Talk:Global Positioning System/Archive 4

Common vs. Public Good
From the third paragraph: "President Ronald Reagan issued a directive making the system available for free for civilian use as a common good." Shouldn't that be public good? Based on the common good (economics) page, GPS would appear to be categorized as non-rivalrous (one person's consumption of GPS does not pleclude another's consumption), which would mean it's a public good. Further, I would consider GPS perfectly analogous to free-to-air television, which is given as an example of a public good. Jtradke (talk) 13:05, 21 May 2008 (UTC)

Simplified method of operation
There is a problem with saying, "The receiver uses the arrival time to compute the distance to the satellites, and then calculates the position of the receiver using geometry and trigonometry." The receiver has to first know the precise time at its own location. It does not know this by default-- getting this precise time requires first calculating the receiver's position. It does this by comparing the times and locations of the satellites from which it is receiving a signal. As an example, if a receiver receives a signal from a satellite that reads "Time x", it can compare this to its internal time and come up with a figure for the distance using the speed of the signal. However, the receiver has no way of knowing when the signal left the satellite by its own internal time, so the distance figure meaningless. If the receiver's internal time is behind by the exact amount of time it takes for the signal to reach it, the calculated distance would be zero! My basic point is that the statement I quoted at the beginning of this post puts the cart before the horse. An accurate statement would be, "The receiver uses the locations of the satellites and the difference in their distances to calculate its own position.  Using that position, the receiver can then use the signals of the satellites to synchronize its internal clock with the precise atomic clocks in the satellites.  The receiver can then use the arrival time of signals to compute the distance to the satellites, and calculates its position using geometry and trigonometry.  However, the imprecision of the receiver's internal clock makes these calculations less and less accurate as it falls further and further out of sync with the satellite atomic clocks.  It is therefore necessary to periodically resynchronize." This is still a simplified view because it does not address the effects of variance in media through which the signal travels, relativity, or positional drifting of the satellites. It also does not address the specific mathematics involved in the calculations. However, failing to mention the importance of first synchronizing with the satellites oversimplifies the operation in that anyone with a basic understanding of high school algebra and physical science would be left with the question, "How does the receiver know how long it took for the signal to reach it if it only knows the time the signal left and not the time the signal was received?" I'd appreciate feedback. RobhdRobhd, November 30, 2007 23:30 (UTC)

I have a problem with the statement below that *If you have an accurate local clock, you need only 3 satellites." I think that you need 4 satellites regardless of the accuracy of the internal clock.  Three spheres will intersect in 2 points not one most of the time.  Therefore a fourth satellite is needed to determine which of the 2 intersections of 3 spheres provides a valid estimate of GPS receiver position.  Do you care to provide an explanation of the basis of this statement?RHB100 (talk) 21:45, 1 July 2008 (UTC)
 * If you assume that the reciever trying to calculate its position is on earths surface (or close to it) you can most of the time reject one of the two points. If both points happens to be on earth, one will have an outrageous speed. Mossig (talk) 21:55, 1 July 2008 (UTC)

Thank you for your responses. I understand your basic point that the earth provides the information for resolving the 2 intersection ambiguity.

Improvements desired for "Using the C/A Code" section include adding figures of 2 and 3 spheres intersecting. In this section or possibly in the trilateration article the method of formulating the equations of the spheres in the planar coordinate system required for trilateration should be explained.RHB100 (talk) 19:33, 3 July 2008 (UTC)


 * Here's a way to think about it. Since the satellites are all fairly close to the same distance away, the intersection circle of two satellites will look like a very large hoop (roughly 20000 km in diameter) with the bottom resting on the earth and the far end *way* out in space.  Now if you intersect this with another sphere, if the 3rd satellite is any angular distance away from the others at all, there will be one solution on the Earth's surface, and one way out in outer space.  The only possible exception is if two of the satellites are in the same direction.  This is theoretically possible but only for an instant as the two satellites cross in their orbit.  So at most you can get one bad fix, assuming you are near the Earth's surface. (and this is enforced by most GPS units, which cut out at high altitude for security reasons).  Also, using the almanac, the GPS can determine that using this satellite combination will result in an extremely bad GDOP anyway, and not use that combination.  On the other hand, a space based GPS might need to worry about this. LouScheffer (talk) 00:28, 2 July 2008 (UTC)


 * Hi! First, the description points this out.  *If* you have an accurate clock local clock, you need only 3 satellites.  Since almost no-one, other than a standards lab, has such a clock, you need 4 satellites, and solve for x,y,z and t.  Computing differences is certainly one way to do this, but not all receivers do so.  A standard technique is from "A Direct Solution to GPS-Type navigational equations" by Krause, IEEE transactions on Aerospace and electronic systems, March, 1987, which explicitly uses ranges and clock biases, and not differences.  As another example, see "ASHTECH GPS technology", by Javad Ashjaee, IEEE PLANS conference, 1990, where he says "Conventionally, 4 pseudoranges are used to compute 3 dimensional position and time".


 * I think this view is reasonable for the overview. The average reader understands that if a car leaves at 3:00, and arrives at 4:00, and was traveling 60 MPH, it must have gone 60 miles.  Only a sophisticated reader will realize that the clocks are in different places, and are not in general sufficiently accurate to make this measurement when the speed involved is the speed of light.  This problem is pointed out in the introduction, and a fuller description is below.


 * Other folks views on the correct explanation for the overview would be good, too. LouScheffer 23:50, 30 November 2007 (UTC)


 * I would like to go into the text "clock makes these calculations less and less accurate as it falls further and further out of sync ". The amount of time that the clock is usable for calculating the position is for all normal circumstances less than a second. Why? Because the error introduced by a quarz clock will give an error greater than you can travel with most methods of transportation. A timedrift of a clock of 10 secs a year, will introduce a timing error of about a 100 meters for each second. With an normal satellite geometry this will increase with the squareroot of 2. (Less if the satellites are close together, more if they are spread appart). This works out to 140 meters a second, this is 500 km/hour or over 300 miles/hour. With an error increasing with this speed the GPS receiver is not usable. Most quartz clocks have a larger timedrift than 10 secs, typical is 30 to a 100 secs a year, making the error even larger. So although the clock is synced to the satellites the clock can not be used in positional calculations not even for a very short time. So for each positional calculation, the x,y,z and t are recalculated only on the basis of the time difference of arrival of the signals of the satellites.Crazy Software Productions 03:08, 1 December 2007 (UTC)


 * That is fine for the technical, geeky portion of the article. But the general concept of how a GPS works should be easily digested—and that explanation is not, no matter how well written.  The "Simplified method of operation" ought to start by assuming there is an accurate, precise GPS clock to compute the delta times.  After expanding that to its climax, add "in practice, few GPS units have sufficiently precise clocks, so the GPS solves for a fourth variable: the time of day, and therefore needs an additional satellite."  —EncMstr 03:31, 1 December 2007 (UTC)


 * But the clock never needs to be stable over periods as long as a second. Receivers measure 4 or more satellites simultaneously (or at least simultaneously within 1 millisecond, the code length).  Then the four distances are reported, and the CPU computes the clock offset *at the time when the simultaneous measurements were made*.  Thus the errors are much less than your back of the envelope calculation by a factor of 1000 or so, making them less than many other error sources.  See, for example, the ZARlink GPS chip data sheet for an example of how this works.  LouScheffer 05:52, 1 December 2007 (UTC)


 * I have explained, to non-technical people, the basics of how GPS receivers calculate their distance. I read the discussion in this section and made the changes that you are discussing.  I think that it is an improvement, so consider it as such before you go and improve it more. &mdash; Val42 18:40, 1 December 2007 (UTC)


 * My reaction was to that: "the internal clock can be used for positional calculations". (After it is synchronised to the satellites.) The clock can not be used for that. The 'timer' can be used for measuring, but then 4 satellites are needed at least. The timer needs only to be accurate for duration it receives the signals from at least 4 satellites. Further I do not think this should be part of the simplyfied explanation. But the simplyfied explanations should not explain wrongly (assuming an accurate clock), and then describing that 'only' a fourth satellite is needed to correct this. It's not a correction and it's not trilateration which is used. From the start four satellites are needed. Calculation is not done by trilateration, but by pseudorange calculation or hyperboliod calculations (or some other methods). Our position is not determined by intersecting 3 spheres but by intersecting 4 spheres or intersecting 3 hyperboloids. (Or as in most (?) implementations our position is determined by intersecting four planes.)


