Nonstationary probabilistic target and clutter scattering models

A probabilistic model for nonstationary and/or nonhomogeneous clutter and target scattering is proposed and developed. The first-order probability density of the scattered power is treated as the expected value of a conditional density that is a function of random parameters. The family of gamma densities is a general solution for the density function of the intensity reflected by objects comprised of several scatterers and is selected as the conditional density. In the general case, the gamma density is a function of two parameters: the mean and the inverse of the normalized variance. Assuming various distributions for a random mean, expressions for the first-order density of the scattered power are derived and used to explain previous experimental and theoretical results. An example of detection performance for nonstationary target fluctuation based on the developed model is also presented.