Statistically robust estimation of source bearing via minimizing the Bhattacharyya distance

Source bearing estimation is a common technique in acoustic array processing. Many methods have been developed and most of them exploit some underlying statistical model. When applied to a practical system, the robustness to model mismatch is of major concern. Traditional adaptive methods, such as the minimum power distortionless response processor, are notoriously known for their sensitivity to model mismatch. In this paper, a parameter estimator is developed via the minimum Bhattacharyya distance estimator (MBDE), which provides a measure of the divergence between the assumed and true probability distributions and is, thus, capable of statistically matching. Under a Gaussian random signal model typical of source bearing estimation, the MBDE is derived in terms of the data-based and modeled covariance matrices without involving matrix inversion. The performance of the MBDE, regarding the robustness and resolution, is analyzed in comparison with some of the existing methods. A connection with the Weiss-Weinstein bound is also discussed, which gives the MBDE an interpretation of closely approaching a large-error performance bound. Theoretical analysis and simulations of bearing estimation using a uniform linear array show that the proposed method owns a considerable resolution comparable to an adaptive method while being robust against statistical mismatch, including covariance mismatch caused by snapshot deficiency and/or noise model mismatch.