Numerical Estimation Of Marcums Q Function Using Monte Carlo Approximation Schemes

The Marcum Q-Function is an important tool in the study of radar detection probabilities in Gaussian clutter and noise. Due to the fact that it is an intractable integral, much research has focused on finding good numerical approximations for it. Such approximations include numerical integration techniques, such as adaptive Simpson quadrature, and Taylor series approximations, induced by the modified Bessel function of order zero, which appears in the integrand. One technique which has not been explored in the literature is the sampling-based Monte Carlo approach. Part of the reason for this is that the integral representation of the Marcum Q-Function is not in the most suitable form for Monte Carlo methods. Using some recently derived techniques, we construct a number of sampling-based estimators of this function, and we consider their relative merits.