Variance bounds for parameter estimation in correlated non-Gaussian clutter

Abstract

We derive a lower bound on the error covariance matrix for any unbiased estimator of the parameters of a disturbance modeled as a mixture of spherically invariant random processes (SIRPs). The bound can be numerically computed in closed form in many practical cases where the computation of the true Cramer-Rao lower bound is infeasible. The proposed bound is particularly useful when the disturbance, conditioned to a vector of unwanted random parameters (nuisance parameters) with apriori known probability density function, can be modeled as a Gaussian process. The case of disturbance 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. The performance of some practical estimators are compared to this bound for three study cases.