Adaptive system identification based on higher-order statistics

The problem of estimating the autoregressive (AR) parameters of a causal AR moving average (ARMA) (p,q) process using higher-order statistic is addressed. It is shown that there is always a linear combination of p+1 slices that gives a full-rank Toeplitz matrix. This derivation proves that consistent estimates can always be obtained with this set of p+1, 1-D slices. These results lead to the development of a new adaptive lattice algorithm with improved performance. Some results are presented comparing this scheme with previous algorithms based on a single slice. Estimation of the MA parameters of the obtained AR-compensated sequence completes the identification of the system. As this method is based on cumulants, the estimation will be unbiased, even in the presence of colored Gaussian noise