Parameter bounds under misspecified models for adaptive radar detection

This chapter aims to provide a comprehensive overview on lower bounds on mean square error (MSE) on the estimation of a deterministic parameter vector under misspecified models. It starts by presenting the theoretical derivation of the so-called misspecified Cramér-Rao bound (MCRB). The asymptotical efficiency of the maximum likelihood (ML) estimator in the presence of model misspecification is then discussed for a general deterministic estimation problem. A constrained version of MCRB is also described. The second part of this chapter describes the application of the proposed framework to the problem of estimating the disturbance covariance (scatter) matrix for adaptive radar detection. This classical radar problem is addressed in the more general context of estimating the scatter matrix of complex elliptically symmetric (CES) distributed measurement vectors under data mismodeling.