 * The simplyfied explanation does not need to contain all this, but should be correct. Further I should think that at the moment there are to many details in the simplyfied operation. Why because the simplyfied operation should explain the concept and not the implemented version, so no specific timings or distances of the implemented version. The principle should be explained in such a way that it is correct for GPS but also for the Russian, and European system based on the same principle, it should even be correct for 'theoretical' system based on the same principle. A simplified explanation is not helped by first presenting a not correct model which is afterwards corrected. That the clock (not the timer) can not, and is not, used is not a detail, but centre to the complete principle.22:46, 1 December 2007 (UTC) —Preceding unsigned comment added by Crazy Software Productions (talk • contribs)
 * I don't know who made the edits since mine, but they look okay. &mdash; Val42 05:48, 4 December 2007 (UTC)

"Chip" in Navigation Signals section -- shouldn't this be "cycle"?
It seems to me that a global search-and-replace went awry in this article, where the letters "chip" were accidentally substituted for the letters "cycle". Note, for example, the following sentences from the "Navigation signals" section:

"C/A code is a 1,023 chip pseudo-random (PRN) code at 1.023 million chips/sec so that it repeats every millisecond. Each satellite has its own C/A code so that it can be uniquely identified and received separately from the other satellites transmitting on the same frequency. The P-code is a 10.23 megachip/sec PRN code that repeats only every week."

Doesn't the author mean "1,023 cycles pseudo-ramdom (PRN) code at 1.023 million cycles/sec," and the "P-code is a 10.23 megacycle/sec PRN code,", etc.?

--Gratefulman (talk) 22:26, 27 December 2007 (UTC)


 * No, chips is right in this context. See the Glossary of GPS terms, for example. LouScheffer (talk) 23:27, 27 December 2007 (UTC)

You are quite correct and I agree with you in what you are saying about the sentence being incorrect. I suggest it would be more correct to say "The C/A code is a 1,023 bit pseudo-random-number (PRN) code at 1.023 million bits/sec so that it repeats every millisecond"

Kind Regards, Dom Evangelsita PEng, Senior Design Engineer, EBOR Computing. —Preceding unsigned comment added by Dom.evangelista (talk • contribs) 00:01, 28 March 2008 (UTC)

Control segment
The section control segmant only mentions 5 control stations i have found infomation that there were an additional 6 control stations added during 2005 these are not mentioned in the artical.

http://www.kowoma.de/en/gps/control_segment.htm —Preceding unsigned comment added by 172.209.6.168 (talk) 19:43, 20 February 2008 (UTC)


 * OK, I added them but put the station locations in a footnote. It seemed to clutter the article to put them in the main text. LouScheffer (talk) 21:03, 20 February 2008 (UTC)

Portal:Satellite navigation systems at MFD
Hi, I have nominated Portal:Satellite navigation systems for deletion. Discussion can be found at Wikipedia:Miscellany for deletion/Portal:Satellite navigation systems. GW_SimulationsUser Page 22:47, 23 February 2008 (UTC)

NAVSTAR not an acronym?
Here's a quote from the article:

"Contrary to popular belief, NAVSTAR is not an acronym."

However, Natural Resources Canada (http://www.ccrs.nrcan.gc.ca/glossary/index_e.php?id=1474) states that NAVSTAR GPS stands for NAVigation Signal Timing and Ranging Global Position System.

Who is correct? —Preceding unsigned comment added by Scattered and collected (talk • contribs) 22:48, 7 March 2008 (UTC)

Caesium or cesium ?
The following is an exchange of views between two editors posted on their respective talk pages and now placed here for a wider debate and consensus:-


 * Hi! I see you have made many spelling changes citing WP:SULF as the reason for the change. Please note WP:SULF is a guideline which supports those spelling changes in articles related to chemistry. Mere mention of cesium in an article is not a sufficient reason to apply this guideline! In other contexts, particularly where "cesium" is the well-established spelling, that spelling should be preferred. (sdsds - talk) 15:05, 17 March 2008 (UTC)


 * I totally agree that where, for example, the name of a Pop group is Cesium-137 then that remains as spelled. Similarly where publications are quoted in which the author spells the element Cesium then that too stands. However, when referring to Caesium clocks, it is indeed the element being referenced - what other sort of Caesium is there in this context? There is not a different Caesium for physics from that in Chemistry - just two properties of the same material - hence the appropriate change in spelling. Will you revert or shall I ? Velela (talk) 15:11, 17 March 2008 (UTC).
 * Hi again! I am perfectly happy discussing this here rather than on your talk page, if that is your preference. But maybe there's a better place to build a community-wide concensus? It might seem like that would be Wikipedia talk:WikiProject Chemicals, but my concern would be the inherently biased sample of editors who would become aware of the discussion. The specific article in question, Global Positioning System, is not even claimed to be within the scope of WikiProject Chemicals! (And as you'll note, that's pretty much my entire point about why the policy you quote is not the spelling policy that is relevant to the GPS article.) So perhaps the best place is Talk:Global Positioning System? Shall we continue the discussion there? (sdsds - talk) 01:31, 18 March 2008 (UTC)
 * Since GPS is a wholly US-owned system, wouldn't the US spelling be most appropriate here? Any links will eventually lead to the IUPAC-approved spelling. Franamax (talk) 19:56, 18 March 2008 (UTC)
 * Exactly so. The guiding policy supporting this view is expressed at WP:ENGVAR. (sdsds - talk) 07:40, 19 March 2008 (UTC)
 * In my opinion, the guideline at WP:ENGVAR would be more appropriate for this article than the one at WP:SULF; though I think the guideline specific to element names should be applied a bit more generally (say to basic science articles) than to just articles that are flagged as being maintained by the chemistry wikiproject. Element16 (talk) 15:25, 20 March 2008 (UTC)


 * I disagree for the following reasons:
 * Where an invention is made is not material in the language used to describe it in Wikipedia, but I am nevertheless content that this article uses American English.
 * The phrase cesium clock clearly refers to a clock in which the element Caesium is the key component.
 * The policy references under WP:SULF although promulgated by  WikiProject Chemicals is a policy intended for use wherever and whenever the element is referred to even where that reference is outside of a Chemical article. For reference examples see the multiple edits by User:Element16 changing Sulphur into Sulfur irrespective of the main tone and content of the article but making the spelling consistent wherever the element is mentioned.
 * Using cesium as the link forces routing via a re-direct which is contrary to Wikipedia policy.
 * Velela (talk) 00:56, 22 March 2008 (UTC)
 * Velela, you're absolutely right about redirects, I changed that. Now the article uses US English and links properly. Can you point to the consensus discussion where we all agreed on a "policy intended for use wherever and whenever the element is referred to"? I'd be interested to see the discussion (honestly, I'm not trolling, I'd like to see it:). Franamax (talk) 01:12, 22 March 2008 (UTC)
 * Cesium is indeed a re-direct to Caesium and so it doesn't actually link according to policy - and as for the discussion this, for the moment, is it; but since this issue has wider implications it might need to be conducted in a rather wider forum to establish a consensus policy once editors have had their say here. Velela (talk) 17:32, 22 March 2008 (UTC)
 * I think the spelling should be Caesium - that is the standard spelling according to IUPAC and the variant "Cesium" should not take precedence over it, provided that it is the actual substance being referred to and not something else (e.g. the rock group mentioned above.)--AssegaiAli (talk) 19:29, 22 March 2008 (UTC)

