Talk:Circular error probable

Discussion 2007
There seem to be two competing definitions in this treatment (1) The 50% circle or median radial miss (2) The expected error (MSE) Either of these could be considered as "Circular Error Probable", but in my experience as a weapon system analyst, the first one is the one typically used. It's the one that is related to damage effectiveness.

Personally, I use "Circle of Equal Probabilities" when introducing the concept of CEP to the uninitiated.

The formula is straightforward for the case in which the distribution is unbiased, circular-normal. But for the general bivariate normal case, it involves iterating a double integral until 50% coverage is attained. Alternatively, one could introduce the "erf" function to make it seem like a single integral.

Think anyone would be interested in some approximations of the calculations?

Comments? —Preceding unsigned comment added by 128.244.81.106 (talk • contribs) 19:02, 2 June 2005


 * For a normal distribution the mean (the expected error) and the median coincide. The mean square error, MSE, is a different concept. I'd be surprised if anyone really uses the general bivariate normal case, but solving a formula involving a double integral isn't a major deal these days. Apart from the usual commercial mathematical codes (Mathematica, MATLAB, etc.) there is good open source code (SciLab, R) available.


 * >Think anyone would be interested in some approximations of the calculations?


 * Yes! Blaise 14:36, 7 March 2007 (UTC)

sorry that I have to respond, but all this article is simply wrong. ANYTHING that is thrown into balistic trajectory will end in probability area with shape of ellipse. And in reality, actually, it would not even be an ellipse, but a close approximation of ellipse, more like a shape of an egg. The probability target areas of balistic vehicles are usually given as two distances, one in the direction of trajectory between minimum and maximum probability points, and a shorter one as a cross section of that. —Preceding unsigned comment added by 194.249.63.239 (talk • contribs) 18:00, 15 August 2005


 * Incorrect. Most ballistic errors are circular when plotted on a plane perpendicular to the munition's velocity vector.  It is only because they impact the ground at an angle that the munition impact points are elliptical.  Since many munitions are designed to impact the ground at or near vertical, many actually have circular errors.(Jeff the Baptist (talk) 14:48, 8 July 2008 (UTC))


 * Downrange error is larger. Pure circle cannot exist here. Period. There are no vehicles with perfect vertical imapct. Both in nature or man-made. Or are extremely rare. We can only discuss very close approximations of circle.

A pleasure to respond.

Depending on the errors that perturb the ballistic missile from its intended trajectory, you could get all kinds of distributions at "impact". Usually, velocity errors tend to induce a larger effect in the downrange direction (gravity effect along with the "flashlight" effect). The CEP, however, is a measure of how close the impacts are likely to be to the target - given some assumed distribution - and thus is a valid concept no matter what shape the distribution has. —Preceding unsigned comment added by 128.244.81.106 (talk • contribs) 19:11, 30 September 2005


 * Downrange error is larger. Pure circle cannot exist here. Period. There are no vehicles with perfect vertical imapct. Both in nature or man-made. Or are extremely rare. We can only discuss very close approximations of circle.

Proposed re-focus
I propose deleting all the unreferenced and unreference-able material about CEPs for particular systems and refocusing the article on the CEP concept.

Any objecions? ComputerGeezer (talk) 20:13, 17 January 2008 (UTC)

CEP and the Normal Distribution
The last paragraph is wrong. CEP is not based on a normal distribution. It is in fact a much more general statistic that doesn't pre-suppose and underlying statistical distribution. CEP can generated using all sorts of distibutions. (Jeff the Baptist (talk) 14:55, 8 July 2008 (UTC))

Rewrite
I've been "bold" and tried to focus this article a bit, showing where the "normal" came from and how it relates to the MSE version of CEP. I think the article is more readable now. ComputerGeezer (talk) 00:42, 21 August 2008 (UTC)

Math errors on this page
The formula given in the last paragraph of this page, at least as I understand it, can't be right. It can be shown with a simple Monte Carlo simulation that if sigma_x=sigma_y, and you assume a Gaussian distribution, that the median of the distribution in r (and hence the CEP) is about 1.1774*sigma. Furthermore, this is a case where the integral can be done analytically and the result is the same. If the formula is used as given on the page it yields 1.41*sigam. In his 1997 Master Thesis, "A Comparison of Circular Error Probable Estimators for Small Samples", Charles Williams outlines a set of approximations that work reasonably well. CEP ~ 0.563* sigma_l+.614*sigma_s where sigma_l is the larger standard deviation and sigma_s is the smaller. There are further corrections if the samples are correlated. Another simple measure is what Williams refers to as the Rayleigh estimate. It is simply .9394*r^bar where r^bar is the mean radius.

