Multi-Layered Recursive Least Squares for Time-Varying System Identification

TL;DR

This paper introduces a multi-layered RLS estimator designed to improve tracking of rapidly changing systems, minimizing mean square error through optimal layer selection and maintaining low computational complexity.

Contribution

The paper proposes a novel multi-layered RLS approach that enhances tracking performance for time-varying systems and provides a method to determine the optimal number of layers.

Findings

m-RLS outperforms classic RLS in tracking rapidly changing systems

Optimal number of layers minimizes mean square error

Complexity of the proposed method is reduced to O(M)

Abstract

Traditional recursive least square (RLS) adaptive filtering is widely used to estimate the impulse responses (IR) of an unknown system. Nevertheless, the RLS estimator shows poor performance when tracking rapidly time-varying systems. In this paper, we propose a multi-layered RLS (m-RLS) estimator to address this concern. The m-RLS estimator is composed of multiple RLS estimators, each of which is employed to estimate and eliminate the misadjustment of the previous layer. It is shown that the mean square error (MSE) of the m-RLS estimate can be minimized by selecting the optimum number of layers. We provide a method to determine the optimum number of layers. A low-complexity implementation of m-RLS is discussed and it is indicated that the complexity order of the proposed estimator can be reduced to O(M), where M is the IR length. In addition, by performing simulations, we show that m-RLS outperforms the classic RLS and the RLS methods with a variable forgetting factor.