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:
“I was thinking what an interesting concept it is to eliminate the writer from the artistic process. If we can just get rid of these actors and directors, maybe we got something here.”
—Michael Tolkin, U.S. screenwriter, and Robert Altman. Griffin Mill (Tim Robbins)
“I think that Richard Nixon will go down in history as a true folk hero, who struck a vital blow to the whole diseased concept of the revered image and gave the American virtue of irreverence and skepticism back to the people.”
—William Burroughs (b. 1914)
“It is impossible to dissociate language from science or science from language, because every natural science always involves three things: the sequence of phenomena on which the science is based; the abstract concepts which call these phenomena to mind; and the words in which the concepts are expressed. To call forth a concept, a word is needed; to portray a phenomenon, a concept is needed. All three mirror one and the same reality.”
—Antoine Lavoisier (1743–1794)