Multichannel Linear Prediction and Maximum-Entropy Spectral Analysis Using Least Squares Modeling

Abstract

Autoregressive data modeling using the least squares linearprediction method is generalized for multichannel time series. A recursive algorithm is obtained for the formation of the system of multichannel normal equations which determine the least squares solution of the multichannel linear-prediction problem. Solution of these multichannel normal equations is accomplished by the Cholesky factorization method. The corresponding multichannel maximum-entropy spectrum derived from these least squares estimates of the autoregressive-model parameters is compared to that obtained using parameters estimated by a multichannel generalization of Burg's algorithm. Numerical experiments have shown that the multichannel spectrum obtained by the least squares method provides for more accurate frequency determination for truncated sinusoids in the presence of additive white noise.