Time-domain approaches to multichannel optimal deconvolution

Using the modern time series analysis method, based on the autoregressive moving average (ARMA) innovation model and white noise estimators, two time-domain approaches to multichannel optimal deconvolution are presented. In the first approach, the multichannel optimal deconvolution estimators are given in the ARMA innovation filters form, where the solution of the Diophantine equations is required. Their global and local asymptotic stability is proved. In the second approach, the multichannel ARMA recursive Wiener deconvolution filters without the Diophantine equations are presented, which have asymptotic stability. The relationship between the ARMA innovation filters and ARMA Wiener deconvolution filters is discussed. Each approach can handle the deconvolution filtering, smoothing and prediction problems in a unified framework. An illustrative example and two simulation examples show their effectiveness.