Pade approximations to matched-filter amplitude probability functions: Rayleigh mixtures and multiple observations

Techniques are presented for deriving approximations to the statistical functions that characterize linear sums of matched-filter outputs. They are derived using two techniques: (1) Pade approximations to the multidimensional characteristic function (CF), and (2) discrete Rayleigh mixtures based on an exact or approximate form of the Rayleigh parameter probability density function. The Pade-based approximations are used for modeling the "clutter-only" case and computing detection thresholds, whereas the Rayleigh mixtures are best suited for modeling the "target-plus-clutter" case and computing target detection probabilities.