Contrary to what is stated above, I have not been making spelling changes irrespective of the main tone and content of the article. I have never said and I do not believe that WikProject Chemistry guidelines are "intended for use wherever and whenever the element is referred to", nor do I believe that any chemists from that project have made that argument. I've made element-spelling changes in chemistry articles and in articles that are in chemistry-related scientific fields. I think WP:ENGVAR takes precedence in articles whose topics are not in any way chemistry related. Also, I have tried to keep all articles that are geographically related in the pertinent variation of English.Element16 (talk) 22:46, 22 March 2008 (UTC)


 * First, there's nothing wrong with linking to a redirect. That's one of the main reasons for the existence of redirects in the first place. Second, the Chemicals style guide is just a collection of guidelines for articles about chemicals. I don't think we should worry about it in this article. Common usage and the English variant convention are more general and should prevail here in my opinion. IUPAC doesn't rule the Universe. (It doesn't even rule chemists, despite what some people in Wikipedia think.) --Itub (talk) 11:02, 24 March 2008 (UTC)

Thanks for your request Velela. I actually (but only vaguely) agree with using cesium, mainly as it's a US-based invention, and seemingly written mostly by US-based authors. I'm a chemist, and I don't use US English, but this exception makes sense. There are (somewhere I believe, I'm not up with all of it) some guidelines on when to ignore the rules. But in the big picture, is it really important? There's another article on lame arguments- not to say that this argument is lame, but probably not worth all the considerable effort you lot have put into it. My two cents. Freestyle-69 (talk) 06:53, 27 March 2008 (UTC)

IMO, this debate is a little too silly for this kind of subject. I'm declaring it closed with a decision to leave the matter as it was before the debate began. The spelling in this article is to remain "cesium". --  Denelson83  13:35, 27 March 2008 (UTC)

connectible gps receivers
include a list with gps receivers, connectable to handehelds, pc's, ... See this website thanks.

81.244.196.114 (talk) 17:00, 1 April 2008 (UTC)

Which John Walsh?
In the first section there is a line: ["...NAVSTAR is not an acronym, but simply a name given by John Walsh, a key decision maker when it came to the budget for the GPS program)."]

Initially I thought it might be the John Walsh from Am.'s Most Wanted, but then thought why would it be, then tried to find another instance of his name to find the link to see which John Walsh it was and couldn't. The statement is so matter of fact that it makes you feel like you should already know who he is, heck, even Ronald Regan got a "President" title AND a hyperlink, as if you might NOT know which Ronald Regan it was (the actor or the President). Maybe explain who he is or make a link to him. I even followed the footnote and got nothing. —Preceding unsigned comment added by BillyNair (talk • contribs) 19:29, 26 June 2008 (UTC)

Movement in France
Due to plate tectonics my GPS figs are going to change where I am in Paris. So what is the annual rate of change here (example - 1 metre per 10 years). Can my GPS longitude and lat remain valid for one human life time? Gilgamesh007 (talk) 11:58, 30 June 2008 (UTC)

Using the C/A code - which explanation?
I think something that we need in order to make this section more readable for a general audience are figures showing two and three spheres intersecting similar to those found on pages 7 ans 8 of GPSGuideforBeginners_Manual.PDF available at http://www8.garmin.com/aboutGPS/manual.html. One picture is sometimes better than 1000 words. These figures would certainly be a very valuable contribution.RHB100 (talk) 20:25, 10 July 2008 (UTC)

Also it should be mentioned that Denelson83 has recently made valuable contributions in improving the notation used for variables in this section. RHB100 (talk) 20:25, 10 July 2008 (UTC)

Two editors (RHB100 talk) and myself, LouScheffer talk) have differing views of how a paragraph in this section should look.

One possible solution is to provide both versions, the LouScheffer version for those who just want an overview and the RHB100 version for those who want more details. We should avoid depriving the more scientifically curious reader of useful and interesting information just for the sake of brevity. Although the majority may want just an overview, this is not a valid reason for depriving the more scientifically curious reader from getting useful and interesting information.RHB100 (talk) 22:00, 7 July 2008 (UTC)

RHB100 prefers:

When pseudoranges are determined for four satellites, an estimate of the GPS receiver position can be made. Trilateration is used to determine the two points of intersection of three sphere surfaces corresponding to three satellites. The surface of the sphere corresponding to the fourth satellite or the surface of the earth is used to determine which of the two intersections provides a valid estimate of GPS receiver position. The valid estimate is the point closest to the surface of the sphere corresponding to the fourth satellite or the surface of the earth. It is likely the surfaces of the three spheres intersect since the circle of intersection of the first two spheres is normally quite large and thus the third sphere surface is likely to intersect this large circle. It is very unlikely that the surface of the sphere corresponding to the fourth satellite will intersect either of the two points of intersection of the first three since any clock error could cause it to miss intersecting a point. However the distance from the valid estimate of GPS receiver position to the surface of the sphere corresponding to the fourth satellite can be used to compute a clock correction. Let R4 denote the distance from the valid estimate of GPS receiver position to the fourth satellite and let P4 denote the pseudorange of the fourth satellite. Let DA=R4-P4. Then the quotient, DEL_T= DA/(speed of light), provides an estimate of UTC - (time indicated by the receiver's on-board clock) and the GPS receiver clock can be moved forward if DEL_T is positive or backwards if DEL_T is negative. The above procedure has not taken into account the change in pseudoranges resulting from the correction to the GPS receiver clock. When the magnitude of DEL_T is small this may be adequate. However when DEL_T is large an iterative procedure should be used. The pseudoranges should be recomputed using the updated GPS receiver clock and a new valid estimate of GPS receiver position should be computed as described above. A new value of DEL_T should then be computed. These iterations should be continued until the magnitude of DEL_T is sufficiently small.


 * Against this explanation. Because, 1 the fourth satellite is not used to determine between the two points of the three intersecting spheres, because there are an endless number of solutions with three spheres, because or the clock drift. So it is needed to get to one (actually two in most situations) point and a distance or time difference (clock error). 2. Because at the start of the problem the distances to the satellites is unknown. Only when the positional solution is known the distances are known. Trilateration can not be used until the distances are known. Further: If the above would be true, GPS receivers would be capable of continuing 3D calculations after they have determined a point but loose the fourth satellite, this does not happen in real world GPS receivers, when loosing the fourth satellite the receiver continues with 2D calculation and loosing another satellite the receiver does not continue calculation the position using the satellite signals. Crazy Software Productions (talk) 21:07, 7 July 2008 (UTC)


 * I think this criticism by Crazy Software above is invalid. The statement "there are an endless number of solutions" is incorrect.  There are always either zero, one or two intersections of three spheres as pointed out in the section on trilateration never an endless number of solutions.  —Preceding unsigned comment added by 96.247.80.42 (talk) 01:11, 8 July 2008 (UTC)
 * There are always either zero, one or two intersections of three spheres. If the radius of the spheres is determined this is true. But if the radius of all spheres is not yet correctly determined (each sphere can expand or shrink with exactly the same amount, because of timedrift), there are still and endless number of solutions. See further on my devils advocate writings.Crazy Software Productions (talk) 23:10, 8 July 2008 (UTC)

Where I prefer When pseudoranges are determined for four or more satellites, an estimate of the GPS receiver position can be made. If the receiver's time is correct, all spheres defined by the pseudo-ranges will meet (or nearly so) at a single point. If they do not, the receiver expands or contracts the spheres (all by the same amount) until they are as close as possible to meeting at a point. The change in radius needed, divided by the speed of light, is the clock correction required. The receiver then adjusts its local clock and tries again, iterating until the correction is sufficiently small. Note that this process requires that all satellite signals used in the computation be measured simultaneously - otherwise the clock correction for each one would be different, due to local clock drift. Then each sphere would require a different correction, and there would be no unique solution.


