Recursive least squares ladder forms for fast parameter tracking

Abstract

A discussion of some of the most interesting recent developments in the area of real time (or "on-line") algorithm for estimation and parameter tracking using ladder canonical forms for AR and ARMA modeling is presented. Besides their interesting connections to stability and scattering theory, partial correlations and matrix square-roots, they also seem to have well behaved numerical properties. Ladder forms seem to be a "natural" form for Wiener (or whitening) filters due to the fact that the optimal whitening filter is time-varying (even for stationary processes), except for ladder form coefficients, which are constants "switched on" at the appropriate time. This leads to the fact that this parametrization is very well suited for tracking rapidly varying sources. Compared to gradient type techniques, our exact least-squares ladder recursions have only a slightly increased number of operations. This increase is due to the recursively computed likelihood variables which act as optimal gains on the data, enabling the ladder filter to lock rapidly on to a transient. Several ladder form applications will be briefly discussed, such as speech modeling, "zero startup" equalisers, and "noise cancelling and inversion". Computer simulations will be presented at the conference