ION Technical Content
Exact Fourth Order CEP Equation
| Abstract: | The present analysis is performed to provide an alternate method for determining CEP , in particular, one which is exact to fourth order in the correlation coefficient and one which does not utilize one or more awkward empirical formulae. The motivation for this analysis is that many guided weapon systems use CEP as a measure of terminal accuracy, especially when establishing their overall system specifications. It is thus desirable to have a closed form, highly accurate single CEP expression to evaluate weapon system accuracy in system performance simulations. In the present scheme, the two correlated gaussian random variables (representing x and y positional errors in the CEP plane ) are first rotated so that they have the same value of variance. Upon expressing the double integral over the appropriate bivariate gaussian density function in polar coordinates, the radial integral is performed and the result expanded to fourth order in the correlation coefficient. This then permits the determination of the integral over the azimuth polar coordinate, the result being that only terms in even powers of the correlation coefficient remain. To obtain the final desired equation for CEP , the expression deduced from the double integral is set equal to 0.5 and solved “backwards” in three steps to yield an equation valid to fourth order in the correlation coefficient. The accuracy of the derived CEP equation is then tested for various values of the correlation coefficient from 0.05 to 0.95. In each case, the accuracy is compared to the exact CEP value (obtained by numerical integration) for all sigma ratios in the range from 0.01 to 0.99. Sigma ratio denotes the ratio of the smallest to the largest standard deviations of the two original random variables. 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: |
Proceedings of the IAIN World Congress and the 56th Annual Meeting of The Institute of Navigation (2000) June 26 - 28, 2000 The Catamaran Resort Hotel San Diego, CA |
| Pages: | 428 - 435 |
| Cite this article: | Krempasky, Jerome, "Exact Fourth Order CEP Equation," Proceedings of the IAIN World Congress and the 56th Annual Meeting of The Institute of Navigation (2000), San Diego, CA, June 2000, pp. 428-435. |
| Full Paper: |
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