 * With some notes I do prefer this second text. Older receivers did time multiplexing and were not measuring simultaneaously, those receivers where still capable of determining the position. If the switching happened within the time off the TDOA timing, the error introduced by this process would only be small. (1 on a million error on a quartz clock will give an error of 3 meters in 1/100 of a second. TDOA times are always smaller than 1/42 of a second but often as small as 1/100 of a second, so the error is not timing simultaneously but at reception time is still acceptable). Even with errors the number of solutions does not alter, the solution itself will be slightly off, but usable.
 * The expanding of contracting of spheres is actually done with the pseudorange calculation and with a close estimate does require one iteration only. (An estimate of 1 km off will still result in a position less than a meter of in one iteration).
 * The description of expanding / contracting spheres is an excelent illustration. The implemantation in GPS receivers is done a littlebit different. If the spheres are intersecting in exactly one point (with a given contraction /expansion), you can imagine (I hope) that further expansion or contraction will result in a second point where all spheres meet. (Mostly this solution is found when the spheres are exceptionally large).
 * Crazy Software Productions (talk) 21:07, 7 July 2008 (UTC)

What do others think? LouScheffer (talk) 02:31, 7 July 2008 (UTC)


 * Many of the scientifically curious will find the RHB100 description of how spheres intersect interesting. It is mathematical but it is geometric rather than equation oriented.  Also it is interesting to know just where trilateration is used.  The link provided to trilateration provides an ideal compromise between those who want at first to get a quick overview and those who are ready to study the actual equations used.  The link is provided in such a way that if you know how to formulate the equation for a sphere you know what equations must be solved by trilateration.  The description provided by RHB100 provides a good introduction to understanding how the GPS algorithn for estimating position and time actually works.  In summary the RHB100 version doesn't just tell you it works, it tells you how it works.  The RHB100 version doesn't just tell you the spheres intersect, it tells you how they intersect.  It tells you how position and time are calculated.RHB100 (talk) 19:39, 8 July 2008 (UTC)

RHB100 (talk) 19:12, 7 July 2008 (UTC)


 * If a geometric rather than equation oriented version is needed, one should revert to hyperboloids, the time difference of two satellites does together with the known position of the satellites does determine all posible places where the receiver can be, this set of positions form a hyperboloid. Intersection two hyperboloids will give a curve where the receiver is. Intersecting a third hyperboloid with this curve will give one or two points where the receiver is. If the first two hyperboloids intersect in a closed curve, normally there will be two points where the extra hyperboloid does intersect. If the first two hyperboloids intersect in a not closed curve the extra hyperboloid can intersect in one point or in two points.
 * The intersection of the expanding and/or contracting spheres will define a hyperboloid. The spheres with the satellites in the middle an with the same difference of time (TDOA) will result in the hyperboloid which determine all posible points were the receiver can be.
 * The model with spheres of a fixed size I think is wrong. If the spheres are allowed to expand and contract than it is very difficult to visualize the actual intersection, so it's better to visualize the hyperboloids, at least they are fixed.Crazy Software Productions (talk) 21:07, 7 July 2008 (UTC)


 * I do not understand the logic in the statement by Crazy Software Productions above, "If a geometric rather than equation oriented version is needed, one should revert to hyperboloids". As I see it the question of whether we use a geometric or equation oriented version in the Wikipedia has nothing whatsoever to do with the decision inherent in the GPS algorithm to use a TDOA (hyperboloids) rather than a TOA (spheres) methodology for estimating position.RHB100 (talk) 19:39, 8 July 2008 (UTC)
 * Hyperboloids do exactly describe were the receiver is. Even with the reception of signals of only two satellites and no known clocktime, te hyperboloid were the receiver is can still be determined. For the signal of two satellites and the model with spheres (and no known clocktime) the position can not be determined. You will need three satellites and a clock to determine any rough position on a sphere, or the signal of four satellites to get a position on a sphere. So the spheres do only work with three signals and a rough clock (then approcimate) or with four signals.
 * The same goes for the pseudoalgoritm where the calculation is actually done with planes. You need four signals to determine theintersection of the planes and you are than on all four planes. (Those are flat planes).
 * So my point is your position is not on spheres (or planes) but your position is a hyperboloid (2 signals), on the intersection of two hyperboloids (3 signals) or the intersection of 3 hyperboloids (4 signals). Without a clock your position is never on a exact sphere, or the intersection of a exact sphere. With a quartz clock yes you are in the nabourhood of a sphere. (A skin of some thickness, within a volume, not on a specific surface).
 * So with spheres you are within a skin of a specific thickness, with hyperboloids you are on the surface of the hyperboloid (a dimension less, because it's not a volume). (This last assumes that the TDOA of the signal is exact and to be fair this is not totaly true. But even with errors the thickness of the hyperboloid is less than meters, where the skin skin-thickness of the sphere can be much larger (and increasing with about 300 meters each second). But for the scale of the system yes this is still considered to be a sphere by most people. For me the sphere is an approximation and the hyperboloid is exact. But maybe I am nitpicking.Crazy Software Productions (talk) 23:10, 8 July 2008 (UTC)

An algoritm to calculate a position using trilateration. (See also trilateration).
Within hidden comment somebody wrote (in the paragraaf: Using the C/A code):

To summerize:
 * 1. Trilateration is NOT used in an implementation in GPS receivers.
 * 2. The fourth satellite signal is NOT used to determine which intersection to use.
 * 3. Calculation with spheres is not implemented in GPS receiver algoritms.
 * 4. Iteration is not done by correcting the time of the receiver.
 * 5. Four satellites are needed for 3D positioning. Three satellites and a known hight can be used for 2D positioning.
 * 6. Distance too the satellites is not known until the actual position of the GPS receiver is known.
 * 7. If the GPS receiver is on the surface of the earth and all satellites which are received are above the horizon, the intersection of the spheres (of correct size) occure at the point of the receiver and very, very high above the earth, there is no satellite constallation where this is not true. This is very simple to prove in 2D; make a drawing of two points (satellites) above one point (the receiver) and see that the spheres with around the two points can only intersect at the receivers point and very high above the two points.

Proof of the contrary (I am playing devils advocate) :

1/2/3/4 Can not be proofed or disproved until manufacturers disclose their implementations. So here we have to do with the prove that it's a possible solution.
 * 1. Trilateration CAN be used to determine position.
 * 2. In combination with trilateration the fourth satellite signal can be used to determine which intersection to use, the error in the system because of clock drift is far smaller than the distance between the two different intersections.
 * 3. Trilateration (as calculating with spheres) can be done.
 * 4. Iteration can be done by correcting the time.
 * 5. With trilateration four satellites are still needed to counteract the clockdrift which must be counteracted for enough accuracy.
 * 6. Pseudo distances are know and although they contain an error, the error is not large on the total scale and can be made smaller with each iteration.
 * 7. That this is true for 2d situations does not prove this is true for 3 D situations.

What is needed to do the trilateration calculation.

The x,y,z coordinates of four satelites (1,2,3,4) and the pseudoranges to these satellites. (The measured distance using the quartz clock).


