Abstract
This paper deals with characterizing all feasible values of a parameter vector. Feasibility is defined by a finite number of tests based on experimental data and priors. It is assumed that some of these tests may be unreliable, because of the approximate nature of the priors and of the presence of outliers in the data. The methodology presented, which can be applied to models nonlinear in their parameters, makes it possible to compute a set guaranteed to contain all values of the parameter vector that would have been obtained if all tests had been reliable, provided that an upper bound on the number of faulty tests is available. This remains true even if a majority of the tests turns out to be faulty. The methodology is applied to the localization of a robot from distance measurements.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
E. Walter (Ed.), “Special issue on parameter identifications with error bounds,” Mathematics and Computers in Simulation, vol. 32, no. 5&6, pp. 447–607, 1990.
J. P. Norton (Ed.), “Special issue on bounded-error estimation: Issue 1,” Int. J. of Adaptive Control and Signal Processing, vol. 8, no. 1, pp. 1–118, 1994.
J. P. Norton (Ed.), “Special issue on bounded-error estimation: Issue 2,” Int. J. of Adaptive Control and Signal Processing, vol. 9, no. 1, pp. 1–118, 1995.
M. Milanese, J. Norton, H. Piet-Lahanier, and E. Walter (Eds), Bounding Approaches to System Identification. New York: Plenum Press, 1996.
E. Walter and L. Pronzato, Identification of Parametric Models from Experimental Data. London: Springer-Verlag, 1997.
H. Lahanier, E. Walter, and R. Gomeni, “OMNE: a new robust membershipset estimator for the parameters of nonlinear models,” J. of Pharmacokinetics and Biopharmaceutics, vol. 15, pp. 203–219, 1987.
E. Walter and H. Piet-Lahanier, “Estimation of the parameter uncertainty resulting from bounded-error data,” Math. Biosci., vol. 92, pp. 55–74, 1988.
L. Pronzato and E. Walter, “Robustness to outliers of bounded-error estimators and consequences on experiment design,” in Bounding Approaches to System Identification (M. Milanese, J. Norton, H. Piet-Lahanier, and E. Walter, eds.), (New York), pp. 199–212, Plenum Press, 1996.
H. Piet-Lahanier and E. Walter, “Characterization of non-connected parameter uncertainty regions,” Math. and Comput. in Simulation, vol. 32, pp. 553–560, 1990.
R. E. Moore, Methods and Applications of Interval Analysis. Philadelphia, Pennsylvania: SIAM Publ., 1979.
L. Jaulin and E. Walter, “Set inversion via interval analysis for nonlinear bounded-error estimation,” Automatica, vol. 29, no. 4, pp. 1053–1064, 1993.
L. Jaulin and E. Walter, “Guaranteed nonlinear parameter estimation from bounded-error data via interval analysis,” Math. and Comput. in Simulation, vol. 35, pp. 1923–1937, 1993.
L. Jaulin, E. Walter, and O. Didrit, “Guaranteed robust nonlinear parameter bounding,” CESA'96 IMACS Multiconference (Symposium on Modeling, Analysis and Simulation), pp. 1156–1161, 1996.
M. Drumheller, “Mobile robot localization using sonar,” IEEE Trans. on Pottern Analysis and Machine Intelligence, vol. 9, no. 2, pp. 325–332, 1987.
W. E. Grimson and T. Lozano-Pérez, “Localizing overlapping parts by searching the interpretation tree,” IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 9, no. 4, pp. 469–482, 1987.
J. J. Leonard and H. F. Durrant-Whyte, “Mobile robot localization by tracking geometric beacons,” IEEE Trans. on Robotics and Automation, vol. 7, no. 3, pp. 376–382, 1991.
E. Halbwachs and D. Meizel, “Multiple hypothesis management for mobile vehicule localization,” in CD Rom of the European Control Conference, (Louvain), 1997.
D. Meizel, A. Preciado-Ruiz, and E. Halbwachs, “Estimation of mobile robot localization: geometric approaches,” in Bounding Approaches to System Identificaton (M. Milanese, J. Norton, H. Piet-Lahanier, and E. Walter, eds.), (New York), pp. 463–489, Plenum Press, 1996.
M. Kieffer, L. Jaulin, E. Walter, and D. Meizel, “Robust autonomous robot localization using interval analysis.” To appear in Reliable Computing, 1999.
M. Kieffer, Estimation ensembliste par analyse par intervalles, application à la localisation d'an véhicule. Phd thesis, Université Paris-Sud, Orsay, 1999.
M. Kieffer, L. Jaulin, and E. Walter. Guaranteed recursive nonlinear state estimation using interval analysis. In Proc. 37th IEEE Conference on Decision and Control, pages 3966–3971, Tampa, Florida, 16–18 december 1998.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1999 Springer-Verlag London Limited
About this paper
Cite this paper
Kieffer, M., Jaulin, L., Walter, E., Meizel, D. (1999). Nonlinear identification based on unreliable priors and data, with application to robot localization. In: Garulli, A., Tesi, A. (eds) Robustness in identification and control. Lecture Notes in Control and Information Sciences, vol 245. Springer, London. https://doi.org/10.1007/BFb0109869
Download citation
DOI: https://doi.org/10.1007/BFb0109869
Published:
Publisher Name: Springer, London
Print ISBN: 978-1-85233-179-5
Online ISBN: 978-1-84628-538-7
eBook Packages: Springer Book Archive