that trilateration is used for GPS positioning. Does anyone know where all this stuff about trilateration is sourced from? Mike1024 (t/c) 16:06, 7 April 2010 (UTC)

Well you should certainly not expect any search of Numerical Recipes or any other book on numerical analysis to contain the word trilateration since trilateration is not a numerical technique. However, you should recognize that finding the value of b which drives da to zero (i.e. finding the clock correction which causes 4 satellite surfaces to intersect) is a root finding problem. Therefore you should search Numerical Recipes for "root finding". RHB100 (talk) 02:05, 13 April 2010 (UTC)

Soure data of the example, the constellation given on: http://www.colorado.edu/geography/gcraft/notes/gps/gps_f.html On the page :   Pseudo-Range Navigation Solution The timing error is made up, the pseudoranges are calculated, from the distances and the timing error. The picture is taken from the main article. The algoritm is implemented as described in the GPS, trilateration articles.

All tekst, building the algoritm and the calculations is original. Therefore there is no source. Because there is no source, the 'proof' is selfcontained, it can easily be verified. There is no need to calculate where the three spheres intersect, you can just verify that the calculated point is on all three spheres. (Use Phytagoras for that.) And therefore the calculated point is the same as the trilateration point. R4 can also be calculated (also with Phytagoras). Calculating the correction then is easy calculate DA (and DA/c), which is supposed to be used as the correction for the clock. The resulting factor DA is the correction for the clock (in meters) or DA/c (in seconds) is the correction for the clock. Because DA varies in sign and in size, it can not be that all values converge to a solution. So some of the anwsers will diverge from the solution. Trilateration has some further flaws. So the remark I added: ''Regrettabilly this does not work, in a single constellation, one can get four different value's for da, depending on which satellite is used as the fourth satellite. Some of the values will converge towards a solution some of the values will not. See the discussion page for an example where the calculated DA values do not converge towards a solution.'', is correct and can therefore be part of the article. I'll await a reaction, but am considering to reinstate the remark. I realy do not think the complete proof of something NOT working should be in a main article.

For a level playing field I expect the text about trilateration to be threated with the same rules as the removed text. Crazy Software Productions (talk) 21:28, 7 April 2010 (UTC)


 * I don't think that such a paragraph will survive. It sounds highly unencyclopedic. Perhaps you can find a way put things right by either (1) challenging the part that is wrong (or unsourced) with tags, or (2) by correcting the erroneous text, with sources. DVdm (talk) 21:40, 7 April 2010 (UTC)


 * Added some citation needed tags - I don't know how the article came to contain so many mentions of trilateration; surely traditional trilateration surveys use round-trip-time electronic distance measurement, and so don't have to worry about receiver clock biases? Mike1024 (t/c) 09:35, 8 April 2010 (UTC)


 * If you get such wildly different da values for each fourth satellite, why not just average them out? --  Denelson83  02:57, 8 April 2010 (UTC)


 * If you've got a system with four equations (i.e. four pseudoranges) and four unknowns (position in x, y, and z, and receiver clock bias) the system is precisely determined - there should be no errors to average out. Allow me to demonstrate!

We can calculate the Euclidean distance from the x,y,z positions of the rover and satellites - Let's call that the true range.


 * In other words: With 4 measurements and 4 unknowns, a solution is available with no error - so there's no point in averaging errors out! Mike1024 (t/c) 11:48, 8 April 2010 (UTC)


 * In reaction to Denelson83 why not just average them out?
 * My point is to show that iteration with trilateration as described in te mentioned articles is seriously flawed, it is not my intention to improve the algoritm and therefore obscure the flaws. Yes it might be possible to improve by taking the average. Or using the two middle values and averaging them. Both methods actually do improve this example, and maybe more constellations will be improved by them, but there is no prove (not even plausibility) that this will improve all situations where there is non-convergence. So to implement such a 'average' only obscures the 'errors' in the method. But as said I am trying to show that the suggested algoritm is not tested sufficiently and therefore it is very unlikely that this is the method used for positioning.
 * (The pseudorange calculation method is wel researched, does not contain this flaw and neither does it contain the flaws suggested in the article, and is probably the basis where most positioning calculation systems are based on.).


 * My reaction to Mike
 * Thanks for the support.
 * Question how did you obtain your results?
 * I had some trouble in replicating your results (in Excel), but this was to the fact that the numbers published above where not exactly the same as the numbers I had used. So using the exact numbers of above I could replicate your result starting of with a first estimate of the centre of the earth within four iterations you get a sub centimeter result, to replicate to your accuracy I needed five iterations, that is also the limit with the amount of digits the calculation is done. Although by the fifth iteration the calculation is accurate to abouth 7 digits after the decimal point, this is still an approximation. In normal circumstances the previous position can be used and one itration will be more than sufficient for all practical purposes.

Crazy Software Productions (talk) 22:40, 8 April 2010 (UTC)


 * Question how did you obtain your results?
 * I used the technique outlined by Bancroft in "An Algebraic Solution of the GPS Equations" - more information available in this assignment sheet. It does not require iteration, but it's unintuitive; IMHO it's complicated enough to be beyond the scope of an encyclopaedia article.


 * Although by the fifth iteration the calculation is accurate to about 7 digits after the decimal point, this is still an approximation.
 * Most calculations end up being performed using 64-bit floating point numbers where the fraction is 52 bits long. You can see some doubles in binary format using this applet. The practical implication of this is: there is a one-bit difference between 22262088.180000000 and 22262088.180000003 meaning smaller additions get lost due to rounding error. Use almost any calculator to calculate 22262088.18 + 0.00000005 - 22262088.18 and see what you get! You can read more about this in "What Every Computer Scientist Should Know About Floating-Point Arithmetic".
 * It's possible to avoid this problem by using Arbitrary-precision arithmetic - where instead of 52 bits of precision, you can have as many bits as you can fit into memory. However, this tends to be slow, because modern processors have hardware-accelerated handling of 64-bit floating point numbers - but no hardware acceleration for arbitrary precision arithmetic. Applications like the Windows XP calculator use arbitrary precision arithmetic so it will get 22262088.18 + 0.00000005 - 22262088.18 right.
 * There's no point in using arbitrary-precision arithmetic for GPS (mostly) because a rounding error of 3 nanometres is much, much smaller than errors due to the ionosphere, measurement noise, ephemeris error, multipath, and so on. Mike1024 (t/c) 09:31, 9 April 2010 (UTC)

GPS article discusses but does not specify algorithm using trilateration
The conclusion, "Iterating using trilateration as described in the article and in the trilateration article is not suitable for positional calculations" made above is based on based on a non existent description.

'''There is no description of the iterative algorithm using trilateration to use in the GPS article. Therefore your conclusion refers to something which does not exist. Most important, there is no description of the function of da for choosing the value of b for the next iteration. Reference is made to the chapter on root finding in the book on Numerical Recipes but the choice of which root finding method to use is the responsibility of the algorithm developer. I have not found any statement of what root finding method you used. If you simply used da/c to estimate the time correction, it is not at all surprising that your algorithm did not converge. You need to thoroughly understand the chapter on root finding in numerical recipes.''' RHB100 (talk) 21:17, 12 April 2010 (UTC)


 * You say that that there is no description of choosing b for the next iteration. At the moment the article seems to contain a few different equations, examples of algorithms, and links to pages like Trilateration which contain other equations ("The article, trilateration, shows mathematically how the equation for this circle of intersection is determined."). Because of this, I think it's easy for a reader to become confused about how the calculations are performed.
 * Also I think because of this confusion, it is difficult for me to know whether the article is right or not; if there are calculations and I don't get the right answer when I perform them, does that mean the calculations are wrong, or that I have misunderstood them or missed steps out? Perhaps we should make the article clear, so that I do not misunderstand or miss steps out - and then when people perform the calculations and get the right answers it will be easy for them to be confident the article is correct!
 * I also think that if it isn't possible to present the calculations clearly and without steps missed out, then maybe instead of presenting the calculations unclearly and confusing people, we should refer them to a credible source where the calculations are made clear and aren't too confusing. What do you guys think? Mike1024 (t/c) 10:10, 20 April 2010 (UTC)


 * I am not convinced that a detailed algorithm is required in an encyclopedia article. The general principles upon which an algorithm may be developed is quite often more important. RHB100 (talk) 20:13, 22 April 2010 (UTC)


 * Surely even if you don't think a working algorithm would be appropriate for the article, you could post more detail to this talk page? For example, here's the code I used to perform the calculations above:
 * As I mentioned above, I used the technique outlined by Bancroft in "An Algebraic Solution of the GPS Equations", which is also explained in this assignment sheet. Would it trouble you too much to provide this much information on how the algorithm in the article works? This way we know there are no omitted steps! Mike1024 (t/c) 22:26, 22 April 2010 (UTC)

Mike1024, I will be happy to post more detailed information. I have now got a FORTRAN program written and the results indicate that it works for all 4 cases. It uses zbrac.f for finding a bracket and rtbis.f for finding the solution using the midpoint method from Numerical Recipes. It uses a routine called trilat.f that I wrote. I will try to further verify that the solution is correct and clean up the code before posting. I am glad to see that you posted that pdf document on the Bancroft method. RHB100 (talk) 22:03, 23 April 2010 (UTC)

Mike1024, I have placed code and results from using trilateration and one dimensional root finding in a separate section below. RHB100 (talk) 03:43, 24 April 2010 (UTC)


 * I think that anything that is not properly backed by secondary sources should be removed from the article. DVdm (talk) 10:18, 20 April 2010 (UTC)

The method involving trilateration is fully backed up by the many references to GPS and trilateration articles below shown below and the book on Numerical Recipes. RHB100 (talk) 20:13, 22 April 2010 (UTC)

Thumbnail sizes
Thumbnails, per guidelines, should not be sized; that way each browser / user can set their preferred default size, and if more clarify is needed they click on the image for the full size version. Currently, almost all the images were sized to similar to thumbnail size, and the two outliers are understandable at thumbnail size.

I goofed on the edit history; those should have been links to Accessibility and IMGSIZE - Davandron | Talk 02:20, 12 April 2010 (UTC)


 * How big have you set your thumbnails? Mine are 200px wide, which I think is the default(?) - I've forced these images to that size to ensure that we're all seeing the same thing, regardless of our settings - and I'm not sure I'd agree that these images are understandable at thumbnail size.


 * Also, I note that Image:ConstellationGPS.gif seems to lose its animation when scaled down. There seem to be periodic mediawiki changes that break/unbreak animated GIF scaling, which might be why it was scaled down in the first place - but can we agree that at present, scaling the image down breaks the animation? Mike1024 (t/c) 08:57, 12 April 2010 (UTC)

Excellent catch on the animation; it shouldn't be a thumbnail at all. Looks like this was already fixed. On the flow diagrams, perhaps they should be removed (style guide "Avoid entering textual information as images" and accessibility "Where possible, any charts or diagrams should have a text equivalent, or should be well-described so that users who can't see the image can gain some understanding of the concept."). Alternatively, I believe they could be edited to increase clarity at smaller sizes, and marked-up as images at a designed size (note, from guide "An image should generally be no more than 500 pixels tall and 400 pixels"). Thoughts? - Davandron | Talk 16:13, 15 April 2010 (UTC)

The proper thumbnail size for these images is 300 px. This is fully allowed by Wikipedia. Also it is quite proper to use text in a diagram. Your quote from what you call the style guide has nothing to do with these diagrams. RHB100 (talk) 03:50, 17 April 2010 (UTC)

Articles relating GPS and Trilateration
There are many articles relating GPS and Trilateration as can be seen at GPS and Trilateration articles. Unfortunately most of these articles seemed to be dumbed down, they talk about circles instead of spheres as if the concept of a sphere were too difficult to comprehend.

One of the better articles in my opinion is "Position Determination with GPS".

It is not difficult to understand that there are so many such articles since one of the fundamental principles in GPS is the determination of location in part by determining the intersections of three spheres. Once the clock error has been approximately driven to zero so that four spheres intersect approximately, an estimate of position will have been obtained.

This is the reason why trilateration as a part of numerical root finding (i.e. finding the value of b which drives da to zero through an iterative process) is one of the two methods discussed in Position calculation, advanced.

The other method discussed is multidimensional root finding. This method does not involve the use of trilateration.

It should be kept in mind that these methods are discussed on the conceptual level. They are not descriptions of algorithms.

It should be kept in mind that there is noting to prevent someone with the capability from adding a description of the Bancroft method. I do not have access to the article on this method. RHB100 (talk) 01:46, 13 April 2010 (UTC)

Code and results from using trilateration and one dimensional root finding
There have been some who have expressed some doubt as to whether the method involving trilateration and one dimensional root finding as discussed in the GPS article would work. It is hoped that this section will clarify that misunderstanding by showing that this method certainly does work. The results of running a Fortran program which uses this method can be seen by clicking show on the bar labelled "Results from using trilateration and one dimensional root finding". Three of the routines that comprise the Fortran program can be seen by clicking show on the indicated bars below. Two of the subroutines, subroutines zbrac and rtbis, cannot be shown because they are protected by copyright. These subroutines can be found in the book on Numerical Recipes. The subroutine zbrac performs the task of finding a bracket for the solution given an initial guess. The subroutine rtbis performs the task of making a binary search to find a small enough bracket of the solution to meet the specified accuracy.

The results below show for each case the positions and psuedoranges of the three satellites which are used for trilateration and the one satellite which is not used for trilateration. The solution, the receiver position is then shown along with RBIAS which is the bias in dimensions of distance rather than time. RHB100 (talk) 21:14, 24 April 2010 (UTC)

   Results from using trilateration and one dimensional root finding

Trilateration Satellites Sat #    X 	            Y 	           Z 	 	PSUEDORANGE 1   15524471.180   -16649826.220    13512272.390    22262088.180  2    -2304058.534   -23287906.470    11917038.110    19908187.050  3   -14799931.400   -21425358.240     6069947.224    21479180.580  Non-trilateration Satellite Sat #    X 	            Y 	           Z 	 	PSUEDORANGE 4   16680243.360    -3069625.561    20378551.050    24554242.170                   X 	       Y 	   Z      RBIAS Solution =   -733186.0  -5443792.0   3231193.0 -300.0 STOP Normal completion in routine main of gps.

[rhb100@localhost gps]$ ./gps.exe Trilateration Satellites Sat #    X 	            Y 	           Z 	 	PSUEDORANGE 1   15524471.180   -16649826.220    13512272.390    22262088.180  2    -2304058.534   -23287906.470    11917038.110    19908187.050  4    16680243.360    -3069625.561    20378551.050    24554242.170  Non-trilateration Satellite Sat #    X 	            Y 	           Z 	 	PSUEDORANGE 3  -14799931.400   -21425358.240     6069947.224    21479180.580                   X 	       Y 	   Z      RBIAS Solution =   -733186.0  -5443792.0   3231193.0 -300.0 STOP Normal completion in routine main of gps.

[rhb100@localhost gps]$ ./gps.exe Trilateration Satellites Sat #    X 	            Y 	           Z 	 	PSUEDORANGE 1   15524471.180   -16649826.220    13512272.390    22262088.180  3   -14799931.400   -21425358.240     6069947.224    21479180.580  4    16680243.360    -3069625.561    20378551.050    24554242.170  Non-trilateration Satellite Sat #    X 	            Y 	           Z 	 	PSUEDORANGE 2   -2304058.534   -23287906.470    11917038.110    19908187.050                   X 	       Y 	   Z      RBIAS Solution =   -733186.0  -5443792.0   3231193.0 -300.0 STOP Normal completion in routine main of gps.

[rhb100@localhost gps]$ ./gps.exe Trilateration Satellites Sat #    X 	            Y 	           Z 	 	PSUEDORANGE 2   -2304058.534   -23287906.470    11917038.110    19908187.050  3   -14799931.400   -21425358.240     6069947.224    21479180.580  4    16680243.360    -3069625.561    20378551.050    24554242.170  Non-trilateration Satellite Sat #    X 	            Y 	           Z 	 	PSUEDORANGE 1   15524471.180   -16649826.220    13512272.390    22262088.180                   X 	       Y 	   Z      RBIAS Solution =   -733186.0  -5443792.0   3231193.0 -300.0 STOP Normal completion in routine main of gps. [rhb100@localhost gps]$

The main routine reads in and writes out the data. A call to trilat and a function evaluation of dacomp help to provide initial estimates of a bounding bracket between BIAS1 and BIAS2. A call to zbrac modifies BIAS1 and BIAS2 if necessary to assure that the solution is bracketed. The subroutine rtbis returns with the solution, RGBIAS, which is the value of the argument of function dacomp required to cause the function to evaluate close enough to zero to satisfy the specified accuracy requirement.

