Circular error probable
It is defined as the radius of a circle, centered on the aimpoint, that is expected to enclose the landing points of 50% of the rounds; said otherwise, it is the median error radius, which is a 50% confidence interval.
The concept of CEP also plays a role when measuring the accuracy of a position obtained by a navigation system, such as GPS or older systems such as LORAN and Loran-C.
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.
CEP is not a good measure of accuracy when this distribution behavior is not met.
Munitions may also have larger standard deviation of range errors than the standard deviation of azimuth (deflection) errors, resulting in an elliptical confidence region.
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.
The Spall and Maryak approach applies when the shot data represent a mixture of different projectile characteristics (e.g., shots from multiple munitions types or from multiple locations directed at one target).
While 50% is a very common definition for CEP, the circle dimension can be defined for percentages.
Percentiles can be determined by recognizing that the horizontal position error is defined by a 2D vector which components are two orthogonal Gaussian random variables (one for each axis), assumed uncorrelated, each having a standard deviation
and doubles as a sort of standard deviation, since errors within this value make up 63% of the sample represented by the bivariate circular distribution.
values for DRMS and 2DRMS (twice the distance root mean square) are specific to the Rayleigh distribution and are found numerically, while the CEP, R95 (95% radius) and R99.7 (99.7% radius) values are defined based on the 68–95–99.7 rule We can then derive a conversion table to convert values expressed for one percentile level, to another.
