Variable gain parameter estimation algorithms for fast tracking and smooth steady state (Q1571082)

The paper deals with discrete-time systems in the form \[ y_i=\phi_i^T\theta_i+v_i,\qquad i=1,2,\dots, \] where \(y_i\in \mathbb{R}\) is the system output, \(\phi_i \in \mathbb{R}^n\) the measurable regressor, \(\theta_i\in \mathbb{R}\) the parameter vector and \(v_i\) the noise. The parameter vector can be time varying in general. Based on the ideas of set-membership identification, the authors present in this paper variable gain least mean-squares and weighted recursive least-squares algorithms. The main result is that the proposed algorithms do not require explicit knowledge of the noise bound. The performance of the algorithms is illustrated by a simulation example.