Generation of new exciting regressors for consistent on-line estimation of unknown constant parameters

TL;DR

This paper introduces a novel method for generating new regressors to ensure consistent online estimation of unknown parameters in linear regression models, especially when excitation is insufficient, improving estimation accuracy.

Contribution

A new procedure for creating exciting regressors from existing data, enhancing the performance of gradient estimators in parameter estimation tasks.

Findings

The new regressors improve estimator convergence.

Simulations demonstrate superior estimation accuracy.

Method outperforms traditional approaches in low excitation scenarios.

Abstract

The problem of parameter estimation from a standard vector linear regression equation in the absence of sufficient excitation in the regressor is addressed. The first step to solve the problem consists in transforming this equation into a set of scalar ones using the well-known dynamic regressor extension and mixing technique. Then a novel procedure to generate new scalar exciting regressors is proposed.} The superior performance of a classical gradient estimator using this new regressor, instead of the original one, is illustrated with comprehensive simulations.