On the ambiguity of COMET-EXIP algorithm for estimating a scattered source

The extended invariance principle (EXIP) has been applied to the structured covariance estimation of a zero mean Gaussian vector; the resulting method was named COMET (covariance matching estimation techniques). This technique has been recently used for estimating separately and efficiently the direction of arrival (DOA) and angular spread of a scattered source. Unfortunately this new technique presents an ambiguity that limits its utilization in practice. We show in this paper the existence and the origin of this ambiguity and we propose a solution to eliminate this problem without introducing bias. Our approach consists first to add a constraint to the original cost function, and then to replace the constrained problem by an unconstrained problem by using the penalty function method.