On Toeplitz-constrained weights for spatially distributed source localization

Two contributions are affordable in this paper. Firstly, we provide a relationship between two well-known methods - redudancy averaging (RA) and weighted covariance-matching (WCM) - for estimating any Toeplitz Hermitian covariance matrix. The analysis presented herein enables us to their connection by mean of optimal weight performed. By applying both Toeplitzi. cations in asymptotic weight determination, another virtue is to propose an improvement on the asymptotic best consistent (ABC) estimator for direction. nding in the presence of spatially distributed source. Since the Toeplitz structure of array covariance matrix is held itself in symmetric angle deviation model, it is thus advantageous to incorporate such a priori knowledge of the matrix structure into consistent weight estimation step. Based on weighted least squares (WLS) criteria, our enforcement upon the Toeplitz structure is pictorially illustrated that, in small or even moderate number of temporal snapshots, the estimations of nominal direction and their associating angular spread with the additional constraint can outperform the conventional approach without preprocessing of structured covariance estimation.