Maximum likelihood array processing in spatially correlated noise fields using parameterized signals

Abstract

This paper deals with the problem of estimating signal parameters using an array of sensors. This problem is of interest in a variety of applications, such as radar and sonar source localization. A vast number of estimation techniques have been proposed in the literature during the past two decades. Most of these can deliver consistent estimates only if the covariance matrix of the background noise is known. In many applications, the aforementioned assumption is unrealistic. Recently, a number of contributions have addressed the problem of signal parameter estimation in unknown noise environments based on various assumptions on the noise. Herein, a different approach is taken. We assume instead that the signals are partially known. The received signals are modeled as linear combinations of certain known basis functions. The exact maximum likelihood (ML) estimator for the problem at hand is derived, as well as computationally more attractive approximation. The Cramer-Rao lower bound (CRB) on the estimation error variance is also derived and found to coincide with the CRB, assuming an arbitrary deterministic model and known noise covariance.