A recursive algorithm for nonlinear least-squares problems

The solution of nonlinear least-squares problems is investigated. The asymptotic behavior is studied and conditions for convergence are derived. To deal with such problems in a recursive and efficient way, it is proposed an algorithm that is based on a modified extended Kalman filter (MEKF). The error of the MEKF algorithm is proved to be exponentially bounded. Batch and iterated versions of the algorithm are given, too. As an application, the algorithm is used to optimize the parameters in certain nonlinear input–output mappings. Simulation results on interpolation of real data and prediction of chaotic time series are shown. A. Alessandri and M. Cuneo were partially supported by the EU and the Regione Liguria through the Regional Programmes of Innovative Action (PRAI) of the European Regional Development Fund (ERDF). M. Sanguineti was partially supported by a grant from the PRIN project ‘New Techniques for the Identification and Adaptive Control of Industrial Systems’ of the Italian Ministry of University and Research. A. Alessandri Department of Production Engineering, Thermoenergetics, and Mathematical Models (DIPTEM), University of Genoa, P.le Kennedy Pad. D, 16129 Genova, Italy e-mail: [email protected] M. Cuneo · S. Pagnan Institute of Intelligent Systems for Automation, ISSIA-CNR National Research Council of Italy, Via De Marini 6, 16149 Genova, Italy M. Cuneo e-mail: [email protected] S. Pagnan e-mail: [email protected] M. Sanguineti ( ) Department of Communications, Computer and System Sciences (DIST), University of Genoa, Via Opera Pia 13, 16145 Genova, Italy e-mail: [email protected] 196 A. Alessandri et al.