Multichannel time-varying ARMA model identification by least squares circular lattice structures

An attempt is made to develop algorithms for the adaptive autoregressive moving average (ARMA) modeling of a linear, slowly time-varying, multichannel system using scalar computations only. The multivariate ARMA process is mapped to an equivalent scalar, periodic ARMA process. By properly defining the input and output vectors corresponding to the scalar process, the problem is formulated as the order-recursive computation of the orthogonal projection of the input vector on an appropriate data subspace. This is carried out by first orthogonalizing the data vectors through the Gram-Schmidt procedure resulting in the least squares circular lattice (LSCL) algorithm. The LSCL algorithm evaluated all possible lower-order ARMA lattice filters. It consists of several identical sections, one for each channel, pipelined in a circular manner, and is therefore well suited for implementation in modular architecture