   MAIN FORTRAN ROUTINE  IMPLICIT DOUBLE PRECISION (A-H,O-Z) C       1         2         3         4         5         6         7 C 3456789012345678901234567890123456789012345678901234567890123456789012 C EXTERNAL DACOMP DOUBLE PRECISION XSAT(5), YSAT(5), ZSAT(5), PRANGE(3), ERRMAT(3) DOUBLE PRECISION ERRTOT(2), SATTIM(3), RSAT(5,3), R4(2), DAA(2) CHARACTER HEAD1*70, HEAD2*70 LOGICAL SUCCES COMMON /COMMDA/ RSAT, PRANGE, SATTIM, PRANTI INW = 25 IOUT = 45 CLIGHT = 299792458. ! meters per second OPEN(UNIT = INW, FILE = 'sat_position_prange.txt'    2, FORM='FORMATTED', ACTION='READ', STATUS='OLD') OPEN(UNIT = IOUT, FILE = 'out1.txt'    2, FORM='FORMATTED', ACTION='WRITE', STATUS='UNKNOWN') READ(INW,*) I_TIME, HEAD2 ! Satellite I_TIME is not for trilateration but for clock correction C	WRITE(6,*) ' Satellite ', I_TIME, HEAD2 READ(INW, *) HEAD1 WRITE(6,*) ' Trilateration Satellites' WRITE( 6, *) HEAD1

K = 1 DO 10, I=1,4 ! Read header lines and data IF(I .NE. I_TIME) THEN READ(INW, *) ISAT, (RSAT(K,J), J=1,3), PRANGE(K) WRITE( 6,'(1X,I2,4F16.3)') I, (RSAT(K,J), J=1,3), PRANGE(K) K = K + 1 ELSE READ(INW, *) ISAT, (SATTIM(J), J=1,3), PRANTI END IF 10	CONTINUE WRITE(6,*) ' ' WRITE(6,*) ' Non-trilateration Satellite' WRITE( 6, *) HEAD1 WRITE( 6,'(1X,I2,4F16.3)')I_TIME, (SATTIM(J), J=1,3), PRANTI

READ (INW,*) IPRINT, HEAD2 C	WRITE(6,*) ' IPRINT = ', IPRINT CLOSE(INW)

C	CALL TRILAT( XSAT, YSAT, ZSAT, PRANGE, NSOLNS) CALL TRILAT( RSAT(1,1), RSAT(1,2), RSAT(1,3), PRANGE, NSOLNS)

C	WRITE(6,*) ' RSAT= ', RSAT

DO 50 I=4,5 ! Distance to 4th sphere for solutions in 4 & 5 SQUARE = 0.0 DO 47 J=1,3 ! X, Y, Z components SQUARE = SQUARE + ( RSAT(I,J) - SATTIM(J)  )**2 47	   CONTINUE R4(I-3) = SQRT( SQUARE ) DAA(I-3) = R4(I-3) - PRANTI 50	CONTINUE

IF( ABS(DAA(1)) .LE. ABS(DAA(2)) ) THEN !Closest solution DA = DAA(1) ISOLN = 1 ELSE DA = DAA(2) ISOLN = 2 END IF

BIAS1 = DA	BIAS2 = DACOMP ( BIAS1 ) CALL ZBRAC(DACOMP, BIAS1, BIAS2, SUCCES) XACC = 0.01 RGBIAS = RTBIS(DACOMP,BIAS1,BIAS2,XACC)

WRITE(6,*) ' ' WRITE(6,*) '                  X 	       Y 	   Z      RBIAS' WRITE(6,150) ' Solution = ', (RSAT(ISOLN+3,J), J=1,3), RGBIAS

CLOSE(IOUT) STOP ' Normal completion in routine main of gps.' 150  FORMAT(1X,A12,3F12.1, F7.1) 200  FORMAT(I3) END 

The subroutine trilat computes any intersections of three surfaces given the sphere centers and radii as described in trilateration.    SUBROUTINE TRILAT  SUBROUTINE TRILAT( X0, Y0, Z0, RADIUS, NSOLNS ) C C       1         2         3         4         5         6         7 C 3456789012345678901234567890123456789012345678901234567890123456789012 C C TRILATERATION FINDS INTERSECTIONS OF SURFACES OF SPHERES C SPHERES CENTERED AT X0(I), Y0(I), AND Z0(I) WITH RADII, R(I) IMPLICIT DOUBLE PRECISION (A-H,O-Z)

DOUBLE PRECISION X0(5), Y0(5), Z0(5), RADIUS(3) DOUBLE PRECISION X1(5), Y1(5), Z1(5), X2(5), Y2(5), Z2(5) DOUBLE PRECISION X3(5), Y3(5), Z3(5), X4(5), Y4(5), Z4(5) DOUBLE PRECISION ERRMAT(3)

C         WRITE( 6, * ) 'NOW IN SUBROUTINE TRILAT' C	DO 10, I=1,3 ! Write data C         WRITE( 6, * ) I, X0(I), Y0(I), Z0(I), RADIUS(I) C10	CONTINUE

C Translate coordinate system so as to put center of sphere 1, p1, at C origin. That is compute expression of vectors, VP2 and VP3 in C coordinate system 1.

DO 20, I=2,3 X1(I) = X0(I) - X0(1) Y1(I) = Y0(I) - Y0(1) Z1(I) = Z0(I) - Z0(1) 20	CONTINUE

C First sphere center, P1, remains at origin, since all axes intersect C at origin. X1(1) = 0.0 Y1(1) = 0.0 Z1(1) = 0.0

X2(1) = 0.0 Y2(1) = 0.0 Z2(1) = 0.0

X3(1) = 0.0 Y3(1) = 0.0 Z3(1) = 0.0

X4(1) = 0.0 Y4(1) = 0.0 Z4(1) = 0.0

C	DO 22, I=1,3 ! Write data C         WRITE( 6, * ) I, 'CS1 = ', X1(I), Y1(I), Z1(I) C22	CONTINUE

C Compute 1st coordinate system rotation angle, ALAMBD, required C to set the y component of P2 to zero, that is make Y2(2) zero. C This rotation is about the positive Z1 axis. IF ( (Y1(2) .NE. 0.0) .OR. (X1(2) .NE. 0.0) ) THEN ALAMBD = ATAN2( Y1(2), X1(2) ) CLAM = COS(ALAMBD) SLAM = SIN(ALAMBD) ELSE ALAMBD = 0.0 CLAM = 1. SLAM = 0. END IF

DO 30 I=2,3 X2(I) = X1(I)*CLAM + Y1(I)*SLAM Y2(I) = -X1(I)*SLAM + Y1(I)*CLAM Z2(I) = Z1(I) 30	CONTINUE

C	DO 32, I=1,3 ! Write data C         WRITE( 6, * ) I, 'CS2 = ', X2(I), Y2(I), Z2(I) C32	CONTINUE

CC	VP2MAG = SQRT( X2(2)**2 + Y2(2)**2 + Z2(2)**2 ) CC	VP2MAG = SQRT( X2(2)**2 + Z2(2)**2 )

C Compute 2nd coordinate system rotation angle, PHI, required C to put P2 on X axis. That is make Z3(2) zero. C This rotation is about the negative Y2 axis. IF ( Z2(2) .NE. 0.0 ) THEN VP2MAG = SQRT( X2(2)**2 + Z2(2)**2 ) PHI = ASIN(Z2(2) / VP2MAG) CPHI = COS(PHI) SPHI = SIN(PHI) ELSE PHI = 0. CPHI = 1. SPHI = 0. END IF

DO 40 I=2,3 X3(I) = X2(I)*CPHI + Z2(I)*SPHI Y3(I) = Y2(I) Z3(I) = -X2(I)*SPHI + Z2(I)*CPHI 40	CONTINUE

C	DO 42, I=1,3 ! Write data C         WRITE( 6, * ) I, 'CS3 = ', X3(I), Y3(I), Z3(I) C42	CONTINUE

C Compute 3rd coordinate system rotation angle, THETA, required C to make Z compenent of P3 zero. C This rotation is aboutthe -X3 axis. IF ( (Z3(3) .NE. 0.0) .OR. ( Y3(3) .NE. 0.0) ) THEN CCC	VP3MAG = SQRT( X3(3)**2 + Y3(3)**2 ) THETA = ATAN2( Z3(3), Y3(3) ) CTHETA = COS(THETA) STHETA = SIN(THETA) ELSE THETA = 0. CTHETA = 1. STHETA = 0. END IF

DO 50 I=2,3 X4(I) = X3(I) Y4(I) = Y3(I)*CTHETA + Z3(I)*STHETA Z4(I) = -Y3(I)*STHETA + Z3(I)*CTHETA 50	CONTINUE

C         WRITE( 6, * ) 'STILL IN SUBROUTINE TRILAT'      C C	DO 52, I=1,3 ! Write data C         WRITE( 6, * ) I, 'CS4 = ', X4(I), Y4(I), Z4(I) C52	CONTINUE

C Now find intersections of 3 sphere surfaces expressed in C coordinatesystem 3.

D = X4(2) D_SQR = D**2 R1_SQR = RADIUS(1)**2 R2_SQR = RADIUS(2)**2 R3_SQR = RADIUS(3)**2 AI = X4(3) AJ = Y4(3)

X = ( R1_SQR - R2_SQR + D_SQR ) / (2.*D) X_SQR = X**2 Y = (R1_SQR - R3_SQR - X_SQR + (X - AI)**2 + AJ**2) /(2.*AJ) Y_SQR = Y**2 Z_SQR = R1_SQR - X_SQR - Y_SQR IF(Z_SQR .GT. 0.0) THEN NSOLNS = 2 ZP = SQRT(Z_SQR) ZM = -ZP ELSE IF (Z_SQR .EQ. 0.0) THEN NSOLNS = 1 ZP = 0.0 ZM = 0.0 ELSE NSOLNS = 0 END IF

C	WRITE(6,*) NSOLNS, ' solutions with X, Y, ZP, ZM = ' C    2              , X, Y, ZP, ZM

C Verify solutions

C	ERRMAT(1) = RADIUS(1) - SQRT( (X-X4(1))**2 + (Y-Y4(1))**2 C     2       +  (ZP-Z4(1))**2 ) C	ERRMAT(2) = RADIUS(2) - SQRT( (X-X4(2))**2 + (Y-Y4(2))**2 C     2       +  (ZP-Z4(2))**2 ) C	ERRMAT(3) = RADIUS(3) - SQRT( (X-X4(3))**2 + (Y-Y4(3))**2 C     2       +  (ZP-Z4(3))**2 ) C	WRITE(6,*) ' Errors = ', (ERRMAT(I), I=1,3)

X4(4) = X	Y4(4) = Y	Z4(4) = ZP

X4(5) = X	Y4(5) = Y	Z4(5) = ZM

DO 60 I=4,5 X3(I) = X4(I) Y3(I) = Y4(I)*CTHETA - Z4(I)*STHETA Z3(I) = Y4(I)*STHETA + Z4(I)*CTHETA 60	CONTINUE

C	ERRMAT(1) = RADIUS(1) - SQRT( (X3(4)-X3(1))**2 C    2       + (Y3(4)-Y3(1))**2 + (Z3(4)-Z3(1))**2 ) C	ERRMAT(2) = RADIUS(2) - SQRT( (X3(4)-X3(2))**2 C     2       + (Y3(4)-Y3(2))**2 + (Z3(4)-Z3(2))**2 ) C	ERRMAT(3) = RADIUS(3) - SQRT( (X3(4)-X3(3))**2 C     2       + (Y3(4)-Y3(3))**2 + (Z3(4)-Z3(3))**2 ) C	WRITE(6,*) ' Errors X3 = ', (ERRMAT(I), I=1,3)

DO 70 I=4,5 X2(I) = X3(I)*CPHI - Z3(I)*SPHI Y2(I) = Y3(I) Z2(I) = X3(I)*SPHI + Z3(I)*CPHI 70	CONTINUE

C	ERRMAT(1) = RADIUS(1) - SQRT( (X2(4)-X2(1))**2 C    2       + (Y2(4)-Y2(1))**2 + (Z2(4)-Z2(1))**2 ) C	ERRMAT(2) = RADIUS(2) - SQRT( (X2(4)-X2(2))**2 C     2       + (Y2(4)-Y2(2))**2 + (Z2(4)-Z2(2))**2 ) C	ERRMAT(3) = RADIUS(3) - SQRT( (X2(4)-X2(3))**2 C     2       + (Y2(4)-Y2(3))**2 + (Z2(4)-Z2(3))**2 ) C	WRITE(6,*) ' Errors X2 = ', (ERRMAT(I), I=1,3)

DO 80 I=4,5 X1(I) = X2(I)*CLAM - Y2(I)*SLAM Y1(I) = X2(I)*SLAM + Y2(I)*CLAM Z1(I) = Z2(I) 80	CONTINUE

C	ERRMAT(1) = RADIUS(1) - SQRT( (X1(4)-X1(1))**2 C    2       + (Y1(4)-Y1(1))**2 + (Z1(4)-Z1(1))**2 ) C	ERRMAT(2) = RADIUS(2) - SQRT( (X1(4)-X1(2))**2 C     2       + (Y1(4)-Y1(2))**2 + (Z1(4)-Z1(2))**2 ) C	ERRMAT(3) = RADIUS(3) - SQRT( (X1(4)-X1(3))**2 C     2       + (Y1(4)-Y1(3))**2 + (Z1(4)-Z1(3))**2 ) C	WRITE(6,*) ' Errors X1 = ', (ERRMAT(I), I=1,3)

DO 90, I=4,5 II3 = I-3 X0(I) = X1(I) + X0(1) Y0(I) = Y1(I) + Y0(1) Z0(I) = Z1(I) + Z0(1) 90	CONTINUE

C	WRITE(6,*) ' X0 = ', (X0(I), I=1,5) C	WRITE(6,*) ' Y0 = ', (Y0(I), I=1,5) C	WRITE(6,*) ' Z0 = ', (Z0(I), I=1,5)

C	WRITE(6,*) ' Now leaving subroutine TRILAT. '

RETURN END 

The function dacomp computes the closest distance from three surface intersections to the fourth sphere surface as a function of its argument, a range bias.

  <div style="line-height: 1.6em; font-weight: bold;; background: #dcc5fc; text-align: center; padding: 2px; font-size: 160%;"> FUNCTION DACOMP <PRE> FUNCTION DACOMP ( BIAS ) IMPLICIT DOUBLE PRECISION (A-H,O-Z) C       1         2         3         4         5         6         7 C 3456789012345678901234567890123456789012345678901234567890123456789012 C DOUBLE PRECISION PRANGE(3), ERRMAT(3), PRTEMP(3) DOUBLE PRECISION ERRTOT(2), SATTIM(3), RSAT(5,3), R4(2), DAA(2) COMMON /COMMDA/ RSAT, PRANGE, SATTIM, PRANTI DO 10 I=1,3 PRTEMP(I) = PRANGE(I) + BIAS 10	CONTINUE PTMTMP = PRANTI + BIAS

CALL TRILAT( RSAT(1,1), RSAT(1,2), RSAT(1,3), PRTEMP, NSOLNS)

DO 40 I=4,5 ! Compute errore for each of 2 solutions DO 35 J=1,3  ! Compute distances to J=1,2,3 satellites SQUARE = 0.0 DO 33 K=1,3 ! X, Y, Z components of error SQUARE = SQUARE + ( RSAT(I,K) - RSAT(J,K)  )**2 33	       CONTINUE ERRMAT(J) = PRTEMP(J) - SQRT( SQUARE ) 35	   CONTINUE ERRTOT(I-3) = SQRT( ERRMAT(1)**2 + ERRMAT(2)**2 +     2       ERRMAT(3)**2 ) 40	CONTINUE

IF( (ERRTOT(1) .GE. 1.E-6) .OR. (ERRTOT(2) .GE. 1.E-6) ) THEN WRITE(6,*) ' Excessive trilateration error ' WRITE(6,*) ' ERRTOT = ', (ERRTOT(I), I=1,2) IPRINT = 1 END IF DO 50 I=4,5 ! Distance to 4th sphere for solutions in 4 & 5 SQUARE = 0.0 DO 47 J=1,3 ! X, Y, Z components SQUARE = SQUARE + ( RSAT(I,J) - SATTIM(J)  )**2 47	   CONTINUE R4(I-3) = SQRT( SQUARE ) DAA(I-3) = R4(I-3) - PTMTMP 50	CONTINUE

IF( ABS(DAA(1)) .LE. ABS(DAA(2)) ) THEN DA = DAA(1) ISOLN = 1 ELSE DA = DAA(2) ISOLN = 2 END IF

C	WRITE(6,*) ' R4 = ', (R4(I), I=1,2) C	WRITE(6,*) ' DAA = ', (DAA(I), I=1,2) C	WRITE(6,*) ' Solution ', ISOLN, ' is closest.', ' DA = ', DA	DACOMP = DA	RETURN END </PRE>

RHB100 (talk) 05:20, 24 April 2010 (UTC)

WP is not a discussion forum
The preceding section is running way out of hand, with even the publishing of written computer code. Wikipedia is not a discussion forum. If you want to explore your original research together, please find a more appropriate place. &minus;Woodstone (talk) 05:09, 24 April 2010 (UTC)


 * This is a discussion page relevant to what goes into Wikipedia. The purpose of showing the code and results is to provide solid proof that the method involving trilateration and one dimensional root finding certainly does work. RHB100 (talk) 05:19, 24 April 2010 (UTC)
 * It is not considered acceptable evidence in WP. See the WP:OR. What you need is independent published sources that state that it is really used in that way. It is not enough that it would work. &minus;Woodstone (talk) 05:48, 24 April 2010 (UTC)


 * But surely you agree that if it would not work, it would be incorrect, and should be removed; we are simply establishing that this is not the case, after Crazy Software Productions raised doubts. I agree with you that citations, not demonstrations, are needed for the main article; that's why the demonstrations are here on the talk page!
 * As to this discussion being original research, my code above links to a peer-reviewed IEEE paper with 149 citations, which contains (almost) the exact algorithm I posted; I only repeated it in case you don't have IEEE journal access. Perhaps I didn't make it clear that the algorithm was from that paper; would my actions really qualify as original research?
 * I agree that these discussions are making the talk page get a bit long - but talk pages can always be archived when discussions are over, right? Mike1024 (t/c) 12:14, 24 April 2010 (UTC)

There are links to trilateration and Numerical Recipes which are more than adequate to establish the validity of the method discussed in the GPS article. I merely used the methods in these more than adequate citations to clearly establish that the method worked since some did not seem to understand the methods. There were also expressions of interest in a detailed description of the algorithm. RHB100 (talk) 21:34, 24 April 2010 (UTC)

Frequency of position information
I had added some information on how frequent a position can be calculated by GPS. This was promptly reverted claiming excessive complexity. It is in my view of primary interest to the reader. Much more so, than how many satellites there are, at what altitude they are orbiting and how many are needed to get a fix. The frequency information is not stated explicitly anywhere in the article. I will give it another try. &minus;Woodstone (talk) 07:16, 16 March 2010 (UTC)


 * The information is interesting, but muddled a simple explanation of another topic. Now that you've added that it can update every 6 seconds, I have to wonder how my Garmin handheld can update approximately twice per second.  —EncMstr (talk) 07:28, 16 March 2010 (UTC)


 * Yes, mysterious. The satellites send a subframe with their identification and time of sending not more frequent than every 6 seconds. Any more frequent positioning must be based on extrapolation. &minus;Woodstone (talk) 07:37, 16 March 2010 (UTC)


