Distribution of general noncentral positive definite quadratic form in K-dimensions

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) 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.<>