An Amendment of Fast Subspace Tracking Methods

TL;DR

This paper proposes an amendment to fast subspace tracking methods to improve stability and eliminate erratic sparks in steady state error by constraining the stepsize during updates.

Contribution

It introduces a modification to existing subspace tracking algorithms, fixing the update process to prevent sparks and enhance stability.

Findings

Sparks in steady state error are caused by update issues in specific planes.

Constraining stepsize at each update eliminates sparks.

The amended method improves stability without sacrificing convergence speed.

Abstract

Tuning stepsize between convergence rate and steady state error level or stability is a problem in some subspace tracking schemes. Methods in DPM and OJA class may show sparks in their steady state error sometimes, even with a rather small stepsize. By a study on the schemes' updating formula, it is found that the update only happens in a specific plane but not all the subspace basis. Through an analysis on relationship between the vectors in that plane, an amendment as needed is made on the algorithm routine to fix the problem by constricting the stepsize at every update step. The simulation confirms elimination of the sparks.