Moving-horizon state estimation for nonlinear discrete-time systems: New stability results and approximation schemes

  • Authors:

  • Angelo Alessandri;Marco Baglietto;Giorgio Battistelli

  • Affiliations:

  • Department of Production Engineering, Thermoenergetics, and Mathematical Models, DIPTEM-University of Genoa, P.le Kennedy Pad. D, 16129 Genova, Italy;Department of Communications, Computer and System Sciences, DIST-University of Genoa, Via Opera Pia 13, 16145 Genova, Italy;Dipartimento di Sistemi e Informatica, DSI-Universití di Firenze, Via di S. Marta 3, 50139 Firenze, Italy

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2008

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Abstract

A moving-horizon state estimation problem is addressed for a class of nonlinear discrete-time systems with bounded noises acting on the system and measurement equations. As the statistics of such disturbances and of the initial state are assumed to be unknown, we use a generalized least-squares approach that consists in minimizing a quadratic estimation cost function defined on a recent batch of inputs and outputs according to a sliding-window strategy. For the resulting estimator, the existence of bounding sequences on the estimation error is proved. In the absence of noises, exponential convergence to zero is obtained. Moreover, suboptimal solutions are sought for which a certain error is admitted with respect to the optimal cost value. The approximate solution can be determined either on-line by directly minimizing the cost function or off-line by using a nonlinear parameterized function. Simulation results are presented to show the effectiveness of the proposed approach in comparison with the extended Kalman filter.