On Nonlinearity Measuring Aspects of Stochastic Integration Filter

Jindřich Havlík, Ondřej Straka, Jindřich Duník, Jiří Ajgl

Abstract

The paper deals with Bayesian state estimation of nonlinear stochastic dynamic systems. The focus is aimed at the stochastic integration filter, which is based on a stochastic integration rule. It is shown that the covariance matrix of the integration error calculated as a byproduct of the rule can be used as a measure of nonlinearity. The measure informs the user about validity of the assumptions of Gaussianity, which is adopted by the stochastic integration filter. It is also demonstrated how to use this information for a prediction of the number of remaining iterations of the rule. The paper also focuses on utilization of the integration error covariance matrix for improving estimates of the mean square error of the estimates, which is produced by the filter.

References

  1. Arasaratnam, I. and Haykin, S. (2009). Cubature Kalman Filters. IEEE Transactions on Automatic Control, 54(6):1254-1269.
  2. Arasaratnam, I., Haykin, S., and Elliott, R. J. (2007). Discrete-time nonlinear filtering algorithms using Gauss-Hermite quadrature. Proceedings of the IEEE, 95(5):953-977.
  3. Bates, D. M. and Watts, D. G. (1988). Nonlinear Regression Analysis and Its Applications. John Wiley & Sons.
  4. Doucet, A., De Freitas, N., and Gordon, N. (2001). Sequential Monte Carlo Methods in Practice, chapter An Introduction to Sequential Monte Carlo Methods. Springer. (Ed. Doucet A., de Freitas N., and Gordon N.).
  5. Duník, J., Straka, O., andS? imandl, M. (2013a). Nonlinearity and non-Gaussianity measures for stochastic dynamic systems. In Proceedings of the 16th International Conference on Information Fusion, Istanbul.
  6. Duník, J., Straka, O., and S? imandl, M. (2013b). Stochastic integration filter. IEEE Transactions on Automatic Control, 58(6):1561-1566.
  7. Genz, A. and Monahan, J. (1998). Stochastic integration rules for infinite regions. SIAM Journal on Scientific Computing, 19(2):426-439.
  8. Ito, K. and Xiong, K. (2000). Gaussian Filters for Nonlinear Filtering Problems. IEEE Transactions on Automatic Control, 45(5):910-927.
  9. Julier, S. J. and Uhlmann, J. K. (2004). Unscented filtering and nonlinear estimation. IEEE Review, 92(3):401- 421.
  10. Kramer, S. C. and Sorenson, H. W. (1988). Recursive Bayesian estimation using piece-wise constant approximations. Automatica, 24(6):789-801.
  11. Li, X. R. (2012). Measure of nonlinearity for stochastic systems. In Proceedings of the 15th International Conference on Information Fusion, Singapore.
  12. Mallick, M. (2004). Differential geometry measures of nonlinearity with applications to ground target tracking. In Proceedings of the 7th International Conference on Information Fusion, Stockholm, Sweden.
  13. Nørgaard, M., Poulsen, N. K., and Ravn, O. (2000). New developments in state estimation for nonlinear systems. Automatica, 36(11):1627-1638.
  14. Ristic, B., Arulampalam, S., and Gordon, N. (2004). Beyond the Kalman filter: Particle filters for tracking applications. Artech House.
  15. Sorenson, H. W. (1974). On the development of practical nonlinear filters. Information Sciences, 7:230-270.
Download


Paper Citation


in Harvard Style

Havlík J., Straka O., Duník J. and Ajgl J. (2016). On Nonlinearity Measuring Aspects of Stochastic Integration Filter . In Proceedings of the 13th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, ISBN 978-989-758-198-4, pages 353-361. DOI: 10.5220/0005983903530361


in Bibtex Style

@conference{icinco16,
author={Jindřich Havlík and Ondřej Straka and Jindřich Duník and Jiří Ajgl},
title={On Nonlinearity Measuring Aspects of Stochastic Integration Filter},
booktitle={Proceedings of the 13th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},
year={2016},
pages={353-361},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005983903530361},
isbn={978-989-758-198-4},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 13th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,
TI - On Nonlinearity Measuring Aspects of Stochastic Integration Filter
SN - 978-989-758-198-4
AU - Havlík J.
AU - Straka O.
AU - Duník J.
AU - Ajgl J.
PY - 2016
SP - 353
EP - 361
DO - 10.5220/0005983903530361