An additional problem is that the tables don't take into account ellipticity for the pattern. The R90 and R95 values depend on the ellipticity as shown by Harter in his 1960 paper. Again, this can be easily confirmed by Monte Carlo calculations.

In any case, what's up on the page does not appear to be correct. There are plenty of references, going back to the original RAND paper in 1952 that could be used to back things up in this article. Should we try getting this right? I will admit that the current article led me down the garden path for a while.

I have recently written notes on this topic "Characterizing rifle performance using circular error probable measured via a flatbed scanner" that are found at www.statshooting.com - Any objection to updating the math in the manner outlined in the paper?

Cfmcmillan (talk) 23:22, 26 October 2008 (UTC)

GPS
GPS accuracy is often given using CEP. --193.40.242.97 (talk) 17:07, 23 October 2009 (UTC)

Agree. CEP is the standard way of expressing navigation accuracy and can no longer be seen as specific to weapon system like current text suggests. The ammunition examples and weapon specific text could be moved to separate topic/section -- 195.218.72.250 (talk) 11:14, 1 February 2010 (UTC)

Defintion & 50% ?
Currently the article (intro) states that CEP "is defined as the radius of a circle, centered about the mean, whose boundary is expected to include the landing points of 50% of the rounds." and later that "While 50% is a very common definition for CEP, the circle dimension can be defined for percentages" (I think the word 'other' is missing here). The first one is sourced to "Circular Error Probable (CEP), Air Force Operational Test and Evaluation Center Technical Paper 6, Ver 2, July 1987, p. 1" while the second is not sourced at all. To the best of my knowledge however, CEP is not "fixed" at 50% but can be any value, with 35, 50 and 90 being the most common (somewhat depending on munition type). I haven't been able to find any online source supporting this though, but this one does somewhat. --Heb (talk) 13:09, 28 August 2013 (UTC)


 * Indeed, CEP90 is a measure commonly used in remote sensing, and it would be useful if this article included such usages. Cesiumfrog (talk) 04:06, 17 August 2016 (UTC)

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Okay, would you mind explaining why?
I thought the rationale for the hatnote was pretty obvious. Specifically, it's WP:2DAB and WP:TWODABS. If you think there's a reason to undo it, I'm interested, but I need some info in the edit comment or talk page explaining why. Do you think I should consider the pendulum definition primary and have a hatnote to this page? Is Only-two-dabs preferred? I'm in the dark here. May we have that discussion, please? 71.41.210.146 (talk) 22:12, 28 December 2015 (UTC) I see that you have already "undone" my revision, so there is no need for a "discussion" here. Having a conversation with a non-registered editor is always somewhat tedious. I wish you a Happy New Year. — &#124; Gareth Griffith-Jones &#124; The Welsh Buzzard&#124; — 08:58, 29 December 2015 (UTC) If you had not already carried out the undo, after reading your opening post this morning, I would have done as you. You must forgive me for my initial misunderstanding of your editing. I would urge you to register; there are so many benefits. Cheers! — &#124; Gareth Griffith-Jones &#124; The Welsh Buzzard&#124; — 12:19, 29 December 2015 (UTC)
 * Good morning!
 * I presume your reasons for the original revert still exist, and I'm actively interested in learning what they are. I'm pretty confident I DTRT per the MoS and all that (which is why I took the unusual step of re-doing the edit; the undo could have been a mis-click or something), but that's not the same as absolute certainty.  The goal is to reach WP:consensus.
 * I'm a big fan of WP:BRD, and I want to get to the "discuss" part. 71.41.210.146 (talk) 11:11, 29 December 2015 (UTC)
 * Good afternoon,
 * Sorry for the misunderstanding; I read the third line if your first reply as "I don't want to talk to you", and thought you were doubling-down on the uncommented revert. It sure didn't sound like "never mind, I'm happy to let your edit stand" or "oops, I reverted too fast".  Thus, it seemed there was very much an active dispute.
 * As for getting an account, that would violate the WP:NOSHARE policy. As it is, we can all share the IP.   71.41.210.146 (talk) 18:02, 30 December 2015 (UTC)