CEP Equation Exact to the Fourth Order

J. J. Krempasky

Peer Reviewed

Abstract: An alternative method is presented for determining circular error probable (CEP), in particular, one that is exact to the fourth order in the correlation coefficient and does not utilize one or more awkward empirical formulae. The motivation for this analysis is that for many guided weapon systems, CEP is used as a measure of terminal accuracy, especially when establishing overall system specifications. It is thus desirable to have a closedform, highly accurate single CEP expression to evaluate weapon system accuracy in system performance simulations. In this paper, the accuracy of the derived CEP equation is tested for various values of the correlation coefficient from 0.05 to 0.95, in each case varying the sigma ratio (ratio of smaller to larger standard deviation) from 0.01 to 0.99. It is found that the deviation of the derived CEP equation from the exact value is less than 2 percent over the range of parameters tested. By comparison, no single empirical CEP expression yields this accuracy over the same range of parameters.
Published in: NAVIGATION: Journal of the Institute of Navigation, Volume 50, Number 3
Pages: 143 - 150
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