A recursive algorithm for nonlinear least-squares problems

  • Authors:
  • A. Alessandri;M. Cuneo;S. Pagnan;M. Sanguineti

  • Affiliations:
  • Department of Production Engineering, Thermoenergetics, and Mathematical Models (DIPTEM), University of Genoa, Genova, Italy 16129;Institute of Intelligent Systems for Automation, ISSIA-CNR National Research Council of Italy, Genova, Italy 16149;Institute of Intelligent Systems for Automation, ISSIA-CNR National Research Council of Italy, Genova, Italy 16149;Department of Communications, Computer and System Sciences (DIST), University of Genoa, Genova, Italy 16145

  • Venue:
  • Computational Optimization and Applications
  • Year:
  • 2007

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Abstract

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.