A hierarchical Bayesian approach to direction finding and beamforming

It is well known in array processing that general multiple signal model based approaches for direction of arrival estimation, such as maximum likelihood (ML) or maximum a posteriori (MAP) estimation, are optimal. The major drawbacks of these approaches, is that not only do we need to know the number of signals a priori, but these methods also involve multivariate nonlinear maximizations which can often lead to an unacceptably large computational overhead. In this paper we propose a hierarchical Bayesian analysis for high accuracy direction finding and the resolution of closely spaced signals. The approach is to use a one signal model posterior distribution to obtain an initial coarse location of the signals. We then take each peak found and analyze it locally with a two signal model. In this way the computational load is kept modest as the optimizations are carried out only locally around the peak and there is no need to know, a priori, the number of signals. It is shown that this approach also provides a basis for the development of robust beamformers through the use of Laplace asymptotic expansions.