Circular Error Probable

The Circular Error Probable ( CEP ; German  scattering circle radius ) indicates the radius of a circle with a circular normal distribution in which 50 percent of all measured values ​​lie. The CEP serves as a measure of the accuracy of a system.

application

The specification of the CEP is mainly used when describing the accuracy of a weapon system with unguided ammunition .

The enclosed percentage is written as an index to indicate CEP (e.g .: CEP for 20%: CEP ₂₀ ). If no index is given, the CEP is meant for 50% of all values.

Mathematical derivation

An approximation based on the assumption of normally distributed impacts with the highest hit density at the origin of the coordinate system is obtained by the following double integral :

${\displaystyle P_{\rho }={\frac {1}{\sqrt {\left|2\pi \Phi \right|}}}\cdot \iint _{x^{2}+y^{2}<\rho ^{2}}\exp \left(-{\frac {1}{2}}\left(x,y\right)^{T}\cdot \Phi ^{-1}\cdot \left(x,y\right)\right)\mathrm {d} x\,\mathrm {d} y}$

${\displaystyle P_{\rho }}$: Probability that the felling within a circle with the radius is ${\displaystyle {\mathcal {N}}\left(0,\Phi \right)}$ ${\displaystyle \rho }$

${\displaystyle \Phi }$: Variance-covariance matrix of the random vector ${\displaystyle \left(x,y\right)}$

${\displaystyle \left(x,y\right)}$: Random vector of the coordinates of the impact

${\displaystyle {\rho }}$: Radius

${\displaystyle T}$: Transpose a vector

Probable spherical error

When looking at the accuracy of a system in three dimensions (for example, in satellite navigation systems ), the value of the radius of a sphere within which the measurement results are located with a probability of 50 percent is referred to as the Spherical Error Probable (SEP).

Individual evidence

1. ^ Homepage The National Academies Press, accessed November 20, 2008