A STATE ESTIMATOR FOR NONLINEAR STOCHASTIC SYSTEMS BASED ON DIRAC MIXTURE APPROXIMATIONS

Oliver C. Schrempf, Uwe D. Hanebeck

Abstract

This paper presents a filter approach for estimating the state of nonlinear dynamic systems based on recursive approximation of posterior densities by means of Dirac mixture functions. The filter consists of a prediction step and a filter step. The approximation approach is based on a systematic minimization of a distance measure and is hence optimal and deterministic. In contrast to non-deterministic methods we are able to determine the optimal number of components in the Dirac mixture. A further benefit of the proposed approach is the consideration of measurements during the approximation process in order to avoid parameter degradation.

References

  1. Alspach, D. L. and Sorenson, H. W. (1972). Nonlinear Bayesian Estimation Using Gaussian Sum Approximation. IEEE Transactions on Automatic Control, AC-17(4):439-448.
  2. Boos, D. D. (1981). Minimum Distance Estimators for Location and Goodness of Fit. Journal of the American Statistical association, 76(375):663-670.
  3. Bucy, R. S. (1969). Bayes Theorem and Digital Realizations for Non-Linear Filters. Journal of Astronautical Sciences, 17:80-94.
  4. Doucet, A., Freitas, N. D., and Gordon, N. (2001). Sequential Monte Carlo Methods in Practice. SpringerVerlag, New York.
  5. Doucet, A., Godsill, S., and Andrieu, C. (2000). On Sequential Monte Carlo Sampling Methods for Bayesian Filtering. Statistics and Computing, 10(3):197-208.
  6. Geweke, J. (1989). Bayesian Inference in Econometric Models using Monte Carlo Integration. Econometrica, 24:1317-1399.
  7. Gordon, N. (1993). Bayesian Methods for Tracking. PhD thesis, University of London.
  8. Hanebeck, U. D., Briechle, K., and Rauh, A. (2003). Progressive Bayes: A New Framework for Nonlinear State Estimation. In Proceedings of SPIE, volume 5099, pages 256-267, Orlando, Florida. AeroSense Symposium.
  9. Huber, M., Brunn, D., and Hanebeck, U. D. (2006). ClosedForm Prediction of Nonlinear Dynamic Systems by Means of Gaussian Mixture Approximation of the Transition Density. In International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2006), Heidelberg, Deutschland, pages 98-103.
  10. Huber, M. F. and Hanebeck, U. D. (2007). Hybrid Transition Density Approximation for Efficient Recursive Prediction of Nonlinear Dynamic Systems. In International Conference on Information Processing in Sensor Networks (IPSN 2007), Cambridge, USA.
  11. Julier, S. and Uhlmann, J. (1997). A New Extension of the Kalman Filter to Nonlinear Systems. In Proceedings of SPIE AeroSense, 11th International Symposium on Aerospace/Defense Sensing, Simulation, and Controls, Orlando, FL.
  12. Kullback, S. and Leibler, R. A. (1951). On Information and Sufficiency. Annals of Mathematical Statistics, 22(2):79-86.
  13. Schrempf, O. C., Brunn, D., and Hanebeck, U. D. (2006a). Density Approximation Based on Dirac Mixtures with Regard to Nonlinear Estimation and Filtering. In Proceedings of the 45th IEEE Conference on Decision and Control (CDC'06), San Diego, California, USA.
  14. Schrempf, O. C., Brunn, D., and Hanebeck, U. D. (2006b). Dirac Mixture Density Approximation Based on Minimization of the Weighted Cramér-von Mises Distance. In Proceedings of the International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2006), Heidelberg, Germany, pages 512-517.
  15. Schrempf, O. C. and Hanebeck, U. D. (2007). Recursive Prediction of Stochastic Nonlinear Systems Based on Dirac Mixture Approximations. In Proceedings of the American Control Conference (ACC 7807), New York City, USA.
Download


Paper Citation


in Harvard Style

C. Schrempf O. and D. Hanebeck U. (2007). A STATE ESTIMATOR FOR NONLINEAR STOCHASTIC SYSTEMS BASED ON DIRAC MIXTURE APPROXIMATIONS . In Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO, ISBN 978-972-8865-84-9, pages 54-61. DOI: 10.5220/0001629600540061


in Bibtex Style

@conference{icinco07,
author={Oliver C. Schrempf and Uwe D. Hanebeck},
title={A STATE ESTIMATOR FOR NONLINEAR STOCHASTIC SYSTEMS BASED ON DIRAC MIXTURE APPROXIMATIONS},
booktitle={Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,},
year={2007},
pages={54-61},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001629600540061},
isbn={978-972-8865-84-9},
}


in EndNote Style

TY - CONF
JO - Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,
TI - A STATE ESTIMATOR FOR NONLINEAR STOCHASTIC SYSTEMS BASED ON DIRAC MIXTURE APPROXIMATIONS
SN - 978-972-8865-84-9
AU - C. Schrempf O.
AU - D. Hanebeck U.
PY - 2007
SP - 54
EP - 61
DO - 10.5220/0001629600540061