Dual estimation approach to blind source separation

Abstract

A dual estimation approach has been proposed towards solving the blind source separation (BSS) problem. The states and the parameters of the dynamical system are estimated simultaneously when only noisy observations are available. The framework assumed for dual estimation is that of dual Kalman filtering. Two separate Kalman filters run simultaneously, the state filter which runs for state estimation and uses the current estimate of the parameters and the parameter filter which runs for parameter estimation and uses the current state estimates. The study of the information theoretical analysis of Kalman filter shows that the filter in its process maximises the mutual information between a state and the estimate indicating that the filter may be a potential solution for BSS problems. The proposed state-space-based dual estimation approach, dual Kalman BSS, has been studied for linear instantaneous BSS and the simulation results validate the proposed approach. The performance comparison carried out against the FastICA, joint-approximate diagonalisation of Eigenmatrices, k-temporal decorrelation separation and BSS algorithm by Zhang, Woo and Dlay for post-non-linear convolutive modelling in terms of signal-to-interference ratio and signal-to-distortion ratio shows that for a good intuitive initialization the proposed approach does better separation.