Advanced Bayesian methods for array signal processing

Abstract

<p>This thesis focuses on the joint detection of the model order and the estimation of the parameters of interest, with applications to array signal processing in both the off-line and on-line contexts. In the off-line mode, Markov Chain Monte Carlo methods are applied to obtain a numerical approximation of the joint posterior distribution of the parameters. The on-line approach uses the sequential implementation of Monte Carlo methods applied to probabilistic dynamic systems. Three problems were addressed in the course of this thesis. (1) A method for joint detection of the number of sources and estimation of their respective directions of arrival in coloured noise with unknown arbitrary covariance was developed. (2) The second algorithm represents an extension of the first one with the addition of the joint estimation of the times of arrival of the pulses, in the spirit of channel sounding for characterization of multipath channels. Both methods were successfully applied to real data, acquired on campus with a channel sounder during an extensive measurement campaign. (3) The final part of this thesis focuses on the sequential implementation of the Monte Carlo methods, i.e. particle filters, for probabilistic dynamic systems. The algorithm recursively estimates the posterior distribution of the evolving parameters of interest, allowing for the on-line detection of the number of sources and the estimation of their respective directions of arrival.</p>