Time-Varying Stabilized Forgetting for Recursive Least Squares Identification

Abstract

Forgetting is a well established technique of enforcing adaptability of a recursive LS estimator, necessary for tracking parameters of time-varying systems. Such systems often appear in the adaptive control and signal processing context. The classical forgetting methods are unconditional in the sense that old data are forgotten even in the absence of appropriate new data. This causes undesired unbounded growth of the algorithm's gain (estimator blowup) and leads to unbounded noise sensitivity and to numerical difficulties. The blowup phenomenon can be avoided by using so called stabilized forgetting, that utilizes contractive covariance matrix update equations having stable finite time-invariant equilibrium for nonpersistently exciting signals. In this paper, the class of admissible stabilized forgetting functions is extended by time-varying functions with possibly time–varying equilibria. Key features of the resulting parameter estimation algorithms, like stability of the covariance matrix and the parameter convergence are discussed and shown to be direction–dependent. These properties and freedom in choice of the forgetting parameters can be further exploited for adaptive tuning of the forgetting profile.