Adaptive system identification using cumulants

A lattice version of the recursive instrumental variable method for adaptive parameter identification of ARMA (autoregressive moving-average) processes is developed. Appropriate choice of the instrumental variables leads to cumulant-based AR parameter estimates. Cumulant-based normal equations may be obtained by using nonconventional orthogonality conditions in the linear prediction problem. The development leads to a pair of lattices, one excited by the observed process y(n), and the other by the instrumental process z(n). The lattices are coupled through order-update and time-update equations. The lattice structure yields the AR compensated residual time series. Hence, adaptive versions of cumulant-based MA parameter identification algorithms are directly applicable. Some convergence results are presented