 * Although you are correct that a subframe begins every 6 seconds, this does not mean that a position can only be calculated every 6 seconds, because once a satellite is being tracked, the start of a subframe is not required to take an observation. While a subframe starts every 6 seconds, there's a new data bit every 20 milliseconds, and a new c/a code chip every 930 nanoseconds. Receivers track all of these.
 * To use an analogy, imagine that you were measuring distances with a long line of 1 metre rulers. You would have to keep track of the start/end of each ruler (the subframe boundaries) but you could measure more precisely than 1 metre, because each meter rule is marked with centimetres and millimetres (the c/a code chips). To measure a distance, you don't have to wait for the next metre rule boundary if you remember passing it 27 centimetres ago! Hence, GPS receivers can make observations and fix positions more frequently than every 6 seconds. This is how many receivers are able to give a fix every second, or more!
 * I think this misunderstanding arises because a lot of the diagrams and things illustrating the article represent the GPS signal as a single circle, as if it were a sonar 'ping' from a submarine - the reality of the signal is that it's a binary sequence of 'pings', each about 300 metres apart (at the speed of light) - but a diagram showing that would have many concentric and overlapping circles, making it very confusing!
 * I haven't edited the article because of 3RR but if you guys are both happy with my explanation, you can go ahead - or if you need more details, go ahead and ask! Mike1024 (t/c) 09:59, 16 March 2010 (UTC)
 * Thanks for the explanation. It helps, but it's not really clear yet. Essentially you are including the doppler effect due to movement of both sender and receiver. The chips sent at the known 930 ns intervals do not arrive at the same interval. The different accumulated times make up for the different distance. The receiver would need to recalculate the orbital position after the nominal 930*n ns and measure the time since frame start at receipt. Correct? I think some explanation of this definitely belongs early on in the article. P.S. the 3RR rule is only for revert by the same editor. I would appreciate someone knowledgeable (you?) to add this. &minus;Woodstone (talk) 15:26, 16 March 2010 (UTC)
 * Each satellite is constantly sending chips (at 930 nanoseconds per chip) and the receiver has a 'tracking loop' for each satellite, which compares the chips received to a 'local replica' - what the receiver expects the satellite to send at a given time. The difference between the received signal and the local replica is used to change the rate of the local replica - if the local replica is lagging behind it's sped up, and if the replica is getting ahead it's slowed down. When a rising or falling edge of a chip is detected, we can adjust the local replica speed, so we know where in the replica we are and how fast that position is changing; between rising and falling edges we can make a fairly good estimate of where in the replica we are, from that position and speed. When the GPS receiver generates a fix, it looks at all the tracking loops at the same time, and asks for that estimate.
 * Because we generate the local replica based on the GPS receiver clock, and we know how much we've had to slow it down or speed it up to make it match up with what we've received from the satellite, the integral of that slow down (or speed up) tells us the time difference between the signal broadcast time (measured by the satellite clock) and the signal reception time (measured by the receiver clock). Take that time difference, divide it by the speed of light, and you have the pseudorange - and you're on your way to calculating your location!
 * As to working out satellites' positions, the local replica is based on our knowledge of what we expect the satellite to transmit at a given time - so when our local replica matches up with the received signal, we also know the time that signal was transmitted. We can use the ephemeris information to calculate the satellite's position at that time.
 * Does this make things any clearer? Mike1024 (t/c) 13:13, 17 March 2010 (UTC)
 * That makes it rather clear. Some explanation of this definitely needs to be in the article. Would you care to give it a try? Thanks a lot. &minus;Woodstone (talk) 14:04, 17 March 2010 (UTC)
 * I suggest adding a new paragraph after the basic introduction topics of time difference times speed of light, and how four satellites are needed (normally) for accurate time. —EncMstr (talk) 16:19, 17 March 2010 (UTC)
 * Something like this:
 * After the ephemeris is downloaded this ephemeris is valid for four hour. Because the timing information is send almost continuesly from the satellites, position calculation can also be done on a continuesly basis.Crazy Software Productions (talk) 12:11, 30 April 2010 (UTC)

Two intersection points
The article talks about things like ''Since the observed satellites are well above the horizon, the intersection of the three spherical surfaces will be two points, one on (close to) the surface of Earth, the other one several thousand kilometers above the surface. [...] For automobiles and other near-earth-vehicles, the correct position of the GPS receiver is the intersection closest to the Earth's surface. For space vehicles, the intersection farthest from Earth may be the correct one.''

I realise that quote is from the simplified section, but would I be right in saying we expect there to be four spherical surfaces and four satellites, and hence no 'choose between two points' issue, in non-simplified calculations? Mike1024 (t/c) 12:13, 30 April 2010 (UTC)


 * In this section you mention above, some hidden comment is placed.
 * The plane the three satellites are in does not have to be a flat plane above the horizon, it can intersect the earth. (This happens when the satellites reach their most northern point, or most southern point and turn. Imagine that the three satellites are in a plane of which one side is red and the other side is green. And the earth is on the red side, after 6 hours the earth will be on the green side, this is only possible if the earth has gone through plane.
 * Most vehicles, will be close to the earth surface, only deep space vehicles will be outside of the radius of the satellites, but depending on the configuration, even then the point closest to the earth can be the correct point. The satellites beam a directional signal towards the earth, so for a deep space vehicle it is more likely to receive the signal from a satellite which is on the other side of the earth than from a satellite which is in the same side of the earth as the deep space vehicle. Using the earth to discriminate between two possible points therefore is not a a good method for deep space vehicles.Crazy Software Productions (talk) 15:27, 30 April 2010 (UTC)


 * Even with four satellites, there is still the possibility of two solutions, it is even possible that both solutions are on the earth surface and both can be with the exact same timing.
 * Most ambiguity can easely be solved choosing the point which is closest to the last calculated position. (Both Bancroft and pseudorange calculations use the last calculated position to solve such an ambiguity.).


 * The following reasoning show that there can be 2 solutions. I'll use the earth surface as a fourth parameter, but will substitute this with a satellite later on. Imagine the situation having three satellites, no correct clock and estimating your position using the earth surface. With for example trilateration you can estimate a point, changing the time-bias will give you a range of points, these points form a curve. If this is an close curve it is an elips, if it is an open curve it is a hyperbole. The curve will intersect the earth surface at some point, I will call this the entry point. If the curve does intersect the earth at one point, it can be that the curve just touches the surface and that this is the only point, but it is far more likely that the curve actually intersects the earth surface at an entry point and intersects the earth surface at another point (the exit point). So for three satellites and the earth surface except when the curve touches the earth in general there are two points.
 * If the earth surface is replaced by an extra hyperboloid (from a timedifference of a fourth satellite), and the first curve was a closed curve the closed curve will intersect the hyperboloid in two places. If the first curve was an hyperbole it still can intersect the hyperboloid in two places, but then it is possible that there is only one intersection point.
 * Going back to the two points on the earth surface from three satellites, if you take the plane which is perpendipular and exactly in the middle of the two points, any 4th satellite in this plane will give exactly those two points on the earth surface. This will only happen for a very short time. But when the satellites are moving, the 2nd point will not disappear (in thin ear), but will move, there still is the second point, first close to the earth but later moving inside or outside of the earth. The point can only disappear when it is at an infinite distance from the earth. An intersection between a plane and a curve can only disappear at infinity).
 * In short, even with four satellites two points are possible, this ambiguity can be solved by choosing the point which is closest to the last calculated point. Even in a worse case situation where the second point pases the first point at close by range and the second point is choosen, then because this point is moving fast the correct point will be choosen within one or a few seconds. The likelyhood of the second point pasing at such a close range is very very small.
 * Crazy Software Productions (talk) 15:27, 30 April 2010 (UTC)

In one of the posts above "CRAZY SOFT ..." said the method involving trilateration and one dimensional root finding would not work. He wasted considerable space with his illogical arguments. Now it has been shown that his assertions were totally and completely false with a demonstration. Now without apologizing for the time and space he wasted, he is putting forth more nonsense. We should realize that this guy is a waste of time. RHB100 (talk) 20:47, 30 April 2010 (UTC)
 * Supposing that you refer to me as "this guy", you are misquoting me. I never said it would not work. I said: "It is not enough that it would work" (for inclusion you need sources that it is used). &minus;Woodstone (talk) 23:57, 30 April 2010 (UTC)


 * The situation described is the one encountered for observers on Earth. The satellites of which signals are received must be well above the horizon, because otherwise surrounding terrain, growth and buildings will obstruct reception. Let's be optimistic and assume a minimum clearance of 1 degree. That makes each of the satellites more than 350 km overhead. So the mirror point more than 700 km, much higher than any plane will fly. If all 3 satellites are in one half of the sky, the plane is very slanted, but also much further away, and the mirror point even further. So there is no chance that the mirror point can be confused with the location. Only for space vehicles this may happen.
 * As discribed above, three satellites can form a plane which intersects the earth, at a certain moment it actually intersects with the earth centre, so the mirrorpoint will be on the earth surface as well. Image three satellites, A,B,C, all traveling Northwards, A is above the equator, B and C are below the equator. The plane they form has two sides, after 6 hours A is below the equator and B and C are above the equator, all traveling south. B and C have not swapped places from east to west. A has swapped places with B and C regarding North South. The side of the plane which was pointing towards the earth is now pointing away from the earth. So the earth (and earth centre) must have traveled through the plane which is formed by the satellites A, B and C. Therefore there must have been a time that a point on the earth mirrored in this plane gave again a point on the earth. This is true for any combination off three satellites, after 6 hours the the earth is on the other side of the plane. Crazy Software Productions (talk) 17:45, 30 April 2010 (UTC)
 * You assume satellites below the equator. I'm not sure what the relevance is. Can you still find an intersecting plane if all satellites are a few degrees above the horizon of the observer. So they are all on the same side of a plane that touches Earth? &minus;Woodstone (talk) 23:57, 30 April 2010 (UTC)
 * No, I do not assume satellites to be specific below (or above) the equator. The describtion with the equator is only used to show that the constellation of the satellites is changed in such a way that the plane is 'inverted'. Usage of the equator is just a convinient way, because each satellite crosses the equater about once every six hours and between two equater crossings the plane is inverted. If three satellites stay close together, this inversion of the plane will happen when the satellites are about furthest removed from the equator. At the moment their plane crosses the earth all three satellites must be visible high above the horizon from somewhere on the earth.
 * Example. At 00:00 three satellites as a group cross the equator in Northern direction, three hours later the group changes from going north to going south. At that moment the plane they form will intersect the earth, all three satellites are visible from some place on earth (Norway for example). Again three hours later the group will cross the equator again, but this time when they cross the equator the plane is inverted. Again three hours later the opposite will happen, the plane crosses the earth again now it is visible somewhere from the southern hemisphere(Africa, Australia, South America ?). Because the three satellites change direction going from a northern to a southern direction (and not the east west direction), the plane they are in becomes 'mirrored'.
 * For pseudorange calculation or for Bancroft this is not a problem because if there is ambiguity between solutions, this is resolved by using the latest calculated solution.Crazy Software Productions (talk) 14:30, 2 May 2010 (UTC)
 * Point conceded. Thanks for the clear elucidation. &minus;Woodstone (talk) 16:51, 2 May 2010 (UTC)
 * I am not in favour of using precisely 4 satellites in the intro, because the four spheres will normally not have a shared intersection point, because of measurement errors. The fourth sphere will not pass through any of the two points determined by the first 3. In reality of course, the GPS system will track more than 4 satellites and make a best fit for its position and clock. As you can see from the animation, most of the time at least 8 satellites are visible. Selecting 3 out of 8 is possible in 56 ways, giving an unmanageable tangle of solutions. &minus:Woodstone (talk) 17:10, 30 April 2010 (UTC)
 * In reality my GPS very often only tracks 4 satellites (an old Map60 gps from Garmin), and with four satellites and using Bancroft or pseudorange calculation this will result in exactly one (or two) exact solutions. Although this is not exact because of errors, mathematically it will be exact, not a best fit but an only fit. Even if you like to think in spheres there is exactly one (or two) solutions where the spheres will intersect exactly (again mathematically). Because the time-bias is part of the solution, there is an (or two) exact solutions, with this time-bias the sphere model also gives an exact intersection for all four spheres.
 * My GPS receiver can work with precisely 4 satellites, that is the minimum that is needed for a 3D fix. It can work with an overdetermined constellation as well. How it does that is propriety information of Garmin. But there is a number of suggestions on the web how this is done. The overdetermined solution often uses the same technique, but weights each part of the solution, which again gives a single (or two) solutions. Crazy Software Productions (talk) 17:45, 30 April 2010 (UTC)
 * It is correct that using 4 satellites and unknown clock error solves exactly (in non-degenerate cases). My GPS (Garmin Oregon 300) almost always shows more than 4 satellites. The manual states that more satellites improves accuracy, so they must be using them in the calculations. &minus;Woodstone (talk) 23:57, 30 April 2010 (UTC)
 * Yes I think so too. But what I tried to say is that it is solved for more than 4 sats at once where the satellites all get a weight, were a larger weight means more influence. More satellites in general will give a better solution on average. It is still posible that 4 sats give a very good solution (e.g. within a meter) and that 10 sats give a less good solution (a few meters of). But in general more satellites is better.
 * With my car navigation system I often get a reception of 7 to 9 satellites. My handheld often shows less satellites, because it's an older less sensitive model. I have worked with GPS receivers which took long (over 40 minutes) to get a first fix, this was on open water on a slow moving boat. Since then there has ben a lot improvement.Crazy Software Productions (talk) 18:37, 2 May 2010 (UTC)

This page should be archived
This page should be archived. It is very long and the issues have been discussed adequately. We now have new issues to discuss. Those who have expertise in archiving should in view of the problems give serious consideration to archiving this page. RHB100 (talk) 21:12, 16 May 2010 (UTC)

Requested move
<div class="boilerplate" style="background-color: #efe; margin: 2em 0 0 0; padding: 0 10px 0 10px; border: 1px dotted #aaa;">
 * The following discussion is an archived discussion of the proposal. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section. 

Closed. Archiving of a talk page is not something that is discussed at WP:RM. If the bot is not working, then a note on the bot's page is the correct approach. 01:40, 19 May 2010 (UTC)

Global Positioning System → [] — article is very long, issues on current page have been discussed adequately, new issues to discuss, Archive_5 is place for most recent archive. RHB100 (talk) 01:27, 19 May 2010 (UTC)
 * The above discussion is preserved as an archive of the proposal. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

Old Requested move
Global Positioning System → [] — request at top of page, article is long, issues on current have been discussed adequately, new issues to discuss, Perform archiving in inverse fashion so as to avoid destroying archives currently in existence. RHB100 (talk) 23:42, 16 May 2010 (UTC)


 * [] → []
 * [] → []
 * [] → []

Can we have a little more explanation as to how these multiple moves will work? I am assuming that the software is smart enough to perform the moves in inverse fashion. That is Archive_4 to Archive_5 will be performed first then Archive_3 will be moved to Archive_4 and so forth so as to avoid destroying any of the currently existing archives. Is this correct? RHB100 (talk) 00:21, 17 May 2010 (UTC)


 * Move request pulled for now; I've tweaked the code for the archiving bot to see if it will do what it is already supposed to be doing. (FYI, we generally archive pages incrementally and not in reverse order.) --Ckatz <sup style="color:green;">chat <sub style="color:red;">spy  02:24, 17 May 2010 (UTC)
 * I looked at the parameters and think the problem was the target name. I changed that to match the talk page name.  Give it 24 hours for the next bot run to see if the problem is fixed. Vegaswikian (talk) 01:47, 19 May 2010 (UTC)
 * Oops, my bad. :-( I've moved all the sections with comments in 2010 into /Archive 6.
 * If you want archiving by year, it can be set up that way explicitly, by moving Archive_6 to Archive_2010 etc., and changing the bot....
 * —WWoods (talk) 07:30, 19 May 2010 (UTC)

Archiving standards
A number of threads have been archived because of exceeding the age of 21 days. This same standard should be applied to all threads at least until the talk page is down to a more reasonable size. I still have a noticeable delay in opening the talk page. algo has been set to old(21d). RHB100 (talk) 01:36, 20 May 2010 (UTC)

What does 1st MiszaBot I do?
What does the first MiszaBot I do? I think I understand the second MiszaBot from reading [User:MiszaBot/Archive_HowTo]. But the first one seems unclear. RHB100 (talk) 01:36, 20 May 2010 (UTC)


 * MiszaBots I, II, and III operate in different parts of Wikipedia, but they do the same thing.
 * —WWoods (talk) 07:48, 20 May 2010 (UTC)

Perhaps the way I asked the question above was misleading. I do not understand MiszaBots I, I do not understand MiszaBots II, and I do not understand MiszaBots III. Now having said that I ask the question.

What does MiszaBot I do? RHB100 (talk) 19:43, 20 May 2010 (UTC)


 * Everyday MiszaBot looks at the page to see if there are any sections in which all the datestamps are older than the limit (in this case, 21 days). If so, it transfers them to the latest archive page — subject to other constraints about the minimum number of sections to be left on the page (<tt>minthreadsleft</tt>) and the minimum number to archive at one time.
 * It didn't work initially because I forgot to fill in the placeholder in <tt>|archive = Talk:NAME/Archive %(counter)d</tt>.
 * —WWoods (talk) 20:46, 20 May 2010 (UTC)

Thank you for your response. I think I understand pretty well what MiszaBot the script shown below is doing. <PRE>

</PRE> But it looks to me that with regard to MiszaBot I, the script, Archive box |bot=MiszaBot I |age=90, shown below does nothing more than cause the display of a somewhat misleading box and that if it were removed it would only have the effect of removing the display of the box. I will continue to believe this unless you can convince me otherwise. <PRE>

</PRE> RHB100 (talk) 01:53, 21 May 2010 (UTC)

Although I have a general understanding of what the script, Archive box |bot=MiszaBot I |age=90, does, I do not know the effect of the parameter, MiszaBot I.

—WWoods, the first time I asked what MiszaBot I does, you responded by telling me that it does the same thing as MiszaBot II and MiszaBot III. The next time I asked what MiszaBot I does, you responded by telling me not what MiszaBot I does but instead what MiszaBot does. I therefore again ask the question.

What does MiszaBot I do? RHB100 (talk) 02:30, 21 May 2010 (UTC)


 * You've been asking about the parameters in the archive box???
 * MiszaBot itself doesn't show up anywhere on the page. The parameters cause the notice,
 * "Threads older than 90 21 days are archived by MiszaBot I."
 * to be displayed within the box, so editors can see what's going on. For pages without an archive box, there's, which serves the same function. E.g.:


 * <tt> </tt>:

auto archiving notice BOX ABOVE IS ONLY AN EXAMPLE NOT A NOTICE OF REAL AUTO ARCHIVING.

