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We present some new results on the dynamic regressor extension and mixingparameter estimators for linear regression models recently proposed in theliterature. This technique has proven instrumental in the solution of severalopen problems in system identification and adaptive control. The new resultsinclude: (i) a unified treatment of the continuous and the discrete-time cases;(ii) the proposal of two new extended regressor matrices, one which guaranteesa quantifiable transient performance improvement, and the other exponentialconvergence under conditions that are strictly weaker than regressorpersistence of excitation; and (iii) an alternative estimator ensuringparameter estimation in finite-time that retains its alertness to tracktime-varying parameters. Simulations that illustrate our results are alsopresented.

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