Standard LSParameter Estimators Ensure Finite Convergence Time for Linear Regression Equations Under an Interval Excitation Assumption

TL;DR

This paper highlights that standard LS estimators achieve finite convergence time in linear regression equations with intervally excited regressors, underlining the importance of IE for parameter identifiability.

Contribution

It emphasizes that under interval excitation, standard LS estimators guarantee finite convergence time, a fact that was previously little known.

Findings

LS estimators ensure finite convergence time under IE

Interval excitation is necessary and sufficient for identifiability

Convergence time equals the duration of IE compliance

Abstract

In this brief note we recall the little-known fact that, for linear regression equations (LRE) with intervally excited (IE) regressors, standard Least Square (LS) parameter estimators ensure finite convergence time (FCT) of the estimated parameters. The convergence time being equal to the time length needed to comply with the IE assumption. As is well-known, IE is necessary and sufficient for the identifiability of the LRE-hence, it is the weakest assumption for the on-or off-line solution of the parameter estimation problem.