A radar application of a modified Cramer-Rao bound: Parameter estimation in non-Gaussian clutter

In this paper, we derive a lower bound on the error covariance matrix for any unbiased estimator of the parameters of a signal composed of a mixture of spherically invariant random processes (SIRP's). The proposed approach represents a special case of the global Cramer-Rao bound for hybrid random and deterministic parameters estimation, and it is particularly useful when the data, conditioned on a vector of unwanted random parameters (nuisance parameters) with a priori known probability density function, can be modeled as a Gaussian vector. The case of signal composed of a mixture of K-distributed clutter, Gaussian clutter, and thermal noise belongs to this set, and it is regarded as a realistic radar scenario. In the radar problem considered here, this bound can be numerically computed in closed-form, whereas the computation of the true (marginal) Cramer-Rao bound turns out to be infeasible. The performance of some practical estimators are compared with it for two study cases.