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

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.