Blind multichannel identification based on Kalman filter and eigenvalue decomposition

A noise-robust approach for blind multichannel identification is proposed on the basis of Kalman filter and eigenvalue decomposition. It is proved that the state vector composed of the multichannel impulse responses is nothing but the eigenvector corresponding to the maximum eigenvalue of the filtered state-error correlation matrix. This eigenvector can be computed iteratively with the so-called ‘power method’ to reduce the complexity of the algorithm. Furthermore, it is found that the computation of the inverse of the filtered state-error correlation matrix is much easier than itself, the wanted state vector can be computed from this inverse matrix with the so-called ‘inverse power method’. Therefore, two algorithms are proposed on the basis of the eigenvalue decomposition of the filtered state-error correlation matrix and its inverse matrix, respectively. In addition, for reducing the computing complexity of the proposed algorithms, matrix factorization such as QR-, LU- and Cholesky-factorizations are exploited to accelerate the computation of the algorithms. Simulations show that the proposed algorithms perform well over a wide range of the signal-to-noise ratio of the multichannel signals.