Multichannel ARMA processes.

Ananthram Swami, Georgios B. Giannakis, Sanyogita Shamsunder

Abstract: Parametric modeling of multichannel time series is accomplished by using higher (than second) order statistics (HOS) of the observed nonGaussian data. Cumulants of vector processes are defined using a Kronecker product formulation, and consistency of their sample estimators is addressed. Identifiability results in connection with the HOS-based parameter estimation of causal and noncausal multivariate ARMA processes are established. Estimates of the parameters of causal ARMA models are obtained as the solution to a set of linear equations, whereas those of noncausal ARMA models are obtained as the solution to a cumulant matching algorithm. Conventional approaches based on second-order statistics can identify a multichannel system only to within post multiplication by a unimodular matrix. HOS-based methods yield solutions that are unique to within post-multiplication by an (extended) permutation matrix; additionally, the multiminimum phase assumption can be relaxed, and the observations may be contaminated with colored Gaussian noise. Frequency-domain methods for nonparametric system identification are discussed briefly. Simulations results validating the multichannel parameter estimation algorithms are provided.<