 * 1. Satellite one is put in the centre of the used grid, so the other satelites are shifted by the coordinates of one. (coordinates of satelite 1 are subtracted)
 * 2. The system is rotated so that satelite two has an y that is equal to zero, rotation over the x axes.
 * 3. The system is rotated so that satelite two has an z that is equal to zero, rotation over the y axes.
 * (Satelite 2 gets the coordinates x=0, y=distance to satellite 1, z=0)
 * (Satelite 3 and 4 get the mentioned same rotations over the x and y axes).
 * 4. The system is rotated so that satelite three has an z equal to zero, rotation over the z axes.
 * (Satelite 3 keeps the x it had after the rotation, y = the distance to the x axes, z = 0)
 * (Satelite 4 gets the same rotation over the z axes).


 * 5. Repeat the following instructions:
 * 5a. Using trilateration calculate the intersection x,y,z point. (See trilateration for this).
 * 5b. Calculate the distance of the x,y,z point to satelite 4.(For both the plus and minus z keep the closest).
 * 5c. Determine the difference between this calculated distance and the pseudorange to 4.
 * 5d. Half this distance and extend or contract all spheres with this halved distance.
 * Until the error is suficient smal (8 or 10 times a second should do it).
 * Until the error is suficient smal (8 or 10 times a second should do it).
 * Until the error is suficient smal (8 or 10 times a second should do it).


 * 6. Now the x,y,z and the correct distance are determined. The correct distance can be used to correct the time.


 * 7. The solution should be rotated back over the z axes, y axes and x axes (reverse rotations from steps 4/3/2) and then the point should be translated with the original coordinates of satelite 1 (reverse step 1; coordinates of satelite one are added).


 * THIS IS A POSSIBLE SOLUTION, IMPLEMENTATION IS POSSIBLE AND THE SOLUTION IS LOGIC AND IT'S UNDERSTANDABLE FOR A LOT OF PEOPLE.

The somebody who wrote the summerization and the Proof of the contrary are both the same person Crazy Software Productions (talk) 22:19, 8 July 2008 (UTC).

Although trilateration can be used to do the determining of the position, it's unlikely that it actually is. This is because the pseudoalgoritm performs better on most counts. Mainly because it's does produce a more accurate result with less calculations. The trilateration algoritm needs more iteration steps (probably around 8 to 10 each second), and makes use of sinus and cosines calculations, whereas the pseudoalgoritm does only needs one iteration each second and no sinus and cosines calculations. Both will deliver a position with any mathematical precision which is required, but never the exact mathematical solution, the pseudorange calculation will do this faster. For a PC with a cpu which consumes enough power to fry an egg on this is no issue, but for older battery driven processors this was (and is ?) an issue.

Crazy Software Productions (talk) 22:19, 8 July 2008 (UTC)

Technical versus encyclopedic. Split request discussion
The C/A part of the article is way too in-depth, most of our audience is from a non-technical background. i consider myself reasonably technically minded and I am lost! May I suggest that an article named "Introduction to the Global Positioning System" would be a much better answer to the semantics presently argued over by two editors to this article, that way non-technical as well as technically oriented readers would obtain the level of detail they require? Many introductory articles have been generated before and are quite good eg: Introduction to viruses.

Please discuss.--Read-write-services (talk) 05:45, 4 August 2008 (UTC)

I also think that the C/A part of the article has been somewhat confusing. I have tried to improve it by putting in paragraphs near the beginning of the section explaining the basic concept of GPS. I have included figures so that hopefully the concept can be visualized. I am hopeful this is better than a total reliance on mathematics. I have also tried to better organize the section by concentrating on two main techniques while lumping somewhat theoretical concepts sach as the one involving light cones into other methods. I hope this helps some. I plan to continue to try to improve the section. RHB100 (talk) 20:55, 6 August 2008 (UTC)


 * Hi RHB100,yes I agree that you have been consistent with trying to make the article a lot more accessible, however, the technical description (although difficult to explain without mathematical formulae and data) is still way too involved. I suggest a split of the article to create 1. An Introduction and 2. A technical analysis of the system, pair of articles, the first three or so sections of this article would be a great intro, while the rest is probably more suited to a highly technical descriptive article. What do you think?--Read-write-services (talk) 22:55, 6 August 2008 (UTC)

I think an introductory article should include an explanation of the basic concept of how spheres intersect and why the GPS receiver is at the intersection of spheres utilizing figures with very little mathematics and ignoring most errors. RHB100 (talk) 01:43, 7 August 2008 (UTC)


 * Could you create this on the new Introduction to the Global Positioning System article? It would give the non-technical person a great understanding of the system without all the errors etc. as you stated. Cheers!--Read-write-services (talk) 03:26, 7 August 2008 (UTC)

Yesterday I split the article using the base article as the starting point of an Introduction to GPS, please discuss and add/edit the articles accordingly i.e technical information to Global Positioning System and non-technical edits to Introduction to the Global Positioning System. cheers --Read-write-services (talk) 22:51, 7 August 2008 (UTC)

Splitting the article is not desirable because it would hinder anyone trying to learn about GPS. The person would first need to know about the existence of the two articles and then make a decision whether the information sought is primarily introductory, technical or a mixture. Such a decision would be especially difficult if the person knows little about GPS already. The article has a lot of value the way it is now, Splitting it will likely diminish its value Roesser (talk) 14:46, 8 August 2008 (UTC)


 * Too late. it has already been done. The Introduction article is shaping up quite nicely, except some complex math is starting to creep in attn: User:RHB100! Depending on your requirements for complexity versus non-technical I believe that the link above both articles advises you of which article YOU may wish to use for reference.--Read-write-services (talk) 22:57, 12 August 2008 (UTC)


 * Where is the complex math to which you refer? I see figures, I see subtraction, multiplication, and division.  I see text.  But where is the complex math?  I would like to know so that I can understand what is considered too technical. RHB100 (talk) 01:00, 13 August 2008 (UTC)

Yes, it was kind of tongue-in-cheek, however I would say leave it to other less technical readers to decide-how simple or complex they want it. My original idea for this article was to aiming it towards about six-seventh grader level. But I must say that I like your present contributions to the article, please keep it up. Cheers!--Read-write-services (talk) 01:32, 13 August 2008 (UTC)

I agree that the GPS article is too long and contains too much technical detail, but I don't think that creating a content fork resulting in two articles with overlapping content is the way to go. The proper way is to move technical sections in the main GPS article into separate articles, per WP:SUMMARY. Han-Kwang (t) 07:50, 21 September 2008 (UTC)

Method of operation
The need for four satellites is definitely the clock uncertainty, not the need to pick among solutions. If the clock is right, then of the two solutions, only one is remotely plausible, so there is no need to use the forth satellite to determine which one. In support of this, there are many references to using 4 satellites to correct the clock. Can you find ones which describe using the fourth satellite to pick among solutions? LouScheffer (talk) 03:40, 22 August 2008 (UTC) This is a detail of manufacturer's software code which the Wikipedia should not pretend to know in the special case of near earth vehicles and a fourth satellite is almost certainly required to determine which intersection is the valid estimate of position in the case of exoatmospheric missiles and space vehicles.RHB100 (talk) 21:53, 27 August 2008 (UTC) -

Note that even in the 'ideal' case of no clock errors, there is no need of the fourth satellite to determine which intersection to choose (the two solution are symmetrical about the plane containing the three satellites, and hence one solution is always very near the earth's surface, and the other way out in outer space. So the fourth satellite is not needed in this case.  However, if the clock is wrong, we don't even know what spheres to intersect, much less pick the right intersection.  So the main purpose of satellite 4 is to correct clock errors.