BOX ABOVE IS ONLY AN EXAMPLE NOT A NOTICE OF REAL AUTO ARCHIVING.
 * —WWoods (talk) 05:43, 21 May 2010 (UTC)

OK, Thank you for trying to explain it to me. Although I still do not completely understand the relationship of MiszaBot to MiszaBot I, I do understand for the most part the Archive box tool and the User:MiszaBot/config tool. RHB100 (talk) 18:58, 21 May 2010 (UTC)

Solving for the intersection of the expanding signals from light cones in 4-space cones
The remark:
 * Solving for the intersection of the expanding signals from light cones in 4-space cones

has been removed, because for positional calculations:
 * 1) It is pointless, the clock in a mobile receiver is less accurate than 1 in 10E6. Time dilation for the satellites is about 1 in 1E9 for the uncorrected clocks and less than 1 in 1E11 for corrected clocks. So the effort for calculating with 'relativity' does not give more accuracy than the normal calculations.
 * 2) Complex. It is prohibitive complex, because clocks are allready corrected, these corrections have to be 'undone'. Then because the satellites are in an eliptical orbid, where speed, gravity and accelerations change all the time it is difficult to calculate the 'correct' clocktime for a certain 'received time'. Only Lorentz transformations will not do it.
 * 3) After the Lorentz transformations have been done and the clocks are corrected, the light cones are still light spheres is seen in the 3D system and the same algoritms apply.
 * 4) There are no authorative reverences that this is used for positional calculations.

For checking the system and for scientific reasons, the relativistic calculations are made, but the measuring is done with well defined groundstations (more than one), and the calculations are done in postprocessing, often only after severall passes of the satellites.

What is realy nice about relativity, is that light spheres expanding with the speed of light, even after Lorentz transformations are still light spheres expanding with the speed of light, this is about the only thing that does not change because of relativity. Dimensions change, 'same' moments change, speed changes, but spheres of light expanding at the speed of light remain spheres of light expanding at the speed of light. Because the light spheres are still 'the same', after the time corrections and the Lorentz transformations, the same algoritms as allready described can be used. Crazy Software Productions (talk) 17:56, 26 May 2010 (UTC)

GPS 2F Series
Amazingly there is almost nothing on GPS 2F series which is an $8 billion 12-satellite system to improve accuracy to 2 feet, thwart jamming, etc., etc. I would start an article but I'm confused by the naming structures. The first satellite was supposed to be launched today but has been delayed to June.Americasroof (talk) 16:10, 27 May 2010 (UTC)

The GPS talk page is not a forum for discussion of issues unrelated to article
The section, "Plane of three satellites intersecting the center of the Earth" is running way out of hand, with even the publishing of invalid proofs unrelated to GPS. Wikipedia is not a forum for discussion of these unrelated issues. If Woodstone and Crazy... want to continue their discussion, they are advised to find a more appropriate place. RHB100 (talk) 20:00, 27 May 2010 (UTC)

Tags at beginning of navigation section should be removed
The tag reading, "This section may be confusing or unclear. Please help clarify the article. Suggestions may be on the talk page. (May 2010)", at the beginning of the navigation section should be removed. This is a vague comment which gives no clue as to what it refers. Repeated attempts to get editor, Ckatz, to state what he is talking about have failed. There is an ongoing effort to try to improve the article. This article has been recently peer reviewed and suggestions of the reviewers were acted upon.

The second template reads, "This section may require copy-editing." copy-editing is a vague jargon type expression which is not found in my dictionary. This problem has been pointed out to editor, Ckata, but he has refused to clarify the meaning of this term.

For the above reasons, both of these tags should be removed. If editor, Ckatz, insists on keeping these tags, then the next step will be some sort of dispute resolution process. RHB100 (talk) 20:35, 28 May 2010 (UTC)


 * I've restored them, as the concerns have not been addressed. (FYI, there was no "refusal" at all; I did attempt to outline issues in the edit summaries.) As per my comments when placing the tags:
 * the section needs a rewrite to make text more encyclopedic
 * it needs to avoid self-references and read as encyclopedia copy rather than lecture notes
 * we have to avoid inline external links, links to Google search results, and "see also" referrals to external sites
 * I made an initial stab at this when I first placed the tags (see here), but it really needs to be done by someone with a thorough understanding of the technology so as not to lose any context. There may well be similar issues with the rest of the page, but I've only really looked at this section. --Ckatz <sup style="color:green;">chat <sub style="color:red;">spy  04:27, 29 May 2010 (UTC)
 * It seems to me that if you, Ckatz, knows what needs to be done to improve the article, then you should go ahead and do it, rather then place tags suggesting someone else do it. The section doesn't appear to be written in an especially confusing manner and should be quite clear to an interested reader. The material is of a technical nature and therefore might not be clear to an uninterested reader, in which case, the reader is referred to a companion article Introduction to the Global Positioning System referenced at the top. The "copyedit" tag doesn't belong here at all, or in any other Wikipedia aricle for that matter. It implies that there exists a copyeditor whose job is to do the copy editing. This violates the collaborative intent of Wikipedia. These two tags should be removed Roesser (talk) 20:15, 29 May 2010 (UTC)

How much of this article is copy&paste & possibly copyvio?
It didn't take me long to find, for instance, that "Two distinct CDMA encodings are used: the coarse/acquisition (C/A) code " and more comes straight from the Knol article here, and "The almanac consists of coarse orbit and status information for each satellite in the constellation, " and more is copyvio from this pdf article. Dougweller (talk) 20:48, 29 May 2010 (UTC)
 * "Although four satellites are required for normal operation" - see Google scholar search, 7 article found. But in this case, who has copied what? This was added in December 2007 although the article was only published this year. Dougweller (talk) 21:18, 29 May 2010 (UTC)
 * Note that all of these appeared after the wikipedia entry (which I wrote in Dec 2007). Also note that using '0' instead of 'zero' in a ship's altitude is probably not right in formal English (and not technically correct - the altitude of the receiver is known, but it's probably not zero as that is the surface of the sea).  So it's pretty sure all of these are copies of Wikipedia.
 * As far as ethics go, there is no ethical violation in using the text from Wikipedia, but it should be acknowledged. Both Wikipedia liceses in use require attribution. (See Reusing Wikipedia content and Reusing Wikipedia content).  An clearly, if the author claims it's their own work, that is an ethics violation.   LouScheffer (talk) 15:37, 30 May 2010 (UTC)
 * And the 'almanac consists of coarse" is this edit 2007, 4 cites at Google Scholar (one a seminar report) all seem later. Google Scholar search. So I may have this wrong, there seems to be copyright violation but not in our article, of our article. Dougweller (talk) 21:30, 29 May 2010 (UTC)

I see much in this Knol article which is a direct copy of what I wrote on Wikipedia. There are also copies of figures that I created. It appears to be a copy of a previous version of the Wikipedia GPS article. RHB100 (talk) 19:26, 31 May 2010 (UTC)

The entries in the Table of Contents of the Knol article link back to the Wikipedia GPS article. It thus appears rather obvious that the Knol people merely copied the Wikipedia GPS article and did not even bother to change the links. RHB100 (talk) 19:31, 31 May 2010 (UTC)
 * Later this month I hope to have time to write to some of the journals which have published articles with text from our article. Is there some way you can contact Knol about this? I don't see why they should get away with copyvio. Dougweller (talk) 19:58, 31 May 2010 (UTC)

Plane of three satellites intersecting the center of the Earth.
In the references there is a remark (numbered 27 on 5-5-2010) which I think should be removed. Somebody put the remark there, so there must be some significance to it. It is not significant at all for Bancroft or pseudorange calculations and I do not think it is significant for other systems. It should be removed because the remark is false.

False: '''The two intersections are symmetrical about the plane containing the three satellites. Unless they are all in the same orbital plane, the plane containing them will not be a vertical one passing through the centre of the Earth, and one intersection will be nearer the earth than the other.'''

True: ''Two intersections are symmetrical about the plane containing the three satellites. Unless they are all in the same orbital plane, the plane containing them will be passing through the centre of the Earth about once every 6 hours.''

Proof:
 * 1 Any three satellites (A/B/C) not in the same orbital plane form a plane. Any 3 non-colinear points form a plane.  It certainly does not matter that the three points are not in an orbital plane. RHB100 (talk) 20:28, 5 May 2010 (UTC)This remark from RHB100 is true, but these points where allready 'excluded' in the references remark (27) and further the following reasoning does not include the three points in the same orbital plane.Crazy Software Productions (talk) 13:26, 6 May 2010 (UTC)
 * 2 At a specific time they form a plane call this situation 1.
 * 3 Six hours later the three satellites still form a plane, call this situation 2.
 * 4 The positions of each satellite in situation 2 is exactly on the other side of the centre of the earth than that satellite in situation 1.
 * 5 The planes in situation 1 and in situation 2 are parallel, the orientation of the sides is the same.
 * 6 Seen from the centre of the earth if (A/B/C) is in situation 1 in a clockwise direction in situation 2 it (A/B/C) will be in an anticlockwise direction.
 * 7 The centre of the earth in lies between the two planes, in situation 1 the middle earth is at one side of the plane, in situation 2 the centre off the earth is on the other side of the plane. Because the centre of the earth is at the other side of the plane it must have travelled through the plane. This seems to be assuming that the plane does not rotate.  But the fact that at 2 different times the planes are parallel certainly does not prove that there has been no rotation in between. RHB100 (talk) 20:28, 5 May 2010 (UTC) There is no assumption that the plane of the 3 satellite is not rotating. The plane must be rotation. After six hours the planes are not only parallel but their sides are (again) in the same direction. See below why the earth is on the other side.Crazy Software Productions (talk) 13:26, 6 May 2010 (UTC)

The fact that the planes are rotating as you admit completely invalidates the statement, "it must have travelled through the plane". You not only have weak points, you have absolutely nothing which in anyway resembles a proof. RHB100 (talk) 21:52, 26 May 2010 (UTC)

Why is the earth on the other side? When three points (A/B/C) form a plane the sides can be defined by the clockwise or anticlockwise order the points are in. The points (A/B/C) are free to move in 3D space, the plane moves with them and also the sides of the plane. A fourth point (centre of the earth) can only get from one side of the plane to the other side by travelling through the plane or by jumping. The plane has two sides, the side were (if looking at it) the satellites (A/B/C) are in a clockwise direction, can be called the front. At the back of the same plane the satellites (A/B/C) are in a counterclockwise direction. If the satellites do not become colinear, on one side of the plane the orientation of the satellites (clockwise or counterclockwise) remains the same.Crazy Software Productions (talk) 13:26, 6 May 2010 (UTC)

Remarks.
 * a. If in situation 1 the centre of the earth is allready in the plane formed by the three satellites, it will also be in the plane in situation 2.
 * b. Because the speed at which the centre of the earth travels through the plane will be high, it will not spend time in the plane. Similar the satellites all cross the equator several times during the day, but is will not spend time on the equator.
 * c. The situation where the satellites are exactly in line is ignored, for most combinations of three satellites this is not possible, in constelleations where it would be possible is would be extremely rare.
 * d. For pseudorange calculation and for Bancroft this situation is not significant at all. But the moment the receiver intersects the plane, the accuracy will be less optimal.

Crazy Software Productions (talk) 11:16, 5 May 2010 (UTC)

The text about intersecting the earth has been replaced by Two intersections are symmetrical about the plane containing the three satellites. Unless they are all in the same orbital plane, the plane containing them will be passing through the centre of the Earth about once every 6 hours.

Reasons for this are: If the plane intersects the middle of the earth, it is also very likely that the plane intersects the location of the receiver. At the moment the plane intersects the position of the receiver there is no problem because both points are at the same location. But before and after the intersection there wil be a finite interval of time where the mirror image produces a location which is close to the actual location of the receiver. Depending on the constellation of the satellites and the location of the receiver this can be very short, but can also be for a longer period. The receiver might be moving in the direction the plane is moving. The plane might be moving slowly. For the centre of the earth the plane will be relatively slowly moving if the three satellites are traveling in the same direction (for example North) and are for example just below the equator, on the equator, and just above the equator, each in their own orbid. All three above the equator at the same time and moving at the same speed would actually result in the middle of the earth 'staying' in the plane, or at least very near to the plane.

The remark: For space vehicles, the intersection farthest from Earth may be the correct one. Has been removed because the intersection nearest to the Earth may be the correct one. This is even more likely because for low earth orbits this will in general be true. For orbits above the orbits of the GPS satellites, the receiver will be more likely to receive signals from satellites on the other side of the earth than from the nearer satellites because it is looking at the back of the nearer satellietes. The satellites at the other side of the earth will at be beaming in the direction of the earth (and also in the direction of the receiver) so the reception of their signals is more likely.Crazy Software Productions (talk) 14:19, 26 May 2010 (UTC)


 * I believe your conclusions are generally correct, but I see some week points in your statements above. The proof is not complete: if the 3 satellites become colinear, the plane is no longer defined for an instant, and the Earth can jump to the other side (your remark "c" needs more substance). In remark "b" above you say the passing speed would be high, but in the remark just above here, you say that in some situations the plane would stay near the centre of Earth. Since the distance between the satellites is quite a bit larger than the Earth's radius, even a small misalignment will make the plane sweep rather quickly over Earth. I did some simulations and it appears that in the cited case, the passing speed is several km per second. Compared to the travel speed of the receiver, the confusion between the two intersections could be only momentary. &minus;Woodstone (talk) 15:35, 26 May 2010 (UTC)
 * If the 3 satellites are in different orbits, and for example crossing the equator at the same time, they are not colinear, because the 3 satellites are all about the same distance from the earth so they are on a curve. Similar to three points on the equator form a plane which intersects the middle of the earth, but if the three points are different points and on the same hight they can not become colinear.
 * I agree that there are some week points in my statements. I would like to prove or show an example where the receiver is near the plane for a longer time. I do not have proof for this. But haven't seen disprove for this as wel.
 * Also I do not think this plane problem is significant as said before, but I will come back to this later.Crazy Software Productions (talk) 18:14, 26 May 2010 (UTC)

The fact that the planes are rotating as you admit completely invalidates the statement, "it must have travelled through the plane". You not only have weak points, you have absolutely nothing which in anyway resembles a proof. RHB100 (talk) 23:46, 26 May 2010 (UTC)
 * How does that completely invalidate the statement, if something is on one side of the plane and after 6 hours it is on the other side of the plane, it must have jumped to the other side or moved through the plane. That the plane is moving and or rotating, does not matter, that the 'something' is moving does not matter, if it is on the other side of the plane it must have got there one way or another.
 * The concept that a plane has two sides can not be to difficult for you.
 * If the concept of which side of the plane is which side and that the middle of the earth is at one moment at one side and six hours later on the other side is to difficult to follow for you, I am prepared to give a more simple example. Woodstone got the concept.
 * Crazy Software Productions (talk) 17:51, 10 June 2010 (UTC)


 * We can first make the reasonable assumption that all satellites orbit on the same sphere. Clearly any straight line has only 2 intersections with that sphere. So unless two of the satellites collide, the three will never be colinear. As a consequence, the orientation of the plane itself is always defined continuously. It has been explained that, seen from Earth the orientation is changed after 6 hours. The only way that can happen is when the Earth moves through the plane.
 * However, probably, the radii of orbit are not exactly equal. Then, if two satellites would be at the crossing simultaneously, they could become colinear with another sattellite at opposite crossing. So it all depends on the timing of the orbits. This can be easily checked. I expect that they are purposely timed not to culminate at the same time. &minus;Woodstone (talk) 08:00, 27 May 2010 (UTC)

Time dilations due to the sun's gravitation
5/5/2010

Why are time dilations due to the sun's gravitational field not included in the sources of error? While a GPS satellite is orbiting Earth, its path may sometimes take it closer to the sun and slow its clock down. It caches up when its orbit takes it away from the sun into earth's night side and it is in synch again at the starting point, but there is a discrepancy of about 23 nsecs between dawn and dusk, a very measurable error. Accel2know (talk) 01:36, 6 June 2010 (UTC)
 * I think it's a bit more complex than that. Because of the gravitaional field of the sun the orbit of the satellite shifts. On the nightside it will come closer to earth, at the day side it will be a bit farther removed from the earth. It could be that these additional effects cancel out against each other.
 * Then there is the additional problem that the earth is in an elips around the sun, this will influence the gravitational field, during the year.
 * And the moon even has a greater gravitational effect than the sun.
 * Crazy Software Productions (talk) 12:20, 6 June 2010 (UTC)

Wikipedia linking guidelines indicate in line links are as good as footnote type numbered links
Linking shows no preference of footnote type links over in line links. At least one editor has gone through the article and in robot like fashion converted in line links to footnote style links. This is not only a waste of time but is actually harmful Both methods of linking have their advantages and disadvantages. In line links have the advantage that the reader can see the site to which he or she is linking. In line links are also faster and more convenient for the reader. The reader can go to an in line link with only one click. To navigate to a footnote type link, the reader must click once to get to the references, then possibly have to look around to fine the specific reference, and then click the reference. Editor should weigh the advantages of these linking styles when making a new link or editing an old link. Robot like changes should be avoided. RHB100 (talk) 00:33, 1 June 2010 (UTC)


 * RHB100, I'll assume optimistically that you are familiar with External links. If that is true then your comments and questions make no sense wrt the edits I have made. I have simply applied standard policy (a major policy at that). If it is the case that you understand the policy then you need to explain your concerns more coherently. You seem to be arguing that you don't like the policy, and obviously this is not the place to debate that. --Mcorazao (talk) 02:09, 1 June 2010 (UTC)
 * P.S. You stated in your previous request for a peer review that you wanted to bring the article to FA. It is unwise to continue attacking people that could help get you there (referring to the attacks on my talk page). --Mcorazao (talk) 02:18, 1 June 2010 (UTC)

Everything I have said is absolute truth. I have not and I do not attack anyone. I make suggestions and sometimes make friendly criticisms but that should not be misconstrued as an attack. RHB100 (talk) 03:06, 1 June 2010 (UTC)

External links clearly states, "The subject of this guideline is external links that are not citations to sources supporting article content." Mcorazao and perhaps others do not understand the difference between a link to an external (i.e. outside of Wikipedia) website for the purpose of verifying content in the Wikipedia article and one for the purpose of diverting readers to another website, especially one with advertising. RHB100 (talk) 18:49, 1 June 2010 (UTC)


 * RHB100, given your attitude I am not inclined to spend time educating you. Suffice it to say that you are only reading enough to rationalize your misconceptions. --Mcorazao (talk) 01:29, 2 June 2010 (UTC)

Mcorazao, the contributions you have made to the Wikipedia GPS are rather miniscule compared to the contributions I have made. I am therefore not concerned about any education you won't be providing. Furthermore, some of the changes you have made are actually harmful. RHB100 (talk) 19:40, 2 June 2010 (UTC)

We should use more common sense in editing. RHB100 (talk) 19:08, 26 June 2010 (UTC)

Should Tags at Beginning of Navigation Section be Removed?
Editor:Ckatz thinks there should be tags reading, "This section may be confusing or unclear. Please help clarify the article. Suggestions may be on the talk page. (May 2010) Acap.svg This section may require copy-editing." at, the beginning of the Navigation Section.

