Performance Enhancement of the Recursive Least Squares Algorithms with Rank Two Updates

TL;DR

This paper introduces new recursive least squares algorithms with rank two updates that improve estimation performance by incorporating both exponential and instantaneous forgetting, supported by theoretical properties and practical evaluation.

Contribution

It presents novel RLS algorithms with rank two updates, combining exponential and instantaneous forgetting, and analyzes their convergence properties and performance in harmonic-rich environments.

Findings

New RLSR2 algorithms outperform traditional methods in harmonic estimation.

Theoretical convergence properties are established for the inverse information matrix.

Algorithms demonstrate improved adaptability in dynamic signal environments.

Abstract

New recursive least squares algorithms with rank two updates (RLSR2) that include both exponential and instantaneous forgetting (implemented via a proper choice of the forgetting factor and the window size) are introduced and systematically associated in this report with well-known RLS algorithms with rank one updates. Moreover, new properties (which can be used for further performance improvement) of the recursive algorithms associated with the convergence of the inverse of information matrix and parameter vector are established in this report. The performance of new algorithms is examined in the problem of estimation of the grid events in the presence of significant harmonic emissions.