Concept
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.
To apply the CEP concept in these conditions, CEP can be defined 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 covariance of 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.
Read more about this topic: Circular Error Probable
Famous quotes containing the word concept:
“The heritage of the American Revolution is forgotten, and the American government, for better and for worse, has entered into the heritage of Europe as though it were its patrimony—unaware, alas, of the fact that Europe’s declining power was preceded and accompanied by political bankruptcy, the bankruptcy of the nation-state and its concept of sovereignty.”
—Hannah Arendt (1906–1975)
“Every new concept first comes to the mind in a judgment.”
—Charles Sanders Peirce (1839–1914)
“Obscenity is a moral concept in the verbal arsenal of the Establishment, which abuses the term by applying it, not to expressions of its own morality, but to those of another.”
—Herbert Marcuse (1898–1979)