I, RHB100 (talk) 20:29, 2 June 2010 (UTC), think these tags should be removed. RHB100 (talk) 20:29, 2 June 2010 (UTC)

These tags should be removed for several reasons. Ckatz has not said what is confusing or to whom it is confusing. Attempts have been made to get him to say what he is talking about but he has not done so. Ckatz has said that the section should be changed so that it is reads more encyclopedia. This statement is certainly false. Encyclopedic means that a broad range of subjects covering many fields is included. The overall Wikipedia should be encyclopedic but the individual articles within Wikipedia should not be encyclopedic. There is not a single example that Ckatz has provided that supports his assertion that the Navigation section is confusing. RHB100 (talk) 20:29, 2 June 2010 (UTC)


 * First off, I have tried to explain the issues to you several times, so your claims about my actions are misleading. (I've also been clear in stating that I feel it is best to have the rewrite done by someone with a deep knowledge of the topic, so as to avoid dropping key points.) Secondly, are you seriously claiming that "the overall Wikipedia should be encyclopedic but the individual articles within Wikipedia should not be encyclopedic"?!? How on Earth do you justify such a statement; it appears to be completely out of sync with the generally accepted standards we adhere to. I'll give you credit for filing the RfC, though, as it may bring fresh eyes to the article to assist in cleaning up the text. --Ckatz <sup style="color:green;">chat <sub style="color:red;">spy  20:41, 2 June 2010 (UTC)

Encyclopedic means covering a broad range of subjects and many fields. The individual articles within the Wikipedia should not cover a broad range of subjects and many fields. The individual articles should be focused on a single subject. Encyclopedic means covering a broad range of subjects and many fields. The individual articles within the Wikipedia should not cover a broad range of subjects and many fields. The individual articles should be focused on a single subject. Encyclopedic means covering a broad range of subjects and many fields. The individual articles within the Wikipedia should not cover a broad range of subjects and many fields. The individual articles should be focused on a single subject. Got it Ckatz? Do you understand now, Ckatz? RHB100 (talk) 00:59, 3 June 2010 (UTC)

Clatz above says "First off, I have tried to explain the issues to you several times". Well if Clatz thinks he has explained the issues we all need to see it in this section, so we can all judge the validity and logic of his explanations. I can recall Ckatz making cute little insults such as by saying that the section looks more like a Professor's lecture notes than a Wikipedia article. But this does not tell you anything about what is confusing in the article. RHB100 (talk) 01:20, 3 June 2010 (UTC)
 * RHB100, I'd hoped to discuss this with you in a productive manner. However, I think your comments here and elsewhere speak for themselves. --Ckatz <sup style="color:green;">chat <sub style="color:red;">spy  07:44, 3 June 2010 (UTC)
 * Is it just the opening paragraph of the 'Navigation' section that is under discussion here? I agree that that paragraph could do with a rewrite?  Martin Hogbin (talk) 21:09, 2 June 2010 (UTC)


 * The Navigation section is very detailed and seems to be a pretty thorough treatment of the subject. At a glance there is nothing obviously contradictory or misleading (but I have not read it in detail). But the writing is extremely verbose and doesn't flow well making it unclear just on that basis. A thorough copy-edit would make a world of difference. --Mcorazao (talk) 02:09, 3 June 2010 (UTC)
 * Mcorazao, thank you for your helpful and collaborative comments. Your observations are similar to mine; there is a great deal of detailed information, but the writing needs to be reworked. I made an admittedly limited attempt when I first posted the tags, but again I feel it requires someone well versed in the material to make sure it is done right. --Ckatz <sup style="color:green;">chat <sub style="color:red;">spy   07:44, 3 June 2010 (UTC)

Here is a sample rewrite for the first part of the section. --Mcorazao (talk) 04:04, 3 June 2010 (UTC)

Could we have a clear statement of what is unclear or confusing in the navigation section. I think it is written in a rather clear manner given the complexity of the subject. However, if there is something that is unclear or confusing I would like to know what it is. What is it that you find unclear or confusing? RHB100 (talk) 18:50, 26 June 2010 (UTC)

Navigation
The navigational signals transmitted by the GPS satellites encode a variety of information including satellite positions, the state of the internal clocks, and the health of the network. These signals are transmitted on two separate carrier frequencies that are common to all satellites in the network. Two different encodings are used, a public encoding that enables lower resolution navigation, and an encrypted encoding used by the U.S. military.

Navigation signals


Each GPS satellite continuously broadcasts a navigation message at a rate of 50 bits per second (see bitrate). The first part of the message encodes the week number and the time within the week, as well as the data about the health of the satellite. The second part of the message, the ephemeris, provides the precise orbit for the satellite. The last part of the message, the almanac, contains coarse orbit and status information for all satellites in the network as well as data to allow correction for distortion from transmission through the atmosphere.

Each complete message is composed of 30-second frames, distinct groupings of 1,500 bits of information. Each frame is further subdivided into 5 subframes of length 6 seconds and with 300 bits each. Each subframe contains 10 words of 30 bits with length 0.6 seconds each. Each individual frame begins at precisely at the beginning of one and one half minute intervals, as determined by the atomic clock on each satellite.


 * {| class="wikitable" style="float:left; margin:0 0 0.5em 1em;" border="1"

! Subframe !! Words !! Description
 * + GPS message format
 * 1 || 1–2 || Telemetry and handover words (TLM and HOW)
 * || 3–10 || Satellite clock, GPS time relationship
 * 2–3 || 1–2 || Telemetry and handover words (TLM and HOW)
 * || 3–10 || Ephemeris (precise satellite orbit)
 * 4–5 || 1–2 || Telemetry and handover words (TLM and HOW)
 * || 3–10 || Partial almanac (satellite network synopsys, error correction)
 * }
 * || 3–10 || Ephemeris (precise satellite orbit)
 * 4–5 || 1–2 || Telemetry and handover words (TLM and HOW)
 * || 3–10 || Partial almanac (satellite network synopsys, error correction)
 * }
 * || 3–10 || Partial almanac (satellite network synopsys, error correction)
 * }

The first two words of every subframe provide synchronization data allowing the receiver to recognize the beginning of the subframe and identify which subframe is being transmitted. The remainder of the data in each subframe contains the actual data.

Subframe 1 describes the satellite clock and its relationship to GPS time. Subframes 2 and 3 provide the ephemeris data, giving the satellite's own precise orbit. Subframes 4 and 5 provide the almanac data, giving a coarse description of the orbits for all satellites in the network, data to allow for correction of distortions due to the atmosphere, and data for relating GPS time to Coordinated Universal Time (UTC).


 * That was just the kind of thing I was thinking of. It looks good to me.  I have not checked it for factual accuracy against the original but it certainly reads much better.  Well done! Martin Hogbin (talk) 09:22, 3 June 2010 (UTC)


 * In the spirit of WP:BOLD I went ahead and incorporated these revisions and some others into the Navigation section. It still needs work but hopefully this is a step in the right direction. Please feel free to change anything I have done. --Mcorazao (talk) 15:00, 3 June 2010 (UTC)

Proposed article organization
For what it is worth I believe that the current split between Introduction to the Global Positioning System and Global Positioning System is a bad idea. I think that intro article should go away. I would instead propose:


 * Global Positioning System - Keep current general content but eliminate the algorithm and calculation details, and truncate tangential topics such as augmentation.
 * GPS signals - Already exists. Move most of the details about the encoding/decoding here.
 * Error modeling for the Global Positioning System - Move most of the error analysis details here.
 * GPS Augmentation - Move most of the Accuracy enhancement details here.

--Mcorazao (talk) 15:22, 3 June 2010 (UTC)

Topics which are more concerned with the communication aspects of GPS than Navigation should be put under a section called called Communication. The Navigation section should be subdivided into a subsection on deriving the GPS equations and a subsection on solving the GPS equations. RHB100 (talk) 19:01, 26 June 2010 (UTC)

Side discussion
We should certainly maintain the discussion of the mathematics and physics associated with GPS and how it is used in the computations. We don't have algorithm descriptions. We discuss basic principles that might be used to solve the equations but we do not get to the level of discussing algorithms. We should certainly maintain this.

We already have a section called Error sources and analysis. This is nothing more than a name change. There have been expressions of interest in the current error analysis. RHB100 (talk) 19:59, 3 June 2010 (UTC)

We already have a section called Accuracy Enhancement and surveying.

The section on Navigation should only include what is now called C/A code and P(Y) code, the sections on position calculation. A new section called Communication should include Message format, Data updates, and Satellite frequencies. RHB100 (talk) 20:45, 3 June 2010 (UTC)

I think Position calculation, advanced might be more clear if it were divided into two sections, one on Statement of the GPS equation and the other on Solution of the GPS equation. RHB100 (talk) 20:09, 3 June 2010 (UTC) RHB100 (talk) 20:09, 3 June 2010 (UTC)


 * RHB100, I really don't know what you are trying to say. I think you completely misread what I wrote so I'd recommend re-reading. --Mcorazao (talk) 20:48, 3 June 2010 (UTC)

What I have said is perfectly clear. If you find that you are unable to understand it, then I cannot help you unless you ask a specific question. RHB100 (talk) 21:10, 3 June 2010 (UTC)


 * "not a part of the current discussion" - How can what I suggested not be part of what I suggested? You seem to have invented some concept of a "current discussion" that you are imposing on the discussion I have started.
 * "We already have a section" - How is that relevant to the proposal? The proposal was to move content so how is it useful to state that the content that is proposed to be moved exists?
 * --Mcorazao (talk) 21:39, 3 June 2010 (UTC)

You state, "Error modeling for the Global Positioning System - Move most of the error analysis details here." What is the purpose of moving the Error analysis to this new section when we already have a section called "Error sources and analysis"? It appears to be nothing more than a name change. If you don't like the name, "Error sources and analysis" then changing the name could be discussed but I don't see any reason for moving anything. Likewise for GPS Augmentation. RHB100 (talk) 21:53, 3 June 2010 (UTC)


 * ? You need to look more carefully. Error modeling for the Global Positioning System is not a "section". --Mcorazao (talk) 22:08, 3 June 2010 (UTC)

Well if it is not a section then it has nothing to do with the topic under discussion. And if your writing is so sloppy that I did not notice it the first time then I am certainly not going to waste my time by looking again. RHB100 (talk) 01:10, 4 June 2010 (UTC)


 * RHB100, I'll take this to mean you have no comment (I notice you attempted to change the positioning of this discussion. Sleazy). --Mcorazao (talk) 04:26, 4 June 2010 (UTC)

Mcorazao, I noticed that you made a mistake in the heading of this section and I corrected it. You should not be putting material below the dispute resolution until it is resolved. This is a very sleazy trick on your part. At the present time based on your writing, I don't think you know what you are talking about. RHB100 (talk) 04:55, 4 June 2010 (UTC)


 * RHB100, I have no idea what to say to you. In any event, since you do not seem to have anything to contribute to the proposal let's not clutter this page with this side discussion. --Mcorazao (talk) 14:26, 4 June 2010 (UTC)

I think the above proposal by Mcorazao is misleading and not very well written, no offense intended. He states a non-existent site and then says move material here. This explanation of moving material to a non-existent site is confusing to clear thinking people. My experience in asking about what he is talking about is that rather than clarify the confusing writing, he insults you by telling you to read the same confusing writing again. It appears that he is unwilling to improve his confusing style of writing when he should be aware that it is confusing. RHB100 (talk) 19:58, 4 June 2010 (UTC)


 * I have not proposed doing anything with any site other than Wikipedia. This and other similar comments demonstrate a fundamental lack of understanding of Wikipedia, its organization, and its purpose. Though it is no sin to lack knowledge, you continue insult those who could help mentor you. --Mcorazao (talk) 17:58, 5 June 2010 (UTC)

The proposal remains vague. He says "eliminate the algorithm and calculation details" and then he says "Nobody is proposing that mathematics need be moved out the article". This gives rise to concern that the proposer may be going to damage the article. RHB100 (talk) 22:51, 6 June 2010 (UTC)


 * Pointless personal attack. --Mcorazao (talk) 05:31, 7 June 2010 (UTC)


 * A problem with the article's compliance with Wikipedia guidelines and its overall quality has been stated (by multiple editors). A proposal has been offered. You have offered no counter-proposal nor any reason for your concerns that shows this article to be unique or somehow deserving of an exemption to the guidelines. Please comment constructively or move on. --Mcorazao (talk) 05:31, 7 June 2010 (UTC)

Mcorazao, you show complete disrespect for honesty and integrity. You state, "You have offered no counter-proposal" but I said "Error analysis belongs in its natural context as a part of the GPS article." Therefore your statement is a lie, an outright lie, and nothing but a lie. The suggestion that what you are doing has something to do with enforcing Wikipedia guidelines is false. Your vague reference to multiple editors is a complete evasion of diswcussion of the disadvantages of this proposal which I have stated above. RHB100 (talk) 18:47, 7 June 2010 (UTC)

Proposal discussion
I've separated the above tangential thread. But any comments on the actual proposal are still welcome: --Mcorazao (talk) 17:35, 4 June 2010 (UTC)
 * Global Positioning System - Keep current general content but eliminate the algorithm and calculation details, and truncate tangential topics such as augmentation.
 * GPS signals - Already exists. Move most of the details about the encoding/decoding here.
 * Error modeling for the Global Positioning System - Move most of the error analysis details here.
 * GPS Augmentation - Move most of the Accuracy enhancement details here.


 * Agree to refactor the article. The large current section on algorithms shows signs of being a patchwork created over time. A clear expose of the various posed problems and their possible solutions is needed, with details spun off in detail articles. &minus;Woodstone (talk) 18:56, 4 June 2010 (UTC)

Mcorazao, state clearly what you are talking about when you say "the algorithm and calculation details". State the specific sections you want to eliminate in whole or in part based on the article as it exists as of this time. RHB100 (talk) 19:09, 4 June 2010 (UTC)

I think the material on the mathematics of GPS contained in the Navigation section is very important for the overall article. I know there are people who hate mathematics but I do not know why Mcorazao apparently wants to deprive others of the beauty and usefulness of the mathematics of GPS. This is all the more puzzling when we already have an introductory section on position calculation. Furthermore, even in the Navigation section there are graphical depictions which should aid those who prefer a geometrical approach over an algebraic and equation oriented approach. The understanding of mathematics applied to physical problems is very important to our nations survival. RHB100 (talk) 19:42, 4 June 2010 (UTC)


 * Moving tangential comments above and out of this discussion --Mcorazao (talk) 17:58, 5 June 2010 (UTC)

I think the above proposal by Mcorazao is misleading and not very well written, no offense intended. He states a non-existent site and then says move material here. This explanation of moving material to a non-existent site is confusing to clear thinking people. My experience in asking about what he is talking about is that rather than clarify the confusing writing, he insults you by telling you to read the same confusing writing again. It appears that he is unwilling to improve his confusing style of writing when he should be aware that it is confusing. RHB100 (talk) 19:58, 4 June 2010 (UTC)

Above comments are quite relevant. RHB100 (talk) 04:51, 7 June 2010 (UTC)


 * Nobody is proposing that mathematics need be moved out the article. It is the length of the article and its readability that are a concern. The current length far exceeds all guidelines regarding length. ---Mcorazao (talk) 17:58, 5 June 2010 (UTC)
 * P.S. Regarding the suggestion to provide full details of everything that might or might not be changed, that is not constructive. This is a general proposal. If the generalities are accepted then we can debate specifics. Arguing over the details at this moment would obscure the point of the discussion. --Mcorazao (talk) 18:33, 5 June 2010 (UTC)

'''There are no stated benefits of this proposal and there do not appear to be any. Therefore this proposal should not be carried out.''' Furthermore there is great potential for harm in carrying out this proposal. We certainly should not "eliminate the algorithm and calculation details" since they are an important part of the article of interest to a great many people. Error analysis should remain a part of the current article. Creating a new article for the error analysis would make it more difficult for people to find it. This new article could be deleted since error analysis alone might not create as much interest as the overall GPS article. The proposal is much too vague and ambiguous and has not received any support. RHB100 (talk) 22:04, 6 June 2010 (UTC)


 * Obviously not true. --Mcorazao (talk) 05:31, 7 June 2010 (UTC)


 * Moved tangential comments above --Mcorazao (talk) 05:31, 7 June 2010 (UTC)

The proposal remains vague. He says "eliminate the algorithm and calculation details" and then he says "Nobody is proposing that mathematics need be moved out the article". This gives rise to concern that the proposer may be going to damage the article. RHB100 (talk) 22:51, 6 June 2010 (UTC)

Error analysis belongs in its natural context as a part of the GPS article. No benefits of moving it have been provided  by the proposer or anyone else. We should discuss this issue before adding links to a new article. Readers will best understand it by accessing it from the GPS article rather than opening a new article to read it. RHB100 (talk) 23:39, 6 June 2010 (UTC)


 * Moved tangential discussion above --Mcorazao (talk) 22:03, 7 June 2010 (UTC)


 * I've taken a stab at expanding the GPS signals article to include a lot of the detail from this aarticle. I have also taken a stab at creating a new version of the Communication section. Since there has obviously been some debate about this I did this on a side page to allow some discussion before changing the main article. The revised version is at Talk:Global Positioning System/Proposed refactoring. Comments welcome. --Mcorazao (talk) 15:45, 9 June 2010 (UTC)

A far more intelligent title for the new page being created and now called Error analysis for the Global Positioning System would be Global Positioning System error analysis. This new page is not a discussion on the subject of error analysis. It is a discussion on a sub-topic of the subject, Global Positioning System. The main subject should always be listed first. When a search is made of Global Positioning System, you should see all pages on the subject as well as its sub-topics. Depending on how the search is made you may not see all the sub-topics when Global Positioning System is a subordinate part of the title. RHB100 (talk) 20:11, 9 June 2010 (UTC)


 * Feel free to rename. I have no particular attachment to any name for that new article. --Mcorazao (talk) 19:33, 11 June 2010 (UTC)

Perhaps I will rename it. But I still have some other concerns. One is will people be able to easily find sub-topics or error analysis such as geometric dilution of precision? RHB100 (talk) 20:37, 11 June 2010 (UTC)

What do horizontal and vertical mean in 3D plotting? E/W vs. N/S?
Alvis asked: 'What do horizontal and vertical mean in 3D plotting? E/W vs. N/S?'
 * Horizontal is in any direction towards the horizon, this means when on a flat surface in any direction on that surface. Vertical is in the direction up or down, so going higher or lower. I do not think that this needs clarification in the main article.
 * In 2D determination, the vertical error is the actual error between the used height and the actual height, this error can be small and can be large, there is no indication what the error is. The horizontal error is not known either because this depends on the vertical error. If the GPS goes from 3D to 2D positioning because of loosing the reception of the fourth satellite and you do not change altitude a lot (boat or relative flat road), the horizontal positioning will be almost as accurate as with four satellites. When the altitude does change a lot (for example in a airplane), the horizontal error can become large as wel, it's not unusual that with a given vertical error the horizontal error is larger than the vertical error.Crazy Software Productions (talk) 20:37, 13 June 2010 (UTC)

Copy-edits
Removed tag after editing. Feedback welcomed. Lfstevens (talk) 02:06, 13 July 2010 (UTC)

Equations and Methods of Solution sections have been further clarified
The Equations and Methods of Solution sections have been further clarified. It is believed that even before this most recent further clarification, the Wikipedia Navigation section including its subsections was the clearest and best explanation to be found anywhere on the Internet or in print. Nevertheless if you find anything that you think is unclear or confusing please state your finding and it can be discussed. RHB100 (talk) 02:58, 23 July 2010 (UTC)

Disadvantage of Multidimensional Newton Method
In February 2009 AxelBoldt did allready write:

I removed the following sentence about Newton's method, then it was reinserted:
 *  A disadvantage of this method is that according to, "There are no good general methods for solving systems of more than one nonlinear equations."

