A modified COMET-EXIP method 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 COvariance Matching Estimation Techniques (COMET). 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 has 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 rigorous solution to eliminate this problem without introducing performance degradation. 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. For the purpose to reduce the computational load of our method, we propose a simple and fast solution to solve this ambiguity problem. Analytical expression for the variance of the unweighted COMET-EXIP estimator is derived and compared with simulation results.