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Authors
Giuseppe Calafiore; Basilio Bona

Digital Object Identifier (DOI)
10.3182/20050703-6-CZ-1902.00206

Page Numbers:
205-205

Index Terms
set-membership filltering,ellipsoidal bounds,nonlinear filters,semidefinite programming

Abstract
In this paper, we develop a numerically efficient scheme for set-membership prediction and filtering for discrete-time nonlinear systems, that takes into explicit account the effects of nonlinearities via local second-order information. The filtering scheme is based on a classical prediction/update recursion that requires at each step the solution of a convex semidefinite optimization problem. The technical results discussed in the paper build upon the recently developed paradigm of uncertain linear equations (ULE) and semidefinite relaxations.

References

[1] Bertsekas, D.P. and I.B. Rhodes (1971). Recursive
     state estimation with a set-membership
    description of the uncertainty. IEEE Trans.
    Aut. Control 16, 117-128.
[2] Calafiore, G. and L. El Ghaoui (2004). Ellipsoidal
    bounds for uncertain linear equations and
    dynamical systems. Automatica 40(5), 773-
    787.
[3] Chernousko, F.L. (1993). State Estimation of Dynamic
     Systems. CRC Press. Boca Raton, FL.
[4] Di Marco, M., A. Garulli, A. Giannitrapani and
    A. Vicino (2004). A set theoretic approach
    to dynamic robot localization and mapping.
    Autonomous Robots 16(1), 23-47.
[5] Durieu, C., E. Walter and B. Polyak (2001).
    Multi-input multi-output ellipsoidal state
    bounding. Journal of Optimization Theory
    and Applications 111(2), 273-303.
[6] Einicke, G.A. and B. White (1999). Robust extended
     kalman filtering. IEEE Transactions
    on Signal Processing 47(9), 2596-2599.
[7] Fabrizi, E., G. Oriolo, S. Panzieri and G. Ulivi
    (1998). A kf-based localization algorithm for
    nonholonomic mobile robots. In: Proceedings
    of the 6th IEEE Mediterranean Conference.
    Alghero. pp. 130-135.
[8] Jetto, L., S. Longhi and G. Venturini (1999). Development
     and experimental validation of an
    adaptive extended kalman filter for the localization
     of mobile robots. IEEE Transactions
    on Robotics and Automation 15(2), 219-229.
[9] Kurzhanski, A.B. and I. Valyi (1996). Ellipsoidal
     Calculus for Estimation and Control.
    Birkhauser. Boston.
[10] Maskarov, D.G. and J.P. Norton (1996). State
     bounding with ellipsoidal set description of
     the uncertainty. Int. J. Control 65(5), 847-
     866.
[11] Schweppe, F.C. (1973). Uncertain Dynamic Systems
     . Prentice-Hall. New York.