Persistent Excitation is Unnecessary for Online Exponential Parameter Estimation: A New Algorithm that Overcomes this Obstacle
Abstract
In this paper, we prove that it is possible to estimate online the parameters of a classical vector linear regression equation $ Y=\Omega \theta$, where $ Y \in \mathbb{R}^n,\;\Omega \in \mathbb{R}^{n \times q}$ are bounded, measurable signals and $\theta \in \mathbb{R}^q$ is a constant vector of unknown parameters, even when the regressor $\Omega$ is not persistently exciting. Moreover, the convergence of the new parameter estimator is global and exponential and is given for both continuoustime and discretetime implementations. As an illustration example, we consider the problem of parameter estimation of a linear timeinvariant system, when the input signal is not sufficiently exciting, which is known to be a necessary and sufficient condition for the solution of the problem with the standard gradient or leastsquares adaptation algorithms.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 arXiv:
 arXiv:2106.08773
 Bibcode:
 2021arXiv210608773K
 Keywords:

 Electrical Engineering and Systems Science  Systems and Control
 EPrint:
 submitted to System and Control Letters