Generalized Forgetting Recursive Least Squares: Stability and Robustness Guarantees

TL;DR

This paper introduces GF-RLS, a generalized recursive least squares method, providing stability and robustness guarantees for fixed and time-varying parameters, along with a survey of existing RLS extensions.

Contribution

It presents a unified framework for stability analysis and robustness guarantees of GF-RLS, encompassing many RLS variants and analyzing their properties.

Findings

Conditions for stability of GF-RLS are established.

Robustness bounds for noisy, time-varying parameter estimation are derived.

A survey of RLS extensions demonstrates GF-RLS's analytical versatility.

Abstract

This work presents generalized forgetting recursive least squares (GF-RLS), a generalization of recursive least squares (RLS) that encompasses many extensions of RLS as special cases. First, sufficient conditions are presented for the 1) Lyapunov stability, 2) uniform Lyapunov stability, 3) global asymptotic stability, and 4) global uniform exponential stability of parameter estimation error in GF-RLS when estimating fixed parameters without noise. Second, robustness guarantees are derived for the estimation of time-varying parameters in the presence of measurement noise and regressor noise. These robustness guarantees are presented in terms of global uniform ultimate boundedness of the parameter estimation error. A specialization of this result gives a bound to the asymptotic bias of least squares estimators in the errors-in-variables problem. Lastly, a survey is presented to show how GF-RLS can be used to analyze various extensions of RLS from the literature.