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Title: Blind source separation based on M autocovariance matrices Authors:  Sara Taskinen - University of Jyvaskyla (Finland) [presenting]
Klaus Nordhausen - University of Jyvaskyla (Finland)
David Tyler - Rutgers (United States)
Abstract: Assume that the observed $p$ time series are linear combinations of $p$ latent uncorrelated weakly stationary time series. The aim of blind source separation (BSS) is to find an estimate for the unmixing matrix which transforms the observed time series back to uncorrelated latent time series. Classical AMUSE (Algorithm for Multiple Unknown Signals Extraction) method solves the BSS problem by jointly diagonalizing the sample covariance matrix and the sample autocovariance matrix with chosen lag. A natural extension of AMUSE is SOBI (Second Order Blind Identification) method, which approximately jointly diagonalizes the sample covariance matrix and several sample autocovariance matrices with chosen lags to solve the unmixing matrix. It is well known that in the presence of outliers, the sample covariance matrix and sample autocovariance matrices perform poorly and yield unreliable unmixing matrix estimates. We propose a robust blind source separation method that utilizes so-called M autocovariance matrices. The M autocovariance matrices are similar to the classical M estimators in that they downweight the outliers using some preselected, bounded weight function. Simulation studies and a real data example are used to illustrate robustness and efficiency properties of proposed methods.