The authors present a series solution using Hermite polynomials to the long-standing problem of computing the probability P that positive definite noncentral quadratic form d(x) of a Gaussian random vector x in R satisfies d(x)>or=r/sup 2/ for any given r in R. This problem has wide applications in radar, tracking, air traffic control, etc. The fast-converging series solution presented is very accurate and can be performed rapidly using the recursion relations for Hermite polynomials.
展开▼
机译：作者提出了一个使用Hermite多项式的系列解决方案，解决了一个长期存在的问题，即计算R中高斯随机向量x的正定非中心二次形式d（x）满足d（x）> = r / sup 2的概率P对于这个R中的任何给定r，这个问题在雷达，跟踪，空中交通管制等方面都有广泛的应用。提出的快速收敛级数解非常准确，并且可以使用Hermite多项式的递归关系快速执行。
展开▼
