A hierarchical Bayesian approach to direction finding and beamforming
Songsri Sirianunpiboon, S.D. Howard, John Asenstorfer · 2006
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.