Recursive nonlinear set-theoretic estimation based on pseudo ellipsoids

The problem of estimating a vector x_ of unknown quantities based on a set of measurements depending nonlinearly on x_ is considered. The measurements are assumed to be taken sequentially and are corrupted by unknown but bounded uncertainties. For this uncertainty model, a systematic design approach is introduced, which yields closed-form expressions for the desired nonlinear estimates. The estimates are recursively calculated and provide solution sets /spl chi/ containing the feasible sets, i.e., the sets of all x_ consistent with all the measurements available and their associated bounds. The sets /spl chi/ are tight upper bounds for the exact feasible sets and are in general not convex and not connected. The proposed design approach is versatile and the resulting nonlinear filter algorithms are both easy to implement and efficient.

[1]  Fred C. Schweppe,et al.  Uncertain dynamic systems , 1973 .

[2]  T. Kerr.  Real-time failure detection: A nonlinear optimization problem that yields a two-ellipsoid overlap test , 1977 .

[3]  M. Milanese,et al.  Estimation theory and uncertainty intervals evaluation in presence of unknown but bounded errors: Linear families of models and estimators , 1982 .

[4]  E. Walter,et al.  Exact recursive polyhedral description of the feasible parameter set for bounded-error models , 1989 .

[5]  J. Deller.  Set membership identification in digital signal processing , 1989, IEEE ASSP Magazine.

[6]  Yih-Fang Huang,et al.  ARMA parameter estimation using a novel recursive estimation algorithm with selective updating , 1990, IEEE Trans. Acoust. Speech Signal Process..

[7]  Dominique Meizel,et al.  Fusion of multi-sensor data: a geometric approach , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[8]  Antonio Vicino,et al.  Estimation theory for nonlinear models and set membership uncertainty , 1991, Autom..

[9]  Federico Thomas,et al.  Set membership approach to the propagation of uncertain geometric information , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[10]  F. Chernousko.  State Estimation for Dynamic Systems , 1993 .

[11]  P. L. Combettes.  The foundations of set theoretic estimation , 1993 .

[12]  Eric Walter,et al.  Set inversion via interval analysis for nonlinear bounded-error estimation , 1993, Autom..

[13]  Gregory D. Hager,et al.  On comparing statistical and set-based methods in sensor data fusion , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

[14]  J. R. Deller,et al.  Least-square identification with error bounds for real-time signal processing and control , 1993, Proc. IEEE.

[15]  K. Passino,et al.  An optimal volume ellipsoid algorithm for parameter set estimation , 1993, IEEE Trans. Autom. Control..

[16]  A. Vicino,et al.  Sequential approximation of feasible parameter sets for identification with set membership uncertainty , 1996, IEEE Trans. Autom. Control..

[17]  U. Hanebeck,et al.  Set theoretic localization of fast mobile robots using an angle measurement technique , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[18]  J. Shamma,et al.  Approximate set-valued observers for nonlinear systems , 1997, IEEE Trans. Autom. Control..

[19]  Uwe D. Hanebeck,et al.  On combining statistical and set-theoretic estimation , 1999, Autom..

[20]  Luc Jaulin,et al.  Interval constraint propagation with application to bounded-error estimation , 2000, Autom..

[21]  Uwe D. Hanebeck,et al.  Fusing Information Simultaneously Corrupted by Uncertainties with Known Bounds and Random Noise with Known Distribution , 2000, Inf. Fusion.

[22]  Uwe D. Hanebeck,et al.  Optimal filtering for polynomial measurement nonlinearities with additive non-Gaussian noise , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).