MULTICHANNEL ARMA MODELING BY LEAST-SQUARES CIRCULAR LATTICE FILTERING

This paper makes an attempt to develop least squares lattice algorithm s for the ARMA modeling of a linear, slowly time-varying, multichannel system employing scalar computations only. Using an equivalent scalar , periodic ARMA model and a circular delay operator, the signal set fo r each channel is defined in terms of circularly delayed input and out put vectors corresponding to that channel. The orthogonal projection o f each current output vector on the subspace spanned by the correspond ing signal set is then computed in a manner that allows independent AR and MA order recursions. The resulting lattice algorithm can be imple mented in a parallel architecture employing one processor per channel with the data flowing amongst them in a circular manner. The evaluatio n of the ARMA parameters from the lattice coefficients follows the usu al step-up algorithmic approach but requires, in addition, the circula tion of certain variables across the processors since the signal sets become linearly dependent beyond certain stages. The proposed algorith m can also be used to estimate a process from two correlated, multicha nnel processes adaptively allowing the filter orders for both the proc esses to be chosen independently of each other. This feature is furthe r exploited for ARMA modeling a given multichannel time series with un known, white input.