On DREM Regularization and Unexcited Linear Regression Estimation

The problem of estimating unknown constant parameters in linear regression with measurement noise is considered in this paper. To analyze different levels of excitation of the regressor, two notions of partial and feeble excitation are introduced. The former implies the absence of persistent or interval excitation, while the latter property states that the excitation is insufficient for an efficient estimation in a noisy setting. The dynamic extension and mixing method (DREM) is used for the problem solution, and to improve its estimation performance, regularization is proposed, and the resulting improvement is investigated analytically. The theoretical findings are illustrated in the simulations.