Circular Error Probable (CEP)

In the military science of ballistics, circular error probable (CEP) (also circular error probability or circle of equal probability) is an intuitive measure of a weapon system's accuracy. It is defined as a circle, centered about the mean, whose boundary is expected to include 50% of the population within it.

The original concept of CEP was based on a circular bivariate normal distribution (CBN) with CEP as a parameter of the CBN just as μ and σ are parameters of the normal distribution. Munitions with this distribution behavior tend to cluster around the aim point, with most reasonably close, progressively fewer and fewer further away, and very few at long distance. That is, if CEP is n meters, 50% of rounds land within n meters of the target, 43% between n and 2n, and 7 % between 2n and 3n meters, and the proportion of rounds that land farther than three times the CEP from the target is less than 0.2%.

This distribution behavior is often not met. Precision-guided munitions generally have more "close misses" and so are not normally distributed. Munitions may also have larger standard deviation of range errors than the standard deviation of azimuth (deflection) errors, resulting in an elliptical confidence region. Munition samples may not be exactly on target, that is, the mean vector will not be (0,0). This is referred to as bias.

In order to apply the CEP concept in these conditions, we can define CEP as the square root of the mean square error(MSE). The MSE will be the sum of the variance of the range error plus the variance of the azimuth error plus the covarianceof the range error with the azimuth error plus the square of the bias. Thus the MSE results from pooling all these sources of error, geometrically corresponding to radius of a circle within which 50% of rounds will land.

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