# Time-Varying Source Separation by Joint Diagnolization on Autocovariances

*2020-03-16*

# Abstract

Keywords: Blind Source Separation, Second-Order Blind Identification, SOBI, Time-Varying Second-Order Blind Identification, TV-SOBI.

Blind Source Separation (BSS) seeks to recover the true signals from the observed ones when only limited information about the mixing matrix and the original sources are available. There are various methodologies established to solve the BSS problems, and notably, Second-Order Blind Identification (SOBI) identifies sources through second-order statistics (Tong et al., 1994). This thesis stretches the Second-Order Source Separation (SOS) model in terms of latent time variation in the mixing mechanism that was initially proposed by Yeredor (2003). An improved algorithm, Linearly Time-Varying SOBI (LTV-SOBI), together with alternatives attempts to estimate mixing parameters and ultimately derives latent independent sources employing sample autocovariance decomposition and joint diagonalization. The performance of LTV-SOBI is analyzed with simulated data by extending the performance metric Signal-to-interference ratio (SIR, Yeredor, 2003) into the time-varying case. Simulation results suggest the superiority of the new LTV-SOBI algorithm compared with Yeredor’s TV-SOBI algorithm, despite overall results are still non-optimal. In addition to the full implementation of LTV-SOBI algorithm in `R`

, an interactive dashboard is designed to enable further outlook of algorithm performance.

### References

Tong, L., Xu, G., & Kailath, T. (1994). Blind identification and equalization based on second-order statistics: A time domain approach. *IEEE Transactions on Information Theory*, *40*(2), 340–349.

Yeredor, A. (2003). TV-sobi: An expansion of SOBI for linearly time-varying mixtures. *Proc. 4th International Symposium on Independent Component Analysis and Blind Source Separation (ICA’03), Nara, Japan*.