Linear State Space Feedforward and Feedback Structures for Blind Source Recovery in Dynamic Environments

摘要

Blind Source Recovery (BSR) denotes recovery of original sources or signals from environments, which may include convolution, temporal variation, and even non-linearity—without necessarily performing explicit environment identification. This paper presents two separate multiple-input multiple-output (MIMO) structures for dynamic linear Blind Source Recovery (BSR) of multiple stochastically independent source signals. We propose linear state space models for both the mixing environment and the demixing (or the recovering) adaptive network. The demixing network may assume either the feedforward or the feedback state space configuration. Separate algorithms have been derived for the adaptive estimation of the feedforward and the feedback demixing/recovering network’s parameters. These algorithms are based on the multivariable optimization theory and utilize the Riemannian contra-variant gradient (or the natural gradient) search under the constraints of a state space representation. Auxiliary conditions for the convergence of these algorithms have also been derived and discussed. Illustrative simulation examples have been included to demonstrate the successful adaptation results for both proposed demixing network structures in the case of an infinite impulse response (IIR)-type mixing environment for example source statistical distributions.