Also, another argument is that the introduction should be as simple as possible, and describe the case with no errors. But the errors are critical to describe why four satellites are needed. So simplifying too far makes the answer wrong, even though it's easier to understand.LouScheffer (talk) 22:01, 23 August 2008 (UTC)

There is a need for 4 conditions to determine position since in the usual case for GPS, 3 sphere surfaces intersect in 2 points. In the special case of a near earth vehicle the solution which is nearest the earth provides a second method for determining which intersection is a valid estimate of position in addition to a fourth satellite. It is not clear that either method has any particular advantage in terms of computational efficiency (i.e. processor time or memory used). This near earth method is almost certainly not usable for exoatmospheric missiles or space vehicles. In the section formerly titled "Method of Operation", there is an exception to the 4 satellite requirement for the special case of near earth vehicles near the bottom of the page. The wording of this exception may need to be clarified. The Wikipedia should not pretend to know the details of manufacturer's software code. The Wikipedia should instead discuss possible methods dictated by principles of science. RHB100 (talk) 21:53, 27 August 2008 (UTC)


 * For exoatmosspheric positional calculation, the correct solution can easely be choosen by choosing the solution closest to the projected trajectory. For exoatmosspheric position calculation (if it's high enough) a larger problem is that the satelites have antennas designed to direct their energie towards the globe, so it's very difficult to receive the signals if in between the satellites or beyond the satellites.
 * But even with 4 satellites there is still the possibility of 2 solutions. So the fourth satellite does not solve that problem for all cases. The second solution though is probably far away, moving fast and has a larger clock error. The presence of the second solution depends on the constellation. As explained elsewhere 2 satellites (one time differece) define a hyperboloid. Intersecting 2 hyperboloids (two time differences) gives an arc, this arc can be an open curve or a closed curve. If it is a closed curve intersecting this curve with a 3th (the third time differece) this gives two points of intersection. So even the fourth satellite can not solve the two solutions problem. (Not always).
 * To be able to addres a point in space 3 parameters are needed, four satellites is the minimum to give 3 (independend) timedifferences, so four satellites is the minimum, (that is if no other parameters are available).
 * Intercontinental balistic missiles fly 'far' lower than the height of the gps satellites, so the problem is not too great for these missiles, just use the same algoritms with the height-, speedlimitations switched off.
 * For objects going further than the gps satellites, they all have communication with the earth, this provides extra information which can be used as an extra parameter. But I doubt that GPS positioning is very important with these extra terrestial vihicles, because of the antenna problem, I think they depend far more on other methods do calculate their position.Crazy Software Productions (talk) 18:55, 3 September 2008 (UTC)

Which is better, TOA (Spheres) or TDOA (Hyperboloids) ?
TOA stands for Time Off Arrival,

TDOA stands for Time Difference Off Arrival.

Trilaterations is based on TAO. (And is sphere based). 2)

Pseudorange calculation is based TDAO. 1)

Hyperbolic positioning is also based on TDAO. 1)

Multilateration is also based on TDAO. 1)

The discussion about Trilateration and Pseudorange calculations (TAO an TDAO) regulary flares up in the main article and in the discussion.

So for GPS purposes which is better?

If less calculations, faster convergence,less (or none) dependend on the clock error, is better, Pseudorange Calculation is better than methods based on trilateration. Also for pseudorange calculation no inteligence is needed to decern between different constellations. Although a second solution may exist, this will not be selected by the pseudorange calculation. Because of the lack of a complete implementation (or a complete detailed algoritm) for trilateration a full comparison can not be made, but even based on the parts which are available for trilateraton, pseudorange calculations does doe better on all the aspects mentioned here.

Crazy Software Productions (talk) 19:58, 3 September 2008 (UTC) Using pseudorange calculations (sometimes this is called hyperboloid calculation) can be used for positional calculations. This method converges fast, it is not influenced by the clockerror and with a close first estimate only one iteration is needed. One of the effects of pseudorange calculation is that the the clockerror is also calculated in the process. The solutions I have seen up to now based on spheres have never been complete. The suggested clock correction in the GPS mainarticle is not always in the correct direction and is often far of by amount. So the method described is not a completely working solution. Then the amount of calculation needed is far more than is needed for pseudorange calculations.

Pseudorange calculations converges very fast. An example with (0, 0, 0) (centre of the earth) as a first estimate gave the following 'errors' (this is independend of the timing error):

0 first estimate, error is 6372836 meters

1 first iteration, error is 1718732 meters

2 second iteration, error is 108173 meters

3 third iteration, error is    333 meters

4 fourth iteration, error is     0.002695871 meters (2 millimeters)

5 fifth iteration, error is       2.8 E-9 meters.

So in most situations only one iteration will be sufficient.

The above numbers where calculated using an implementation of the pseudorange calculation in a spreadsheat, only using + - * / and the squareroot. (Spreadsheat is available).

The number of calculations needed for one iteration for the pseudorange calculation can be as low as 69 additions/subtractions, 42 multiplications, 22 divisions and 4 squareroots. Because only one iteration is needed in most situations, this is thus the amount of calculation needed for one positioning. I have not analysed the trilateration but having seen parts of the algoritm I estimate that the amount of calculations for one iteration does exceed the above numbers and the number of iterations needed is larger as wel.

So my conclusion is that TDAO is far better than TOA. Based on the amount of calculation needed and based on the number of iterations needed. (But because I haven't seen the complete algoritm or implementation of TOA a real comparison can not be made). If anybody can show that TOA does produce better numbers than the above I will be very interrested.

1)Pseudorange, Hyperbolic positioning and Multilateration can also be used if differences off distances is known. It's not neccesary that they are measured using time differences. But to my knowledge all practical applications are based on measuring the differences in Time.

2)Trilateration can be used if distances are known. There are a multitude off ways to measure (or estimate) a distance.

Crazy Software Productions (talk) 14:48, 10 September 2008 (UTC)

Multidimensional Newton-Raphson for GPS
Don't you think this section seems out of place? It's at an excruciating level of detail with equations galore. Perhaps it should go on a sub-page related to the math and physics behind GPS...

The rest of the article seems to be a general overview. —Preceding unsigned comment added by 76.100.66.155 (talk) 02:23, 11 September 2008 (UTC)

Isn't the 7th section - Multidimensional Newton-Raphson for GPS a little too involved to be included in an introductory article? —Preceding unsigned comment added by Shreyaspotnis (talk • contribs) 16:59, 6 September 2008 (UTC)

This section is placed near the end of the article so that it will not interrupt the discussion for someone who is not interested in the mathematics. One has to click a link to get to this section from the section "Position calculation advanced". It is recognized that some readers will not be interested in this section. However, I think it will be useful for readers who are interested in algorithms and mathematics.RHB100 (talk) 21:37, 12 September 2008 (UTC)

Velocity and Direction
GPS does _not_ provide velocity and direction data (to can be calculated using further analysis of more data, of course), but to imply otherwise is akin to claiming that iron ore mining produces steel girders. Given that clarification on the matter seems to have confused even other editors, I am going to remove the reference entirely. 87.254.72.172 (talk) 04:14, 13 September 2008 (UTC)
 * In several newsgroups this has been discussed.
 * First: All velocity and direction is directly connected to the workings of the GPS system. A fix to a satellite can only be achieved if the correct dopplershift is choosen.
 * Second: Speed is a important component in the positioning. The earth rotates at hundreds off meters each second, this has to be corrected for, why? Because the signal reaches the receiver in 0.06 to 0.09 seconds (for multichannel receivers), the earth has shifted up to about 40 meters in that time. Or there could be a shift of up to 13 meters between the reception of different satellites. Even in in a single positioning, this has to be corrected for. For two channel receivers the times between the reception of different satellites will be more.
 * In the NMEA "$GPRMC" sentence the speed is directly available, if the "$GPGLL" sentence is used then the speed has to be calculated based on two positions and timings.


