Multivariate ARMA modeling by scalar algorithms

The authors develop fast algorithms for multichannel autoregressive moving average (ARMA) model identification that use only scalar operations. The given multivariate (vector) ARMA process is mapped (one-to-one) to an equivalent univariate (scalar), periodic ARMA process. The scalar ARMA parameters are identified and then the inverse mapping is used to identify the multivariate model. The univariate AR parameters are estimated by deriving a set of modified Yule-Walker type equations and then developing a Trench-Zohar type algorithm to solve them. The algorithm, besides employing computation of scalar quantities only, is well suited for parallel implementation with the processors connected in a ring-like manner, the number of processors being the same as the number of channels. The identification of the MA part (scalar) of the model needs estimates of the input samples. The MA estimation algorithm, using least squares techniques, also employs scalar computation only and is equally well suited for parallel implementation.<>