# New Results on Parameter Estimation via Dynamic Regressor Extension and Mixing: Continuous and Discrete-time Cases

## TL;DR

This paper advances parameter estimation techniques in linear regression models by unifying continuous and discrete-time approaches, introducing new regressor matrices, and ensuring finite-time convergence with improved transient performance.

## Contribution

It provides a unified framework for continuous and discrete-time estimators, introduces two novel regressor matrices, and offers an estimator for finite-time parameter convergence.

## Key findings

- Unified treatment of continuous and discrete-time cases
- Introduction of two new extended regressor matrices
- Finite-time parameter estimation with tracking of time-varying parameters

## Abstract

We present some new results on the dynamic regressor extension and mixing parameter estimators for linear regression models recently proposed in the literature. This technique has proven instrumental in the solution of several open problems in system identification and adaptive control. The new results include: (i) a unified treatment of the continuous and the discrete-time cases; (ii) the proposal of two new extended regressor matrices, one which guarantees a quantifiable transient performance improvement, and the other exponential convergence under conditions that are strictly weaker than regressor persistence of excitation; and (iii) an alternative estimator ensuring parameter estimation in finite-time that retains its alertness to track time-varying parameters. Simulations that illustrate our results are also presented.