Unsupervised Bayesian Estimation and Tracking of Time-Varying Convolutive Multichannel Systems

In this paper we focus on Bayesian blind and semi-blind adaptive signal processing based on a broadband MIMO FIR model (e.g., for blind source separation (BSS) and blind system identification (BSI)). Specifically, we study in this paper a framework allowing us to systematically incorporate various types of prior knowledge: (1) source signal statistics, (2) deterministic knowledge on the mixing system, and (3) stochastic knowledge on the mixing system. In order to exploit all possible types of source signal statistics (1), our considerations are based on TRINICON, a previously introduced generic framework for broadband blind (and semi-blind) adaptive MIMO signal processing. The motivation for this paper is threefold: (a) the extension of TRINICON to Bayesian point estimation to address (3) in addition to (1), and (b) more specifically to unify system-based blind adaptive MIMO signal processing with the tracking of time-varying scenarios, and finally (c) to show how the Bayesian TRINICON-based tracking can be formulated as a sequence estimation approach on arbitrary partly smooth manifolds. As we will see in this paper, the Bayesian approach to incorporate stochastic priors and the manifold learning approach to exploit deterministic system knowledge (2) complement one another very efficiently in the context of TRINICON.