 * So there is a reason why speed and direction are within a single point positioning and there is a technique (dopplershift) for this problem.


 * With 7 formulas with 7 unknowns this problem can be solved and delivers the x,y,z, delta-T and the (x,y,z) speedvector.


 * Swinging your GPS to and fro (by hand or by means of a mast (in top) on a sailing boat), you get higher speeds than can be explained by just calculating the speeds between two points. Using a one measurement per second track you can varify the point to point speed on a PC and this does not give the same speeds.
 * Crazy Software Productions (talk) 16:58, 13 September 2008 (UTC)

Flight 007
Hi! What is the point you are trying to make? What do you think happened? LouScheffer (talk) 00:47, 18 September 2008 (UTC)

Communism is not only an evil and immoral economic system because of its opposition to pure laissez faire capitalism, it is also evil because of this deliberate mass murder of innocent people flying on this Korean airline. We must not let the left wing, communist sympathizers justify this barbaric act. RHB100 (talk) 01:21, 18 September 2008 (UTC)


 * Here's a quote from the referenced ICAO document, "The flight crew of KE 007 did not implement the proper navigation procedures to ensure the aircraft remained on its assigned track throughout the flight, resulting in KE 007 eventually penetrating prohibited areas of USSR sovereign airspace." This is very explicit, and by the international organization responsible for air safety, not an allegation of a communist government.  LouScheffer (talk) 02:04, 18 September 2008 (UTC)


 * Here is an additional quote from this document that seems to have been ignored, "It was determined that the intercepting USSR aircraft did not comply with the ICAO standards and recommended practices related to the interception of civil aircraft before the attack on KE 007. No attempt was made by the USSR to contact the crew of KE 007 by radio, according to the report." RHB100 (talk) 20:23, 18 September 2008 (UTC)


 * It's being properly ignored since it's not relevant to this article. Sure the Russians used excessive force, but the main problem (certainly from the point of view of GPS, and from the safety report as well) was that they strayed into prohibited airspace in the first place.  This is the reason that Reagan opened up GPS to the public, which is the point of the sentence.  LouScheffer (talk) 01:55, 19 September 2008 (UTC)

Two solutions for positioning.
In Method of operation from Introduction to the Global Positioning System it says:

''It might seem that three satellites would be enough to solve for a position, since space has three dimensions. However it turns out that three spheres usually intersect in two points. Thus the sphere corresponding to the fourth satellite is needed to determine which intersection is the GPS receiver position. Also a fourth satellite is needed to correct the GPS receiver clock by a method which will be described below.''

The suggestion is made that adding a fourth satellite, that this can be used to determine which of the two points is the correct point. This is not true.

Example. Receiver on (0,0,0), three satellites on (3,4,10), (-3,4,10), (3,-4,10), with the fourth satellite on (0,4.9,9.9), there is a second solution on (0,0,7.48). A both the positions you get the exact same timing of signals from all four satellites. (The timing error is different but very smal). Changing the Z value of the fourth satellite from 9.5 to 10.24 the Z goes from minus infinity to plus infinity. So the second point can be anywhere in distance as well.

Changin one of the parameters slightly will not dissolve the second point, but the point will move. With the positions of the first 3 satellites all points on the axes (0,0,Z) are a correct solution. This can be generalized to any constellation for three satellites, because there is always a middle.

The second point is very instalble and changing the parameters a lot the second point will go beyond infinity and then there is no second solution anymore.

Inconclusion:

Even with four satellites there can be two solutions.

The second solutions can be close and far away.

So the fourth satellite can not be used to determine which of the intersections is the correct one. Crazy Software Productions (talk) 11:26, 27 September 2008 (UTC)


 * A solution, by definition, is a value required to make all equations in a system equal one another, and thus for a system of spheres to have a solution, all four spheres have to intersect at one point. It's not possible to have more than one non-trivial solution for a system of four equations in four unknowns (x, y, z and t), unless all the equations are the same, at which point you would have infinitely many solutions. --  Denelson83  05:59, 28 September 2008 (UTC)
 * For lineair equations it it true that four (independend) equations with four unknowns will give one solution, but this is not true for all types of equations. For quadratic equations, equations about distances (circles and spheres), or distance differences (hyperboles and hyperboloids) there can be more solutions. A simple illustration of this is that in a 2d system two non parallel lines intersect in exactly one point. Two circles can intersect in two points.
 * The example does illustrate this for the four satellites (3,4,10), (-3,4,10), (3,-4,10) and (0,4.9,9.9). And the given timings of 5, 5, 5, 4.865927.
 * Distances and timings are all in the same scale. 1 unit of distance is traveled in 1 unit of time
 * There are 2 x,y,z,t solutions for this,
 * 1. x=0, y=0, z=0      and dt = -6.18034
 * 2. x=0, y=0, z=7.48733 and dt = -.59585


 * The numbers are choosen so this can easely be checked. Perfect timing (no clock error) would give the following receive times.
 * 1. 11.18034, 11.18034, 11.18034, 11.04627
 * 2. 5.595854, 5.595854, 5.595854, 5.461774
 * Both solutions fit all equations in the system. Without further information, it is not known which of the two solutions is the correct solution. I do not see that one of the solutions is trivial. Neither can I discard one of the solutions.
 * Neither is this a rare occurance. There are loads of 'normal' satellite configurations where there are two solutions.
 * Crazy Software Productions (talk) 20:50, 29 September 2008 (UTC)

Not clear about GPS satellites (SV) numbers!?
Sorry for this, maybe a little amateurish, question, but I really need to clarify this!!!

HOW MANY SATELLITES OF THE GPS ARE ORBITING RIGHT NOW? 24/31/32 ... I have searched everywhere (of cours mostly on the web) and didn´t find any information about the changed numbers of satellites except here!

Why is that? And where does this information comes from? Is it possible to have an official source or link for it?

''Thanx

Adrian'' —Preceding unsigned comment added by 195.49.188.227 (talk) 09:29, 30 September 2008 (UTC)


 * See reference 77 in the main article: ^ "United States Naval Observatory ((USNO) - Block II Satellite Information". Crazy Software Productions (talk) 21:06, 5 October 2008 (UTC)

GPS receiver
I propose to make a new article called GPS receiver where all receivers can be noted. These include stand-alone, PDA and laptop-connected types (USB, Serial, PCMCIA).

Also, the article may link to GPS_navigation_software which need to add


 * free and proprietary GPS software (free: google maps, Opensource gps, OpenStreetMap, freedrive, mapmonkey (see http://www.mp3car.com/vbulletin/gps/104477-best-2007-gps-software-laptop.html


 * commercial: DeLorme Street Atlas 2009, ALK CoPilot Live Laptop 11, Destinator, nRoute, Microsoft Streets and Trips 2009, ... see this site and this site

A small list of the most popular gps-units (DeLorme Earthmate GPS LT-20 USB GPS with Street Atlas USA 2008, The NAVMAN GPS e Series, US GlobalSat BU-303 GPS Receiver seem to be most popular USB-receivers; prices are relatively low too; 61, 110 and 80 $ respectively) can also be added.