While it is true that there are no good general methods for solving nonlinear systems, I don't think that this can be counted as a disadvantage of Newton's method, for two reasons: AxelBoldt (talk) 23:58, 10 February 2009 (UTC)
 * to solve GPS, we don't need a "good general method" for nonlinear systems, we only need a method that works well for the specialized quadratic systems arising in GPS. The given reference doesn't talk about the quality of Newton as it applies to these specific systems. I don't have a reason to believe that Newton is not a "good method" when applied to those systems.
 * even if the reference claimed that there are no good methods to solve the quadratic systems arising in GPS, which it doesn't, then that criticism would apply to all methods, not just to Newton's method.

And I do agree with Axel, if this is an issue it is an issue for the problem not for the solving method. The Bancroft method has sufficiently shown that this advantage has been overcome, allthough also Bancroft still is not a general method. It is more general than Newton and iteration with trilateration. Why? In a case of multiple solutions both Newton Raphson and iteration with trilateration will only find one solution, Bancroft can find two solutions. So this does disqualify Newton and also iteration with trilateration as a general method, therefore the remark does not apply to the Newton method and should not be placed in text only concerning the Newton method. The sentence should be removed. Crazy Software Productions (talk) 12:58, 27 June 2010 (UTC)

No reaction has come up to why this disadvantage does apply to the Newton Raphson method and not to the other methods. Neither has there been given a reference that this disadvantage does apply to the Newton Raphson method. The writer does invite to come to the talk page, and could have replied by now. In absence of this reply and in absence of a reference, I am going to remove the line in the main article. If the author of the line wants the line in the article it should not be in a specific area describing Newton Raphson. Crazy Software Productions (talk) 14:46, 7 July 2010 (UTC)

None of the above comments seem relevant. The quote of AxelBoldt is obsolete since the statement has been changed since then. The mention of Bancroft is irrelevant since Bancroft's method is algebraic not numerical. Trilateration is irrelevant. I have not bothered to comment on the above since it is not clear what he is trying to say, what point he is trying to make. I did not want to waste my time discussing vague and ambiguous comments. But the statement below stating a disadvantage of multi-dimensional root finding methods as compared to single dimensional root finding methods is quite valid.

A disadvantage of this multidimensional root finding method as compared to single dimensional root findiing is that according to Numerical Recipes, "There are no good general methods for solving systems of more than one nonlinear equations." RHB100 (talk) 19:03, 7 July 2010 (UTC)
 * The text: "There are no good general methods for solving systems of more than one nonlinear equations." is not disputed. Please do supply a reference why this undisputed text would be mentioned in connection with the Pseudorange calculation. As for Bancroft; the implementation of Bancroft is numerical (so it's still a method), so does the text apply to the implementation of Bancroft? No it does not but it doesn't apply to the Pseudorange calculation either. Even itereation with trilateration attempts to calculate the same solution, this solution is multidimensional and it does try to solve more than one nonlinear equation. So as the guidelines of Wikipedia state please supply a reference to why the statement does affect the pseudorange calculation and not the other methods for solving more than one nonlinear equation. Crazy Software Productions (talk) 17:14, 27 July 2010 (UTC)

Relativity
I'm a bit confused by the recent edit (so far here, here and here)s, which introduce a full 180 (from "Relativistic effects cause additional errors that would render GPS useless if uncorrected" to "Relativistic effects do not cause measurable errors in GPS results") without any sort of discussion, so I'm starting one here.

First of all, two sources were removed, claiming that they don't contain or confirm the "relativity is important, yo" statements.

The first one says: "All these effects - and other, even more subtle, relativistic effects - must be accounted for if GPS is to provide positional accuracy of one meter. [...] If relativistic corrections are not applied to the time registered by the atomic clocks on board GPS satellites, the system does not work. [...] Without general relativity we would get the timings incorrect, and the system would be worthless [...]"

The second one says even in the Introduction: "If [the relativistic effects on the rate of clocks] were not corrected, the system would not be operative after a few minutes. In a day of operation, they would produce an error of more than 11 km in the horizontal positioning of the receiver. In a week, the error accumulated in the vertical positioning would be of 5 km approximately."

Secondly, the source introduced in the second edit is misquoted in my opinion since the quote seems to be along the lines of "Not all relativistic effects matter right now": The quote comes after (if I read this correctly) an article-long discussion of how certain relativistic effects are significant and need to be corrected.

I'm not a physics expert, which is why I'm coming here first, but the sudden change from "Yes, they do" to "No, they don't" and the fact that the sources all seem to point towards "Yes, relativistic effects need to be corrected" make me frown deeply.

I definitely welcome more opinions, but unless I completely misunderstood everything I described above, I really think these edits should be reverted to the August 8 version. I might do it myself tonight, depending on feedback here. --Sid 3050 (talk) 12:58, 10 August 2010 (UTC)


 * It bothers me, too. The only effect specifically mentioned as being required for GPS to work is the clock adjustment for gravitational adjustments to the rate of time flow, and that is overriden by steering the satellite clocks, anyway.  (Note:  I worked for a number of years on WAAS, so I know what adjustments need to be made.)  — Arthur Rubin  (talk) 09:34, 11 August 2010 (UTC)


 * By "the only effect specifically mentioned" do you mean mentioned in the article? If you look at the table of contents, the two subsequent sections ( "9.7.1 Special and general relativity" and "9.7.2 Sagnac distortion" are subsections of "9.7 Relativity". I figured section 9.7 didn't need to duplicate all the info given in sections 9.7.1 and 9.7.2; the reason I left a single example in (that satellite clocks are tuned to compensate for time dilation) was to illustrate what I mean by relativistic effects being accounted for in GPS positioning.
 * It could be argued that, relativistic effects which are compensated for do not belong in the "9 Error sources and analysis" section as they are no longer error sources by virtue of their having been compensated for. But we compensate for receiver clock bias as well and that's in the same section, so I figured we were using section "9 Error sources and analysis" to discuss both compensated and uncompensated error sources. Mike1024 (t/c) 10:32, 11 August 2010 (UTC)
 * I meant, the only effects specifically mentioned as not being too small to effect the results are otherwise compensated for. As the satellite atomic clocks are steered by the ground atomic clock, the relativistic correction of the satellite atomic clock speed, although it would make the system useless if not steered, doesn't effect the usefulness of the system.  (As an aside, atmospheric or ionospheric effects far exceed most of the relativistic effects, except in case of using GPS for determining precise positions of objects outside the Earth's magnetosphere.  Those effects can rarely be compensated for.)  — Arthur Rubin  (talk) 17:44, 11 August 2010 (UTC)
 * However, I missed the Sagnac effect. Carry on.  — Arthur Rubin  (talk) 18:02, 11 August 2010 (UTC)

Political context
Sid 3050 is confused because he didn't know about the other half of what's going on -- that GPS has been dragged into a right-wing attempt to discredit relativity for political reasons.

Our saga begins at the always-good-for-a-laugh Conservapedia, which has an article titled "Counterexamples to Relativity". According to this font of conservative wisdom, "The theory of relativity is ... heavily promoted by liberals who like its encouragement of relativism and its tendency to mislead people in how they view the world." With an intro like that, anyone familiar with Conservapedia can tell where this is going. The article is, indeed, a grab-bag of attacks on relativity.

Someone at the politically left website Talking Points Memo was evidently amused at this attack on a scientific theory for political motives. TPM ran an article titled "Conservapedia: E=mc2 Is A Liberal Conspiracy". This flap was picked up Rachel Maddow, who ran a segment about the overall right-wing war on brains. (The brief reference to relativity and Conservapedia begins at about 3:30 of the clip.)  The TPM article itself didn't single out the GPS issue, but some of the comments mentioned GPS performance as a confirmation of the theory of relativity.

I assume that this little flurry is the reason for the sudden interest in attempting to shift our article 180 degrees, as Sid 3050 correctly notes. People associated with Conservapedia have misleadingly excerpted sources to attempt to convey the false impression that experience with GPS does not confirm relativity, when in fact it does.

This distortion begins with the founder of Conservapedia, Andrew Schlafly. He is apparently (per this edit to the Conservapedia article) the author of the footnote currently numbered 11, which reads:

"Contrary to the claims of Relativists, the GPS system has never been based on Relativity. The Time Service Department, U.S. Navy, observed that 'the Global Positioning System (GPS) does not include the rigorous transformations between coordinate systems that Einstein’s general theory of relativity would seem to require' in part because 'the effects of relativity, where they are different from the effects predicted by classical mechanics and electromagnetic theory, are too small to matter – less than one centimeter, for users on or near the earth.”" He doesn't provide a link but I assume he's referring to this paper (hosted on the Navy website but actually written by two people at The Aerospace Corporation).

Schlafly's clear intent is to portray the Navy as supporting his view that the theory of relativity is false. Of course, even the quotation he uses doesn't show that, because all it says is that relativistic effects are small, not that they're nonexistent. Even more inconvenient for Schlafly is the rest of that paragraph from the paper: "However, a new class of users, who employ satellites that obtain time and position in space from GPS, cannot be satisfied with the approximations in the current [Operational Control System]. ... In this paper, we compare the predictions of relativity to those of intuitive, classical, Newtonian physics; we show how large or small the differences are, and how and for what applications those difference are large enough to make it necessary to correct the formulas of classical physics."

Clearly, the authors believe that, where relativity is inconsistent with classical physics, it is relativity that is accurate and it is classical physics that must be corrected. (Most of the paper is over my head, but it appears to be a careful examination of specific relativistic effects.)

After the Talking Points Memo article, the battle expanded to Wikipedia. Our article on GPS had for some time stated, correctly, that relativistic effects "would render GPS useless if uncorrected." That statement was properly cited to this source, which fully supports it. Because the statement would make Schlafly and Conservapedia look foolish, however, it could be expected to come under attack, and that proved to be the case.

Wikipedian Ed Poor, who is also a Sysop at Conservapedia, deleted the offending statement and its citation. He wrote, "This reference does not mention 'additional errors that would render GPS useless if uncorrected' so I deleted it". In fact, however, the cited reference discusses three of the relativistic effects that were listed in the passage that Ed deleted (time dilation, gravitational frequency shift, and eccentricity). The source concludes: "All these effects -- and other, even more subtle, relativistic effects -- must be accounted for if GPS is to provide positional accuracy of one meter."

I don't know if Ed is hairsplitting about the word "useless". A system telling you your position to within fifty meters would probably have a lot of usefulness, so perhaps our original statement should have been edited by changing "useless" to "measurably less accurate". Certainly, however, the cited source does support the basic point that relativistic effects exist and that they have practical consequences for GPS. That information should not have been deleted from our article.


 * No, I simply read the source too hastily: when I didn't see specific mention of errors that would render GPS useless I deleted the reference. (I had assumed that the main use of GPS is for navigation, which does not require one meter accuracy.) I thank my fellow contributors for catching and correcting my error. --Uncle Ed (talk) 19:53, 18 August 2010 (UTC)

Ed's next edit emulated Schlafly by snipping a scientific paper so as to give an inaccurate (but politically convenient) impression. Ed referred to this paper, titled "General relativity in the global positioning system", by Neil Ashby of the University of Colorado. Ashby states: "Apart possibly from high-energy accelerators, there are no other engineering systems in existence today in which both special and general relativity have so many applications." He then goes on to discuss specifics, including three issues mentioned in the passage that Ed removed from our article: time dilation ("Time dilation of moving clocks is significant for clocks in the satellites as well as clocks at rest on earth"), the Sagnac effect ("The Sagnac effect has an important influence on the system"), and eccentricity ("if the orbit is eccentric, an additional correction arises ....").


 * My comment was According to the physics department at LSU, the effects are "too small to affect the system at current accuracy levels" and my edit was, "Relativistic effects do not cause measurable errors in GPS results, someday the system might be accurate enough for these effects to matter." I had nothing political in mind, but (as before) had failed to read the entire article. Once again, I thank those who found and corrected my error. --Uncle Ed (talk) 19:53, 18 August 2010 (UTC)

Ashby further confounds the Conservapedians by pointing out that this dispute was settled years ago. He states, "At the time of launch of the first NTS-2 satellite (June 1977), which contained the first Cesium clock to be placed in orbit, there were some who doubted that relativistic effects were real." He then reports the observations obtained since then and concludes: "The difference between predicted and measured values of the frequency shift was only 3.97 parts in 1012, well within the accuracy capabilities of the orbiting clock."

In sum, the Ashby paper is a straightforward refutation of the right-wing position concerning GPS and relativity.

Why, then, did Ed cite this paper? He cited it because Ashby, after laying out in detail how GPS must take account of major relativistic effects, then comments in passing: "Several relativistic effects are too small to affect the system at current accuracy levels, but may become important as the system is improved; these include gravitational time delays, frequency shifts of clocks in satellites due to earth's quadrupole potential, and space curvature." That's the sentence that Ed quotes from Ashby's paper. Ed's ES makes explicit the impression he wants to convey: that "the effects are 'too small to affect the system at current accuracy levels'".

The edit is at best grossly misleading. Ashby didn't say that about "the" effects; he said it only about a handful of minor effects, and he said it after demonstrating that the major relativistic effects, the ones mentioned in the passage that Ed deleted, were indeed significant enough to affect the system at current accuracy levels.


 * Excuse me, but I had no particular impression to convey; I simply made a mistake due to hasty reading, and it has been corrected, thanks "with many eyes all bugs are shallow". --Uncle Ed (talk) 19:53, 18 August 2010 (UTC)

I agree with Mike1024's point about including errors that are compensated for, such as relativistic effects. Alternatively, however, if such matters are excluded from this section, then the material about GPS and relativity should be included elsewhere in the article, because it's important and well-sourced information. It belongs in our article even if, heaven forbid, it makes Conservapedia look bad. JamesMLane t c 16:50, 11 August 2010 (UTC)


 * Actually, I cited it because I did a superficial web search. If you'll look on my user page, you'll find some balancing quotes by a physicist. I have no bone in the dog fight: I'm just wondering what the various sides are and hoping to "describe all sides fairly", per NPOV. --Uncle Ed (talk) 18:30, 13 August 2010 (UTC)


 * We try to describe all sides fairly, but that doesn't include "sides" that are crackpots. I've seen nothing from any reputable scientific source that would support the "side" of saying that relativistic effects play no role in GPS, or even that they are too small to affect the system at current accuracy levels.  Your quotation from Ashby gave a false impression to that effect, but that's only because you quoted his comment about some minor effects while omitting his extensive discussion of the effects that actually matter.


 * If there is some genuine scientific controversy about a particular point, then, yes, we should include "balancing" quotations to present both sides fairly. So far, though, I haven't seen such a controversy. JamesMLane t c 14:49, 14 August 2010 (UTC)


 * I emailed a physicist about relativity corrections in GPS, and he replied that "the correction would be practically irrelevant in practice anyway (given the fact that the timings are made differentially and not by means of direct comparison to a ground clock)." Is there a way to verify this? Is this a "marginal viewpoint"? What actual relativistic corrections are made on the satellites in the sky and in the receivers on the ground? --Uncle Ed (talk) 14:54, 18 August 2010 (UTC)


 * Does this physicist have his/her results published anywhere, so that we can cite them in the article? Mike1024 (t/c) 15:57, 18 August 2010 (UTC)


 * He has this page on his website. Is that good enough? (Please bear in mind, that unlike most of the company I keep - in other projects we need not mention here - I have no agenda here. I just want to describe all the viewpoints.)


