zbMATH — the first resource for mathematics

Set-membership state estimation with fleeting data. (English) Zbl 1260.93153
Summary: This paper deals with offline nonlinear state estimation where measurements are available only when some given equality conditions are satisfied. For this type of problems, which are often met in robot localization when sonar or radar are involved, the data are qualified as fleeting because the measurements are available only at some given unknown dates. In this paper, the first approach able to deal with nonlinear estimation with fleeting data is presented. An illustration related to offline robot localization with a laser rangefinder will be given.

93E10 Estimation and detection in stochastic control theory
93C85 Automated systems (robots, etc.) in control theory
Full Text: DOI
[1] Abdallah, F.; Gning, A.; Bonnifait, P., Box particle filtering for nonlinear state estimation using interval analysis, Automatica, 44, 3, 807-815, (2008) · Zbl 1283.93262
[2] ()
[3] Berz, M.; Makino, K., Verified integration of ODEs and flows using differential algebraic methods on high-order Taylor models, Reliable computing, 4, 4, 361-369, (1998) · Zbl 0976.65061
[4] Chabert, G.; Jaulin, L., QUIMPER, A language for quick interval modelling and programming in a bounded-error context, Artificial intelligence, 173, 1079-1100, (2009) · Zbl 1191.68628
[5] Combastel, C. (2005). A state bounding observer for uncertain non-linear continuous-time systems based on zonotopes. In CDC-ECC ’05.
[6] Durieu, C., Polyak, B., & Walter, E. (1996). Ellipsoidal state outer-bounding for MIMO systems via analytical techniques. In Proceedings of the IMACS-IEEE-SMC CESA’96 symposium on modelling and simulation. Vol. 2, Lille, France(pp. 843-848).
[7] Glynn, J. M. (2007). Acoustic calibration and bathymetric processing with a KLEIN 5410 sidescan sonar. PhD thesis. University of New Hampshire, US.
[8] Gning, A.; Bonnifait, P., Constraints propagation techniques on intervals for a guaranteed localization using redundant data, Automatica, 42, 7, 1167-1175, (2006) · Zbl 1117.93367
[9] Goldsztejn, A., & Jaulin, L. (2006). Inner and outer approximations of existentially quantified equality constraints. In Proceedings of the twelfth international conference on principles and practice of constraint programming. (CP 2006). Nantes (France). · Zbl 1160.68546
[10] Jaulin, L., Nonlinear bounded-error state estimation of continuous-time systems, Automatica, 38, 1079-1082, (2002) · Zbl 1026.93015
[11] Jaulin, L.; Kieffer, M.; Braems, I.; Walter, E., Guaranteed nonlinear estimation using constraint propagation on sets, International journal of control, 74, 18, 1772-1782, (2001) · Zbl 1023.93020
[12] Jaulin, L.; Kieffer, M.; Didrit, O.; Walter, E., ()
[13] Kurzhanski, A.; Valyi, I., Ellipsoidal calculus for estimation and control, (1997), Birkhäuser Boston, MA · Zbl 0865.93001
[14] Leonard, J.J.; Durrant-Whyte, H.F., Dynamic map building for an autonomous mobile robot, International journal of robotics research, 11, 4, (1992) · Zbl 0760.68008
[15] ()
[16] Moore, R.E., Methods and applications of interval analysis, (1979), SIAM Philadelphia, PA · Zbl 0417.65022
[17] Raissi, T.; Ramdani, N.; Candau, Y., Set membership state and parameter estimation for systems described by nonlinear differential equations, Automatica, 40, 1771-1777, (2004) · Zbl 1067.93019
[18] Sam-Haroud, D. (1995). Constraint consistency techniques for continuous domains. PhD dissertation 1423. Swiss Federal Institute of Technology in Lausanne. Switzerland.
[19] Thrun, S.; Fox, D.; Burgard, W.; Dellaert, F., Robust Monte Carlo localization for mobile robots, Artificial intelligence, 128, 99-141, (2000) · Zbl 0971.68162
[20] van Emden, M., Algorithmic power from declarative use of redundant constraints, Constraints, 4, 4, 363-381, (1999) · Zbl 0949.68041
[21] van Hentenryck, P.; Michel, L.; Deville, Y., Numerica – a modelling language for global optimization, (1997), MIT Press Cambridge, Massachusetts
[22] Videau, G., Raïssi, T., & Zolghadri, A. (2009). Guaranteed state estimation for nonlinear continuous-time systems based on qLPV transformations. In Proceedings of European control conference ECC’09. Budapest. Hungary.
[23] Walter, E.; Pronzato, L., Identification of parametric models from experimental data, (1997), Springer-Verlag London, UK
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.