Robust Wiener Design of Adaptation Laws with Constant Gains

Abstract

Filters can be introduced into LMS-like adaptation algorithms to improve their tracking performance. This paper discusses the systematic model-based design of such filters. Parameter variations in coefficients of linear regression models are modeled as ARIMA-processes. The aim is to provide high performance filtering, prediction or fixed lag smoothing estimates for arbitrary lags. The properties of the time-varying parameters are in general not known exactly, so a robust design for a set of possible models will be of interest. We minimize the average tracking MSE, based on probabilistic descriptions of the model uncertainty. The method is based on a novel signal transformation that recasts the algorithm design into a robust Wiener filtering problem. The performance is illustrated on the tracking of mobile radio channels in IS-136 systems, based on a model of the time-variations affected by parametric uncertainty.