Hope to see this article gets approved and made. Thanks, 81.245.181.224 (talk) 12:11, 23 October 2008 (UTC)

GPS system accuracy repeatibility
One thing that's always bugged me reading the sections on GPS accuracy is that it suggests there shouldn't be much accuracy as I get from my handheld Garmin eTrex Vista. Depending on which section one reads, accuracy shouldn't be better than 15m or 3+m. But my experience is that it's much better than that. If I take a waypoint at a solidly fixed object (the NW corner of a park bench built into the ground) and use the "find waypoint" function to be guided to the waypoint, I get less than 20 cm accuracy for the next few minutes (up to 15-20), and slightly better than a meter day after day, month after month. What gives? —EncMstr (talk) 21:14, 5 November 2008 (UTC)


 * I've managed to get as good as 2 metre horizontal accuracy repeatedly with the GPS receiver I use. We just need to find a reliable source demonstrating this.  Meanwhile, I've acknowledged your observation in the article. --  Denelson83  21:49, 5 November 2008 (UTC)

Basic operation, again
Two comments:


 * The whole idea of a 'basic operation' is to give a simple overview, understandable to all. There is no point in bringing up ambiguous solutions, clock corrections, etc.  in this paragraph.  To anyone who cares, this is covered in detail later.


 * The display part is not really part of the GPS operation. Many GPS systems have no display at all, and just output coordinates, as is explained later in the article.  So a choice of 2 displays seems wrong - saying consumer devices often display in more convenient forms seems more accurate.


 * As always, opinions by all on this are appreciated. LouScheffer (talk) 00:09, 9 November 2008 (UTC)

Two spheres and a circle...
Newbie here...

Regarding the following:

Thus we know that the indicated position of the GPS receiver is at or near the intersection of the surfaces of four spheres. In the ideal case of no errors, the GPS receiver will be at an intersection of the surfaces of four spheres. The surfaces of two spheres, if they intersect in more than one point, intersect in a circle. So what? I'm missing the big picture here and how those 2 sentences are related.

Why is this fact useful? I understand that the description at this point is conceptual and does not relate to actual implementation. Is the idea to suggest that these circles can be used collectively to provide a position estimate in presence of error?

Roughly, how big are those spheres, anyway? Lylenorton (talk) 04:12, 17 November 2008 (UTC)

Yes, these circles can be used collectively to provide a position estimate in presence of error or in the absence of errors. The purpose of the discussion of how sphere surfaces and circles intersect is to provide a geometric explanation supplemented by figures of the basic GPS concept. Some people with scientific curiosity prefer a visual, graphical explanation as opposed to a mathematical explanation involving equations. That is the reason for the choice of a geometric explanation supplemented with figures. RHB100 (talk) 21:32, 25 November 2008 (UTC)


 * If the signal of two satellites is received and the receiver's clock is perfectly synchronised. First the distance to each satellite can be calculated (roughly between about 20200 km and 27000 km). Then there are two (virtual spheres) with a radius of the distance and. The intersection of the two spheres form a circle. The radius of the circle is in the order of 20000 km, the diameter of the circle is around 40000 km. This is a bit more than the size of the earth. Our position is 'probably' near the earth surface and near the intersection of the huge circle with the earth surface.
 * Perfect timing and one satellite puts us on a sphere. (a large sphere, with a diameter larger than 40000 km).
 * Perfect timing and two satellites puts us on the intersection of two spheres. (A large circle, with a large diameter).
 * Perfect timing and three satellites puts us on the intersection of a circle an a sphere. (Two points)
 * In the above sentence there is a very LARGE IF, that is a perfectly synchronised receivers clock. For all normal GPS receivers this is not happening. So the model of the large spheres and the large circle does not work in real live. The GPS receiver is on a hyperboloid defined by the two satellites positions and the difference in time the signal of both sats is received. Adding another satellite (no 3). We are at the intersection of two hyperboloids, (this is a curve). A fourth satellite is needed for another hyperboloid which intersecs the curve. Giving one or two points. We are at (or close to) one of these points.
 * Crazy Software Productions (talk) 19:34, 20 November 2008 (UTC)

I don't know how you conclude that clock errors imply that three sphere surfaces do not intersect in two points. RHB100 (talk) 21:08, 25 November 2008 (UTC)
 * Sorry if my description gave the impression that with a clock error there are no two intersection. This is certainly not what I wanted to convey. (And do not read from my own text). What I was trying to convey was that with the normal clock errors on start up of a GPS, that the intersecting points (if they exist) do not need to be in any vicinity of the receiver. My own receivers after a week of being switched of, would give a position beyond the moon. (My Garmin GPS has a clock error of just over 1 second a week).
 * But now that we are in direct communication, I still would like to see the algoritm for positioning which uses trilateration. Because all the algoritms I build do not perform very well. The suggested algoritm in the main article does not always itterate towards a solution, sometimes it goes further from the solution. (In the main article it is suggested to use the differenc between one of the intersection points and the fourth sphere, this distance can be positive or negative. It is suggested that this difference can be used to correct the clock. But this difference is no indication for either direction or size of the correction. Using the same set of satellites, sometimes the difference has to be added sometimes it has to be substracted, depending on the order in which the satellites are used.)
 * I did build several algoritms around trilateration. But even the best performing one is still far more calculation intensive than pseudorange calculations and the performance varies a lot. Both not good for a GPS receiver (a few years ago). Also there are constraints when the algoritm can be used. (Example; is the clock is about 0.06 seconds slow, there probably will be no intersecting spheres.)
 * The pseudorange calculation algoritm I implemented (it can be found on several sites on the web) does perform wel, consistend and the normal terrestial situation always works. It is well known, is smaller (in coding) than any solution using trilateration and as allready indicated is a lot faster.
 * Crazy Software Productions (talk) 12:50, 26 November 2008 (UTC)

Better performance with the algorithm involving trilateration might be obtained by using one dimensional Newton-Raphson as documented in the chapter, "Root Finding ...", in "Numerical Recipes" by Press, Flannery, Teukolsky, and Vetterling. Using a derivative or estimated derivative to determine the next try would probably result in faster convergence. Multidimensional Newton-Raphson could be used without the necessity of trilateration on each step, but of course the disadvantages of the multidimensional case have already been discussed.RHB100 (talk) 19:26, 17 December 2008 (UTC)

Accuracy of comments about RTCM
I wanted to discuss a few problems I think exist about RTCM under the user segment heading:

GPS receivers may include an input for differential corrections, using the RTCM SC-104 format. This is typically in the form of a RS-232 port at 4,800 bit/s speed. Data is actually sent at a much lower rate, which limits the accuracy of the signal sent using RTCM. Receivers with internal DGPS receivers can outperform those using external RTCM data. As of 2006, even low-cost units commonly include Wide Area Augmentation System (WAAS) receivers.

I would propose the paragraph should start out as follows to mention proprietory formats:

GPS receivers may include an input for differential corrections, using the RTCM SC-104 standard or a proprietory format. RTCM SC-104 messages are typically transferred over an RS-232 port at 4800bps.

I think the next two sentences are unreferenced and not true. Other than fairly small protocol overheads I've never heard of RTCM having to be sent at a much lower rate, and I thought WAAS corrections were only in the order of 250bps anyway? Not to mention the corrections change at a fairly slow rate so it's questionable if a small amount of latency has any measurable impact on performance. It also ignores the fact the RTCM correction stream could be coming from a local reference source that is more accurate than WAAS.

PJohnson (talk) 07:34, 8 December 2008 (UTC)

Inline comments
Wow, there's a lot of inline comments in the article markup. I've removed a couple related to old cleanup tags, but there are some that seem to form mini discussions - they would be better placed here on the talk page. In particular the section which starts "CITE THIS! DO GARMIN RECEIVERS USE MULTILATERATION?  DO TRIMBLE UNITS USE MULTILATERATION?  SHOW US SOME COTTON-PICKIN' PROOF!!!..." and goes on for a dozen paragraphs or more; and another section starting "Compared to a few years ago, GPS technology for handsets has matured considerably..." goes on for four paragraphs. Astronaut (talk) 03:59, 21 December 2008 (UTC)