 * At this point, I haven't seen enough - on any website or in any book - to determine whether GPS is or is not related to relativity. I want the article to help me know this. --Uncle Ed (talk) 19:01, 18 August 2010 (UTC)


 * This archived discussion seems relevant here since it apparently involves exactly these calculations by this guy (and comments by the guy himself - he's not exactly a stranger on Wikipedia from the looks of it). Without having evaluated how that discussion impacted the article at that time and without verifying the calculations (I'll leave that to more knowledgeable people), I just have to comment that I find it interesting that apparently, all relativistic effects (as other sources pointed out, there are several effects - not all of them large enough to matter at the current accuracy) are calculated in just a few lines. Call me a skeptic, but I tend to frown at amazingly short solutions for complex problems (especially when they go against what several longer sources say). Of course, I'm no expert on GPS or relativity, so it's possible that I'm wrong. --Sid 3050 (talk) 19:33, 18 August 2010 (UTC)

Please see my interspersed comments above, inside JamesMLane's long 14:49, 14 August 2010 post. --Uncle Ed (talk) 19:53, 18 August 2010 (UTC)

Relativity without politics
This issue should be treated without the distraction of politics.

At the beginning of the section on Relativity, it is stated "GPS positioning is one of the few everyday events in which relativistic effects must be accounted for". The reference given leads to a blank page. It is not at all clear that this statement is true for the case when position is being determined by solving the navigation equation as opposed to surveying and when there is the one day accumulated clock error of 38 microseconds.

One way in which clock error might cause an error in the computed receiver position is through incorrect satellite positions since time is needed to determine position. But with the satellite velocity of about 4 km/sec, the error in position is only about 15 centimeters.

Another way it might be though that clock error could cause position error is in computing the distances from satellites to receiver. But in solving the navigation equations, b the computed value of receiver clock correction would cancel the effect of satellite clock error on computed receiver position since the satellite clock error due to relativity is the same for all satellites. There would be an error in time computed by the receiver but not an error in position.

I do not question relativity theory but I do question the effect of this satellite clock error on computed receiver position.

Does anybody disagree with anything that I have said? RHB100 (talk) 01:11, 12 August 2010 (UTC)


 * I agree with and heartily endorse your assertion that this is better discussed without politics, if that helps. I'm not well-versed enough on the technical side to know what's what, though. — Gavia immer (talk) 01:26, 12 August 2010 (UTC)


 * I should clarify that I didn't intend my allusion to the politics to be included in the article. I just thought it would be useful for editors to be aware of the potential for politically motivated edits.


 * As for the specifics of what you say, I think I've read that the cumulative errors, if relativistic effects were ignored, would be significant -- far more than 15 centimeters. I think part of the issue may be that, with different clocks keeping time at different rates, the discrepancy just keeps on growing (if uncorrected).  Thus, what starts out as a minor error eventually becomes one measured in miles.  I'll see if I can find that reference. JamesMLane t c 03:15, 12 August 2010 (UTC)


 * "At the beginning of the section on Relativity, it is stated "GPS positioning is one of the few everyday events in which relativistic effects must be accounted for". The reference given leads to a blank page." The link still works for me; here is a screenshot of what I see. If that gives you trouble, I'm trying to link to page 451 of "Linear algebra, geodesy, and GPS" By Gilbert Strang and Kai Borre. If you prefer, you may also reference page 75 of "GPS satellite surveying" By Alfred Leick or page 144 of "Global Navigation Satellite Systems" by Bernhard Hofmann-Wellenhof et. al. Mike1024 (t/c) 08:56, 12 August 2010 (UTC)

I have the 1995, 2nd edition of the book by Leick. On page 68, Leick states, "Relatavistic effects are important in GPS surveying". But he says nothing about the importance of relatavistic effects in GPS navigation. Since the solution of the navigation equations must compute the correct value of receiver clock error (i.e. deviation from satellite clock) and the three components of receiver position (i.e. the intersection of 4 sphere surfaces) the effect of a consistent error in satellite clocks would not significantly effect the solution of the navigation equations. There might be an error of at most 4*15 cm = 60 cm due to incorrect satellite position for a one day build up of a 38 microsecond satellite clock error. If you understand these references to which you refer, please quantitatively explain how this consistent clock error affects the solution of the navigation equations. Keep in mind these references could be wrong. RHB100 (talk) 20:14, 12 August 2010 (UTC)

Thank you for providing the screen shot. I took a look at it. It is just words not analysis. There is no mathematics. There is no evidence that the writer has thought throough how these clock errors effect the solution of the navigation equations. RHB100 (talk) 20:21, 12 August 2010 (UTC)


 * RHB, it seems to me that you may be calling for an analysis that would violate WP:NOR. We can cite a reliable source even if you think that source is wrong.  (Reliable doesn't mean infallible.)  If there is some published reliable source that draws the distinction between surveying and navigation, or better yet one that expressly disagrees with the source cited by Mike, then we can cite that, too, and present the reader with the differing professional assessments.  We can't discount a reliable source, however, and suppress the point entirely, just because you find the quoted passage to be unpersuasive.  Is your point of view backed up by something we can cite? JamesMLane t c 09:18, 13 August 2010 (UTC)

No, JamesMLane, I am not calling for an analysis that would violate WP:NOR. There are no rules against thinking, analyzing, and making judgements with regard to the accuracy and reliability of references. All reliable sources make a distinction between navigation and surveying. The book by Leick is on surveying and the comments on relativity clearly state that it is with regard to surveying that relativity is important. RHB100 (talk) 20:07, 13 August 2010 (UTC)


 * If you would like a more in-depth numerical analysis, how about "Relativity and the global positioning system" by Neil Ashby in Physics Today (2002, Vol 55, no 5, p. 41-47) which contains detailed calculations and states "In fact, relativistic effects are about 10 000 times too large to ignore. Suppose one wanted to improve GPS spatial precision so that receiver positions could be determined with an uncertainty of only a centimeter. A radio wave travels 1 cm in 0.03 ns. So one would have to account for all temporal relativistic effects down to a few hundredths of a nanosecond. But the second-order Doppler shift of an orbiting atomic clock, if it were not taken into account, would cause an error this large to build up in less than half a second. An effect of comparable size is contributed by the gravitational blueshift, which results when a photon--or a clock--moves to lower altitude. If these relativistic effects were not corrected for, satellite clock errors building up in just one day would cause navigational errors of more than 11 km, quickly rendering the system useless." Now, I don't have the expertise in relativity to verify or debunk Ashby's paper, but a peer reviewed journal article with 150+ citations seems like as credible a source as we're going to find - unless there's another credible source presenting an alternative view? Mike1024 (t/c) 10:21, 13 August 2010 (UTC)


 * Fwiw, I have provided a "proper" wiki-citation for that page 451. It can now be accessed directly by clicking on the link Chapter 14 p. 451. DVdm (talk) 19:11, 13 August 2010 (UTC)

Relativity not relativism
Having read above about the political attacks on this article, I feel obliged to point out the fundamental confusion that such attacks rest on: they think relativity and relativism are the same thing. We know that relativity has nothing to do with morality and is based on the idea that the laws of physics must stay the same whatever your reference frame, whereas the "relativism" they want to attack is the idea that the "laws of morality" can be whatever you like---not only a totally different concept but in some ways an opposite one.

Would a note to this effect in the article help to deter some of the vandalism? I realise this is in some ways a political comment, but it's also one aimed at helping to keep political edits out of the article. Musiconeologist (talk) 22:38, 15 August 2010 (UTC)


 * I think this article would be an odd place for this sort of note since it doesn't focus on relativity. And the Relativity disambig already has a "See also" link at the bottom, and Theory of relativity has a note at the top.
 * And I somewhat doubt that this sort of edit is based on a simple misreading of a word. For example, take a look at Conservapedia's "Moral relativity" article and you will find that they indeed know that it's not the same as the theory of relativity... but "moral relativists seized on the theory of relativity to legitimize their views" and "liberal professors heavily support the Theory of Relativity and try to use it to draw followers away from Biblical morality". And their "Theory of relativity" article has an entire section on political aspects.
 * Simple notes won't solve this problem, I'm afraid. I'm not sure what exactly motivates some people to make this connection, but it definitely goes beyond a simple misreading. But these pages (as could be seen in this instance) are watched by several people, so the articles should be fine, I guess. --Sid 3050 (talk) 00:47, 16 August 2010 (UTC)


 * If we find that there's a sustained political attack on the article, then the note suggested by Musiconeologist could become an appropriate solution. For the moment, though, I share Sid 3050's optimism that it won't be necessary. JamesMLane t c 10:52, 16 August 2010 (UTC)

We continue to get suggestions that those who question the over emphasis of relativity's importance do so for political reasons. It is neither relativity nor relativism that is the problem. It is the use of exaggeration rather than explanation that is one cause of the skepticism of the importance of relativity. An example of this is the statement, "relativistic effects are about 10 000 times too large to ignore". —Preceding unsigned comment added by RHB100 (talk • contribs)


 * Not all skepticism is politically motivated, but there are people and sites that claim that relativity is some little fantasy liberal professors dreamed up and defend in order to justify moral relativism and that this relativism is pushed because of an anti-Christian agenda. I really wish I was joking here, but I'm not.
 * This here quite likely was such a case. Take a look at the Conservapedia entries for "Counterexamples to Relativity" and "Theory of relativity" - the former entry very recently hit the blogs and online news and is a hot topic on Conservapedia right now. And then consider that the editor who made the recent edits here (which completely changed the meaning of the key sentence, removed valid sources and then misquoted another one) is an active Senior Administrator at that site and is currently suggesting that the lack of published anti-relativity papers may be a case of "scientific censorship" (on par with other "ideas which we know to be true (or at least likely)," such as global warming denial and Intelligent Design.
 * Nobody is suggesting that everybody who questions the claims of relativity here is politically motivated. We should try to assume good faith (see my very initial post on this page), and I'm all for explaining things precisely, but we shouldn't ignore strong hints that some people are driven by more than curiosity and skepticism. Especially not when they express it by completely turning around the meaning of a key sentence without any kind of discussion. --Sid 3050 (talk) 22:49, 16 August 2010 (UTC)
 * I'm flattered that you consider the views of an unpublished writer (me! ;-) important enough to review them here, but (a) WP contributor activity offsite is irrelevant to their contribution here and (b) I'm not a verifiable source who can be quoted in a ref for a WP article. So thanks for the flattery, but let's get back to the topic, shall we?
 * All that really matters here is (1) what verifiable sources say about GPS and relativity; particularly, what sorts of calculations are done on the satellites and in the receivers to compensate for relativistic effects - and (2) what various verifiable sources have said about the linkage between relativity and relativism or the lack thereof.
 * Your opinion and my opinion doesn't matter, because WP is not an opinion board but an encyclopedia. --Uncle Ed (talk) 23:33, 16 August 2010 (UTC)
 * Ed, please drop the innocent act about simply being curious and about needing to lecture us about how WP works - it doesn't really work after you remove a valid source because it didn't contain the exact same phrase used in the article and then misquote another source to completely turn around the meaning of the sentence - all without even a single talk page post. (See my opening of the "Relativity" section above.) From what I can see, Reliable Sources state that relativistic effects cause measurable errors that need to be corrected. If you want to dig further to determine which exact correction is done where and how, be my guest. If you find a RS that states that relativity doesn't matter, feel free to present it here - you can see that there are plenty of knowledgeable people here to discuss such things. And finally: If you're indeed curious about the subject, I suggest you actually read the sources you remove and insert - preferably before you remove/insert them.
 * And regarding your "What I do elsewhere doesn't matter!" handwave: We're not saying "Ed is from CP and does silly things there, so his edits are wrong!" (the content of your edits was discussed above), but this is about the potential for Wikipedia edits that are motivated by more than simple curiosity and about how/if to deal with it. And the fact that an active Conservapedia Senior Admin completely changes the meaning of the relativity section here (through questionable means, IMHO) to fall in line with Conservapedia's anti-relativity views (on the very day those views made it to Talking Points Memo) certainly makes a plausible case for such "motivation". --Sid 3050 (talk) 00:40, 17 August 2010 (UTC)

Oh, we have to post on the talk page before editing article now? When did that rule come into being?

And why are you still harping on (what you imagine is) my motivation? I thought personal remarks were off limits.

Can we please get back to talking about how to improve the article? I have a bunch of quotes on my user page which state that relativistic effects cause measurable errors that need to be corrected. You are welcome to copy them, if necessary.

Why are we still discussing a "complete change in meaning" which was corrected last week? Do I have to shout mea culpa or something? Sheesh! --Uncle Ed (talk) 00:55, 17 August 2010 (UTC)

Relativistic corrections
I'd like the article to describe the corrections that have to made - or, better yet, are currently being made - on the satellites and in earthbound receivers, to compensated for relativistic effects. (FWIW, I'm not interested in whether the theory of relativity is true or not. That is an issue that WP is not interested in, per NPOV and OR.)

I've found some websites which imply that no corrections are being made for relativity, but I've seen others that say either that such corrections are being made (or what is subtly different) that they would have to be made, to get enough accuracy.

Will those who are interested in GPS and relativity please help me by studying this matter with me? Here are some references I've found:


 * No corrections needed:
 * In principle, the critics of GPS in the relativity debate have not been completely wrong. The neglected gamma factor could hurt us. The OCS software should be reformulated. Nevertheless, in practice, neglect of relativity does not now contribute measurably to the GPS error budget, as the OCS software is currently configured.
 * "As the satellites are at a distance of around 20000 km (=2.109 cm), the positional error due to relativity should actually only be 4.4.10-10 . 2.109 cm = 0.8 cm! This is even much less than the presently claimed accuracy of the GPS of a few meters, so the Relativity effect should actually not be relevant at all!" Thomas Smid (M.Sc. Physics, Ph.D. Astronomy)
 * Corrections are needed:
 * "The purpose of this article is to explain how relativistic effects are accounted for in the GPS. Although clock velocities are small and gravitational fields are weak near the earth, they give rise to significant relativistic effects. These effects include first- and second-order Doppler frequency shifts of clocks due to their relative motion, gravitational frequency shifts, and the Sagnac effect due to earth’s rotation. If such effects are not accounted for properly, unacceptably large errors in GPS navigation and time transfer will result" Neal Ashby

Does anyone else but me see these source as (A) verifiable yet (B) in conflict with each other? --Uncle Ed (talk) 20:14, 18 August 2010 (UTC)


 * I think your question is already answered with the statement, "satellite clocks are tuned to 10.22999999543 MHz before launch, to compensate for the effects of gravitational time dilation and achieve a frequency of precisely 10.23 MHz once in orbit", in the Relativity section. RHB100 (talk) 21:13, 18 August 2010 (UTC)


 * To get an idea of the reliabiliy of this Thomas Smid source you might check his contributions on sci.physics.relativy on Usenet. I don't think this personal website would count as a WP:RS. DVdm (talk) 22:10, 18 August 2010 (UTC)


 * Speaking as an amateur, I feel like asking how dated some sources are. This is a question for this section and also in general. For example, both Ed's paper ("GPS and Relativity: An Engineering Overview") and I think at least one of the sources mentioned here (Ashby?) recently spoke of things like "current accuracy levels", but I think GPS became a lot more precise during the past years (for example, the User Range Error mentioned in the Engineering Overview paper is now apparently a lot lower than the 6 meter specification from way back). So maybe some effects were not critical back then... but what about now? I'm really not familiar with the development history of GPS, the technical aspects or relativity, but maybe this might explain some of the apparently conflicting messages? --Sid 3050 (talk) 00:38, 19 August 2010 (UTC)


 * Thanks for crediting me with a paper! But I only cited it; didn't write it.


 * Are we going to come to an editorial consensus on how to write about this? There are three possibilities:
 * Every engineer and scientist addressing the issues agrees that there are no relativistic effects worth correcting for, and that neither the satellites nor the receivers make any corrections.
 * At least one important engineer or scientist says that the satellites or receiver are programmed to make relativistic corrections, or that they ought to (sooner or later) - although others disagree.
 * All these sources agree that corrections for relativistic effects are being made.


 * Can we at least agree that these are the only possibilities? --Uncle Ed (talk) 03:06, 19 August 2010 (UTC)

There is no controversy among reliable sources whatsoever. Relativistic effects are important and appropriate corrections are made. For example, a paper by this guy states, "[...]the Global Positioning System (GPS), the ﬁrst technological application of GR, or the ﬁrst large scale technology that needs to take GR eﬀects into account." References given for that statement in that paper are: ▻Tim Shuba (talk) 04:46, 19 August 2010 (UTC)
 * BW Parkinson, JJ Spilker eds, “Global Positioning System: Theory and Applications” Progr in Astronautics and Aeronautics, 163-164 (Amer. Inst Aero Astro: Washington 1996).
 * ED Kaplan, “Understanding GPS: Principles and Applications”, Mobile Communications Series (Artech House, Boston 1996).
 * B Hofmann-Wellenhof, H Lichtenegger, J Collins, “Global Positioning System Theory and Practice” (Springer-Verlag, New York 1993).


 * Ed, I don't see the statements you quoted at the top of this section as being in conflict. The problem lies in your phrase "corrections are needed", which is ambiguous as between these two meanings:
 * (1) If GPS were designed solely according to classical Newtonian mechanics, it would quickly become quite inaccurate. Therefore, the equations of classical Newtonian mechanics must be corrected to incorporate relativistic effects.
 * (2) GPS as currently implemented is rendered inaccurate by relativistic effects. Therefore, the readings of a GPS device must be corrected to allow for these effects.


 * Statement #1 is true and statement #2 is false. As RHB100 pointed out, the reason is that the design and construction of GPS actually does take account of relativistic effects, with the result that the readings of the devices are accurate.  This is confirmed in the very paper you cite (from The Aerospace Corporation), which states (page 193) that "each GPS space vehicle (SV) clock is offset from its nominal rate by about -4.45xlO-'O (= -38 microseconds per day) to allow for the relativistic offsets between the differences between the SV and the ground."


 * You should also note the context of the passage you quote, which comes at the end of a section addressing a particular problem. Here's the introduction to that section, which puts it in context:
 * "The GPS Operational Control System ... corrects the pseudoranges measured by its Monitor Stations for the sum of the gravitational and the velocity effects as discussed in the previous section, but computes the velocity effect only for the mean orbital speed of the satellite, which is about 3.87 km/sec. The question has been raised: why doesn't the operational sohare calculate the velocity effect using the speed of each satellite relative to each Monitor Station, which varies sinusoidally as the Monitor Station is carried around the rotating earth? In principle, it should, but the effect is negligible....(, p. 194)"
 * Note that the gravitational and velocity effects referred to in the first sentence are the General Relativity and Special Relativity effects, respectively, which are corrected by the 38-microsecond offset. So the passage you quote means only that the GPS, in calculating the velocity effect, doesn't take account of the velocity of the Earth's rotation, which is pretty slow by relativistic standards.  The authors explain that this omission does indeed introduce an error but its effect is only about 2.5 millimeters.


