Talk:Circular error probable

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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?

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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.

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.

[edit] 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)