A generalized projection estimation algorithm

• Published in: Automatica (Oxford) 2025-01, Vol.171, p.111942, Article 111942
• Main Authors: Tomei, Patrizio, Marino, Riccardo
• Format: Article
• Language: English
• Subjects: Discrete-time systems; Exponentially convergent estimation; Linear regression model; Parameter estimation; Persistency of excitation; Projection estimation algorithm
• ISSN: 0005-1098
• DOI: 10.1016/j.automatica.2024.111942

Given a linear regression model in discrete-time containing a vector of p constant uncertain parameters, this paper addresses the problem of designing an exponentially convergent parameter estimation algorithm, even when the regressor vector is not persistently exciting (not even in a finite time interval). On the basis of the definition of lack of persistency of excitation of order q for the regressor vector, 0≤q≤p (which coincides with the classical definition of persistency of excitation when q=0), a generalized projection estimation algorithm is proposed which guarantees global exponential convergence of the parameter estimation error and allows for the on-line computation of the order q of the lack of persistency of excitation. When the lack of persistency of excitation is of order zero, global exponential convergence to zero of the parameter estimation error is obtained, recovering a well-known result and the projection estimation algorithm as a special case.