 * Thus, your quotation from the Aerospace Corporation is similar to your quotation from Ashby in your earlier edit to the article. Each paper describes significant relativistic effects that must be, and are, taken account of to make GPS work properly, but then notes that not all relativistic effects are that significant.  An error of 2.5 millimeters isn't worth including in the GPS error budget, which lists errors of up to 30 meters that can arise from atmospheric disturbances.


 * The ambiguity about "corrections" also affects the first of the three possibilities you list -- whether "there are no relativistic effects worth correcting for" depends on whether you mean correcting Newtonian mechanics or correcting the output of a GPS device that you can go out and buy today.


 * Finally, I agree with Tim Shuba that there is no genuine controversy on the role of relativity in GPS. JamesMLane t c 10:13, 19 August 2010 (UTC)

Possible reorganization to clarify relativity discussion
In the initial section above on, Mike1024 wrote: "It could be argued that, relativistic effects which are compensated for do not belong in the '9 Error sources and analysis' section as they are no longer error sources by virtue of their having been compensated for. But we compensate for receiver clock bias as well and that's in the same section, so I figured we were using section '9 Error sources and analysis' to discuss both compensated and uncompensated error sources."

The article will be clearer if we recognize the distinction that Mike draws. The "Error sources" section should be restricted to factors that might cause errors in the readings of a GPS device as the system is currently operating. Some people will come to this article wanting to know, "How reliable and accurate is this gadget that my kids want me to buy?" If there's a problem, such as relativistic time dilation, that's known to the designers of the system and is corrected for, and is therefore not an issue in assessing possible errors in a GPS device that someone might go out and buy today, then that issue shouldn't be in this section.

Here's my suggestion: My third point is deliberately vague because I don't have the technical knowledge be confident in identifying exactly which other effects should be moved. JamesMLane t c 18:00, 23 August 2010 (UTC)
 * 1) Take the existing material about relativistic effects and make it a separate section, parallel to the "Error sources" section (i.e., a heading marked by == instead of ===).
 * 2) In the "Error sources" section, include a short subsection on relativity to note the uncompensated-for relativistic effects and the small errors that result (e.g. the 2.5 millimeter error mentioned in the Aerospace Corporation paper).
 * 3) Similarly remove from the "Error sources" section, and move to a separate section, any other issues now discussed therein that are compensated for and so don't currently give rise to errors.


 * Well, there are also sources of error that are partially corrected by modelling. For example, estimated parameters for the Klobuchar model of ionospheric delay are broadcast by the GPS signal, but it's not a perfect model - so it reduces error but doesn't eliminate it all together. If a SBAS satellite is in view, they can broadcast grid ionosphere vertical errors - more precise corrections in 5-degree grid - which can allow greater reduction in ionospheric errors, but still not their elimination all together. So I'm not sure the compensated for/not compensated for line is as clear as I may have made it sound! Mike1024 (t/c) 09:36, 24 August 2010 (UTC)


 * I see your point. How about this: Any error that's not completely compensated for should be included in the section on errors, with, of course, an explanation of the extent to which it is compensated for.  This would include a subsection describing the relativistic effects that do produce errors.  I wouldn't lump all SR/GR effects together, though.  There's no reason this section should address time dilation arising from the satellites' motion when that's already factored into the system.  There should be a separate section on relativistic effects because it's interesting that GPS involves a practical application of relativity.  Anything else that's worth treating in its own right, without regard to its potential for creating errors, could also be addressed in its own section.  (It may be that there's no such material now in the errors section.)


 * My basic idea is that some readers will be interested in knowing the limits on the accuracy of GPS while other readers will be interested in the application of relativity to make the system work well. We can cater to both sets of readers by separating out a lot of the relativity material that's now in the errors section. JamesMLane t c 20:33, 24 August 2010 (UTC)

GPS signal vulnerability to 2012-2023 solar storm
According to this report, the GPS signals are especially vulnerable to the magnetic interference of the upcoming solar storm. As this may result in malfunctioning, ... it should be mentioned. 91.182.101.65 (talk) 16:55, 2 September 2010 (UTC)

A new section
Yesterday a decision was made in the first case concerning GPS surveillance before the ECHR. Maybe there should be a section on legal aspects of GPS, use by police forces etc? --Harac (talk) 12:58, 4 September 2010 (UTC)


 * The people who designed, built and operate the system do not care in the slightest how people are using it, so why should we?  Best practice would be to first discern the significance of the case, and if it passes that notability test, then it should be added to the ECHR article, not here.  A back-link to GPS would be most suitable as well.  mdf (talk) 17:07, 4 September 2010 (UTC)

Relativity and GPS without the discussion of relativism
In the section, Special and general relativiy, the statement, "Without correction, errors in position determination of roughly 10 km/day would accumulate", is made. This statement seems to be based on the fact that c*(38 microseconds) = (299792.5 km/sec)*(.000038 sec) is roughly 10 kilometers. But in solving the navigation equations the receiver's clock error must be determined and corrected. This clock error correction causes the receiver's clock to be very accurate relative to the clocks of the sattelites. The computed receiver position is also approximately correct not off by roughly 10 kilometers as it would be without the correction of the receiver' clock. This needs to be clarified. RHB100 (talk) 21:07, 18 August 2010 (UTC)


 * Yes, the statement needs to be removed. The receivers compute (t,x,y,z) based on transmissions from the satellites.  In an 'uncorrected' system, where the clocks in the satellites ran at 10.24Mhz, the 't' component that a receiver near the surface of the Earth computes would indeed drift 38us/day -- but the (x,y,z) would be virtually unchanged because the light time from the satellite to receiver is only a fraction of a second, not an entire day.


 * As far as I can recall the only significant relativistic effect that is directly corrected for in GPS is due to the slightly eccentric orbits of the satellites. By "directly corrected", I mean that the satellites themselves broadcast information to carry out the correction, and a receiver that opts to ignore these terms will endure ~15m errors in the (x,y,z).  mdf (talk) 17:43, 4 September 2010 (UTC)

OK, I am gload to get your agreement on this point. RHB100 (talk) 02:14, 7 October 2010 (UTC)

Multidimensional Newton-Raphson for GPS - Can't make heads or tails of it
Do you think we could get an animated graphical demonstration of this process? --  Denelson83  02:05, 23 October 2010 (UTC)
 * Let us attempt to isolate where some of the confusion lies. This will provide a first step toward providing any needed clarification.  Do you find it clear down through equation (1)?  If not, can you state clearly what in your opinion is not clear: RHB100 (talk) 21:52, 26 October 2010 (UTC)
 * Yes, the part ending with equation (1) is clear. --  Denelson83  05:37, 27 October 2010 (UTC)

I would rather see proper sourcing for this subsection. As it is now, it does not need clarification, but sources. Otherwise I'm sure we can safely remove the subsection as classic case of wp:original research. I have tagged the section. DVdm (talk) 22:00, 26 October 2010 (UTC)


 * References have been added to show the published equations on which this section is based. In view of the statement that it does not need clarification, the templates are no longer needed.  RHB100 (talk) 00:43, 27 October 2010 (UTC)


 * That's a start, but I don't think this is sufficient. When I said that "it does not need clarification, but sources," that means that the entire derivation (i.e. every single equation) needs to be sourced. We don't just need a source with "published equations on which this section is based", together with a source that explains Newton-Raphson. Using both sources together to produce this exposé, is still a classic case of wp:SYNTH, and thus of wp:OR, as clearly these equations do not qualify as trivial calculations (see wp:CALC). So, unless we have a single source that solidly backs the subsection, I think it will have to go. Now, even if/when it can be properly sourced, i.m.o. this entire subsection does not belong in this article. It should be largely sufficient to write a single sentence saying that N-R can be used to calculate some equations and then point to the (single) source that does so, or that says that it can be done. DVdm (talk) 11:35, 27 October 2010 (UTC)

I suggest you thoroughly study the references provided before making any judgement as to whether they are adequate or not. I see no evidence from your comments above that you have read the references provided. Also I suggest that you take into consideration that your lack of interest in the useful mathematics provided does not imply that all other people have this lack of interest in useful mathematics. Leaving out material that interests a small minority does grave damage. Leaving in material that may not interest a large majority does essentially no damage. RHB100 (talk) 18:49, 27 October 2010 (UTC)

DVdm, you have completely disrupted a discussion I was having with Denelson83. Denelson83 had responded to my attempt to take an organized approach to see how the section could be improved. Then you jump in and say it does not need clarification and now you are saying it does need clarification. RHB100 (talk) 19:03, 27 October 2010 (UTC)


 * Here is the question: Are the equations from the article literally present in the sources? If they are not, it is very simple: they must go. Whether I am interested in useful mathematics or not, and whether I have disrupted a discussion you were having with Denelson83, is irrelevant. Either the listed equations are in a source, or they are not. I they are not, they should go per elementary policy as spelled out in wp:SYNTH, wp:OR and WP:V. So, please answer the question: are the equations from the article literally present in the sources? What do other contributors think about this? DVdm (talk) 20:00, 27 October 2010 (UTC)

The fact that you ask the question in the paragraph above indicates that you have not read the source material. This indicates that you are not qualified to make any judgement on the section. Whether you like it or not, you have got to educate yourself so as to overcome your ignorance before you are qualified to do productive work. Your comment that it is very simple is a result of your ignorance. RHB100 (talk) 00:28, 28 October 2010 (UTC)


 * Indeed, I have no access to the journal, but that is not relevant. That is why I ask you, who does have access: are the equations from the article literally present in the sources? This is a very simple question that you can answer, so please do. DVdm (talk) 06:46, 28 October 2010 (UTC)


 * This section discusses the NR solution method, which is obviously a suitable method for this application. However another unsourced method "trilateration and one dimensional numerical root finding" is mentioned, of which I seriously doubt if it is ever used in a real GPS device, as it is not extensible to more than four satellites. Perhaps that should go first. &minus;Woodstone (talk) 14:44, 28 October 2010 (UTC)


 * Hi Wood, sure, if it cannot be sourced, it should be removed, but the fact that it is not or hardly used in a real GPS device, whereas NR is indeed extensively used, is not really relevant to the question whether the NR-exposé should remain here. The policies are clear on this: if the pack of equations does not appear in a reliable source, it is wp:OR and has no place here - Wikipedia is not a textbook (wp:NOT). Feel free to tag or even remove the trilateration bit already. DVdm (talk) 17:56, 28 October 2010 (UTC)

I added a reference to Bancroft's algorithm a few months ago. Prior to that time we did not have any readily viewable souce to Bancroft's algorithm. In adding this reference I stated that "Bancroft's method is perhaps the most important method of solving the navigation equations since it involves an algebraic as opposed to numerical method". No repetition of Bancroft method was provided in the GPS Wikipedia article, since the reference provided was an excelleb source, clearly explained the Bancroft method, and I did not think I could provide a better explanation. RHB100 (talk) 21:56, 28 October 2010 (UTC)

Now I couldn't care less if the numerical methods are removed now that we have access to an excelent external document with the Bancroft method. However, these two numerical methods have at least one and possibly two advantages. One is they are somewhat easier to understand. And two they may have applications to surveying although I am not certain about this since I have limited knowledge of surveying applications of GPS. RHB100 (talk) 21:56, 28 October 2010 (UTC)

I disagree with the view of DVdm stated above that anything that is not a literal copy is original research. I think this view is based on a lack of mathematical maturity. RHB100 (talk) 21:56, 28 October 2010 (UTC)


 * So it is clear that the equations in the section do not appear in the cited sources ("These equations are based on those found in..."), and are therefore a clear cut violation of wp:original research and wp:synth. I will therefore remove them per elementary policy. RHB100, I have left a note about your personal comments on your talk page. DVdm (talk) 19:17, 29 October 2010 (UTC)

Accusations that Multidimensional Newton-Raphson for GPS section violates Wikipedia policy are false
The accusations by DVdm that the Multidimensional Newton-Raphson for GPS section violates Wikipedia policy of no original research are false. I have provided two references either one of which alone provides more than an adequate source for the contents of the section. Yet DVdm has by his own admission not even read the reference on "The Mathematics of GPS" by Langley and in spite of his admitted ignorance has removed the section on Multidimensional Newton-Raphson for GPS. DVdm has made the idiotic statement that every equation needs to be sourced. There is no Wikipedia policy that requires every single straightforward, routine mathematical statement needs to be sourced. We don't need to source the mathematical statement, 2+3=5, and we don't need to source the straightforward and routine evaluation of a partial derivative. And partial differentiation is a straightforward, routine mathematical statement, which differs from the statement, 2+3=5, in the operation used.

The statements in the section, Multidimensional Newton-Raphson for GPS, are based on the reference, Numerical Recipes. The meaning of the word, recipes, is important. As applied to its usual use, cooking, it means that someone has performed the original research research to come up with a method of cooking a particular dish. The cook who uses the recipe follows the instructions in the recipe but does no original research just rote following of instructions. With regard to mathematical algorithms, the user of the recipes in a book such as Numerical Recipes does no original research but instead relies on the original research provided by the authors of Numerical Recipes. The equations provided in the section, Multidimensional Newton-Raphson for GPS, are not original research but instead rote following of the recipe found in Numerical Recipes.

Another useful reference is the section, Navigation Solution, in GPS World by Torralbas, Roberto and Alvarez Jose Manuel. — Preceding unsigned comment added by RHB100 (talk • contribs).


 * Please have a very careful read of wp:NOR and specially wp:SYNTH and wp:CALC. This is a classic example. The pack of equations definitely does not fall under "This policy allows routine mathematical calculations, such as adding numbers, converting units, or calculating a person's age...". Indeed we don't need to source the mathematical statement, 2+3=5, but we definitely do need to source the evaluation of a partial derivative, as they may be straightforward and routine to you and me, but not to the average Wikipedia reader. That is exactly why the statement at wp:CALC is formulated the way it is. If you want to question or change some of our basic policies, this is not the place for it, so please take this elsewhere. Thank you. DVdm (talk) 09:14, 1 November 2010 (UTC)
 * I also have left another personal comments warning on your talk page.
 * DVdm (talk) 09:14, 1 November 2010 (UTC)

You, DVdm, still do not display any indication that you have read the reference, "The Mathematics of GPS" bu Langley. Without bothering to check the reference provided, you have merely assumed that the Wikipedia section on Multidemensional Newton-Raphson for GPS, does not contain proper sourcing. This is highly irresponsible on your part. '''You should take the necessary steps to obtain the reference provided and thoroughly study it to see if proper sourcing is provided. At present you are completely unqualified to say if it is properly sourced or not.''' RHB100 (talk) 21:53, 1 November 2010 (UTC)


 * The equations in the removed section do not appear in the cited sources ("These equations are based on those found in..."), and are therefore a violation of wp:ORIGINAL RESEARCH, wp:SYNTH and wp:CALC. If you want to question or change Wikipedia policies, you can take this to Wikipedia talk:Original research. As it is now, you are disrupting this article talk page. Please stop doing that.
 * I also have left another personal comments request on your talk page.
 * DVdm (talk) 22:29, 1 November 2010 (UTC)

DVdm, I don't see anything in your comments that convinces me that you have read with comprehension all of the cited sources. You recently said you did not have access to the journal containing one of the cited sources. How did you acquire it so quickly and what can you say about it to convince me that you have actually read and comprehend it. RHB100 (talk) 00:41, 2 November 2010 (UTC)


 * None of this matters. If the equations are in the source, they might be allowed in the article, otherwise they are original research. Since they are not in the source (("These equations are based on those found in..."), they are original research and do not belong in the article. Please do read the policies, and if you don't like them, take this elsewhere. You are disrupting this talk page per wp:TPG. Please stop. DVdm (talk) 10:21, 2 November 2010 (UTC)

DVdm, don't you dare accuse me of disrupting this page. You are an outright worthless liar in accusing me of disrupting this page. All of the other statements you have made in the paragraph above are lies and idiotic nonesense. The statement, "they are original research" is an outright lie and indicates a failure to understand the meanng of original research. You have shown yourself to be a dishonest person and I don't want to hear from you again. This dispute between you and me is going to have to be settled by somebody with better sense than you. RHB100 (talk) 19:23, 2 November 2010 (UTC)

My God, what have I triggered here? Please, cool down, you guys. --  Denelson83  21:51, 2 November 2010 (UTC)


 * You just asked for a clarification for a piece of an article, but it turned out that the section was original research. No problem, I think your inquiry was warranted, but properly sourced content should not sollicit clarification. DVdm (talk)

RHB100, I have opened an entry at Wikiquette_alerts. DVdm (talk) 22:02, 2 November 2010 (UTC)

DVdm, you have made false accusations against me as documented above. You have also accused me of entering material that was not sourced properly when in fact by your own admission you do not even have access to the journal containg the source provided. This is lack of etiquette in the extreme on your part. RHB100 (talk) 02:01, 3 November 2010 (UTC)


 * As user conduct is off topic here, I have replied at Wikiquette_alerts. DVdm (talk) 08:19, 3 November 2010 (UTC)

By the way, RHB100, would this by any chance be the Langley source you had in mind with this edit? I had seen and read this, but looking at the page numbers (pp 45-50) I had assumed that it was a different source than the one you cited. Is this the source? DVdm (talk) 14:51, 3 November 2010 (UTC)

timekeeping as civilian application
May I suggest adding a bullet point under civilian applications for timekeeping? The Precision Time Protocol page (long quotation near beginning) places PTP in the context of NTP (Network Time Protocol) and "GPS", which might be better termed "GPS-based protocols", whatever those might be. IOLJeff (talk) 21:29, 29 November 2010 (UTC)

Assisted GPS in the timeline
The timeline lists November 2004 as the date when Assisted GPS was tested. This is not completely correct. The reference shows assisted GPS tested in 2004 for WCDMA 3G (GSM) networks, but in fact aGPS has been around since at least 2002 on CDMA IS-95 networks such as Verizon Wireless in the USA. Ryan (talk) 22:11, 29 November 2010 (UTC)