In this article, we consider the online parameter estimation problem for overparameterized linear regression models. Many estimation methods require at least the interval excitation condition, which is not always fulfilled for such models, especially in normal operation. To relax the required excitation level, we detect linearly dependent columns in the regressor, obtain the reduced model and estimate parameters in a finite time. On the last step, the parameters of the initial model are recovered. The proposed method efficiency is demonstrated on a simple overparameterized model and a magnetic levitation system.

This paper is devoted to the application of a recently proposed globally convergent adaptive position observer to non‐salient permanent magnet synchronous motors. Following the Dynamic Regressor Extension and Mixing Based Adaptive Observer (DREMBAO) approach, a new finite‐time robust observer is presented that allows to track adaptively the rotor position by measuring only the currents and voltages and without knowledge of mechanical, electrical and magnetic parameters. A numerical example for the case with different rotor speeds and time‐varying load torque is considered to reveal the advantages of the proposed approach in comparison with other existing methods. Experimental studies of the proposed robust nonlinear observer implementation are presented to illustrate the efficiency of the new design technique in different speed modes together with adaptive estimation of unknown parameters.

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