Blind Source Recovery in a State-Space Famework: Algorithms for Static and Dynamic Environments

Abstract

This paper describes a generalized state space Blind Source Recovery (BSR) framework obtained by using the Kullback-Lieblar divergence as a performance functional and the application of optimization theory under the constraints of a feedforward state space structure. Update laws for both the non-linear and the linear dynamical systems have been derived for the domain of dynamic blind source recovery along both ordinary stochastic gradient and the Riemannian contra-variant gradient directions. The choice of the rich state space demixing network structure allows for the development of potent learning rules, capable of handling most filtering paradigms and convenient extension to non-linear models. Some particular filtering cases are subsequently derived from this general structure and are compared with material in the recent literature. Some of this reported work has also been implemented in dedicated hardware/software. An illustrative simulation example has been presented to demonstrate the online adaptation capabilities of the proposed algorithms.