On the Kalman Filter Parameter Estimation Methods for Blind Source Separation

Blind Source Separation (BSS) is a well-known problem in signal processing and still receives attention from the scientific community, given its applicability in different areas. This work presents a theoretical background overview of the Kalman Filter formulation and its applicability to the BSS problem as a parameter estimator in two different approaches: joint (JEKF) and dual parameter estimation (DEKF). These approaches are evaluated in different scenarios for first-order autoregressive source signals, with analysis of the initialization details, presenting simulation results and performance comparison with classic algorithms, SOBI and SONS, evaluated by SIR, MER and MSE. The results showed that both the JEKF and DEKF algorithms can perform separation in a two-source-two-mixture scenario. In general, over the scenarios studied, DEKF presented a better performance when compared to the JEKF on the evaluated metrics. However, neither algorithm correctly estimated the parameters for mixtures involving more than two sources, showing convergence issues and sensitivity to initialization for an increased number of sources.