Computation of a useful Cramer-Rao bound for multichannel ARMA parameter estimation

Abstract

It has been shown earlier that the problem of multichannel autoregressive moving average (ARMA) parameter estimation can be tackled in a computationally efficient way by converting the given process into an equivalent scalar, periodic ARMA process. The authors present methods used to compute the Cramer-Rao bound associated with the identification of the scalar ARMA equivalent of a given multichannel ARMA process. The elements of matrix are obtained by a few very simple operations like periodic AR filtering of certain downsampled versions of the input and output sequences and then cross-correlating the filter outputs. The filter is easily obtainable from the model equation and is common for all the parameters.