Skip to main content
SpringerLink
Log in

Kalman filter with hypothesis testing: A tool for estimating uncertain parameters

  • Published:
Circuits, Systems and Signal Processing Aims and scope Submit manuscript

Abstract

In this paper we present a simple and practical algorithm for the estimation of uncertain parameters of linear systems. The uncertainty is twofold, involving random observation noise, and possible jumps in the parameter values. The jumps may occur at unknown points in time, and are of unknown magnitudes and directions. The algorithm is based on the Kalman filter, with a single-sample hypothesis test, which is used to employ a three-state decision rule (yes, no, maybe). The “maybe” choice invokes a fading memory Kalman filter. The overall algorithm contains the constant parameter filter, fading memory filter, and the set of tests and rules that enable it to switch back and forth between the two filters. Application examples are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. L. Aravena, Finite memory estimation: Moving window Kalman filter,Proc. 2nd Symposium of ACCA, Santiago, Chile, 1984.

  2. B. R. Barmish,New Tools for Robustness of Linear Systems, Macmillan Publishing Company, New York 1994.

    Google Scholar 

  3. A. Benveniste, Advanced methods of change detection: An overview,Detection of Abrupt Changesin Signals and Dynamical Systems, LNCIS no. 77, 77–96, 1986.

    Google Scholar 

  4. S. P. Boyd, A note on parametric and nonparametric uncertainties in control systems,Proc. Amer. Contr. Conf., 1847–1849, 1986.

  5. L. Campo, P. Mookerjee, and Y. Bar-Shalom, State estimation for systems with sojourn-time-dependent Markov model switching,IEEE Trans. Automat. Contr., 238–243, Feb. 1991.

  6. H. Chapellat, S. P. Bhattacharyya, and M. Daleh, Robust stability under structured and unstructured perturbations,IEEE Trans. Automat. Contr., vol. AC-35, 1100–1108, 1990.

    Google Scholar 

  7. F. N. Chowdhury, On-line detection and estimation of parameter jumps, Ph.D dissertation, Louisiana State University, Dec. 1988.

  8. F. N. Chowdhury, Neural networks for stochastic system identification,Proc. World Congress on Neural Networks, vol. IV, 684–689, Portland, OR, July 1993.

    Google Scholar 

  9. F. N. Chowdhury, On-line fault detection in multi-output systems using Kalman filter and neural network,Proc. Amer. Contr. Conf., vol. 2, 1729–1731, June 1994.

    Google Scholar 

  10. F. N. Chowdhury, J. A. Christensen, and J. L. Aravena, Power system fault detection and state estimation using Kalman filter and hypothesis testing,IEEE Trans. Power Delivery, vol. 6, no. 3, 1024–1029, July 1991.

    Google Scholar 

  11. P. W. Davall, and G. A. Yeung, A software design for a computer based impedance relay for transmission line protection,IEEE Trans. PAS, vol. PAS-99, no. 1, 235–245, Jan./Feb. 1980.

    Google Scholar 

  12. M. Fu, A class of weak Kharitonov regions for robust stability of linear uncertain systems,IEEE Trans. Automat. Contr., vol. AC-36, 975–979, 1991.

    Google Scholar 

  13. G. C. Goodwin and R. H. Middleton, Adaptive control of time varying linear systems,IEEE Trans. Automat. Contr., vol. AC-33, 150–155, 1988.

    Google Scholar 

  14. A. Jerbi, E. W. Kamen, and J. F. Dorsey, Construction of a robust adaptive regulator for time-varying discrete time systems,Int. J. of Adaptive Control and Signal Processing, vol. 7, no. 1, 1–12, Jan.–Feb. 1993.

    Google Scholar 

  15. L. H. Keel, S. P. Bhattacharyya, and Jo W. Howze, Robust control with structured perturbations,IEEE Trans. Automat. Contr., 68–78, Jan. 1988.

  16. G. Lorden, Procedures for reacting to a change in distribution,Annals of Mathematical Statistics, vol. 42, no. 6, 1897–1908, 1971.

    Google Scholar 

  17. L. Mili, T. van Custem, and M. Ribbens-Pavella, Decision theory for fault diagnosis in electric power systems,Automatica, vol. 23, no. 6, 335–353, 1987.

    Google Scholar 

  18. D. M. Perriot-Mathonna, Recursive stochastic estimation of parameters subject to random jumps,IEEE Trans. Automat. Contr., 962–969, Nov. 1984.

  19. L. Sheng, Discrete time adaptive control of deterministic fast time-varying systems,IEEE Trans. Automat. Contr., vol. AC-32, 444–447, 1987.

    Google Scholar 

  20. A. N. Shirayev, On optimum methods in quickest detection problems,Theory of Probability and its Applications, vol. 8, no. 1, 22–46, 1963.

    Google Scholar 

  21. E. Wahnon, Tracking algorithm designed by local asymptotic approach for sequential detection of parameter jumps in linear systems,IEEE Trans. Automat. Contr., 440–443, Apr. 1990.

  22. A. S. Willsky, Detection of abrupt changes in dynamic systems, inDetection of Abrupt Changesin Signals and Dynamical Systems, LNCIS no. 77, Springer-Verlag, Berlin and New York, 1986.

    Google Scholar 

  23. E. Yaz, Generalized uncertainty threshold principle for discrete-time linear systems with jump Markov parameters and white multiplicative noise,IEEE Trans. Automat. Contr., 942–944, Aug. 1990.

  24. D. S. Yoo and M. J. Chung, A variable structure control with simple adaptation laws for upper bounds on the norm of the uncertainties,IEEE Trans. Automat. Contr., vol. AC-37, 860–864, 1992.

    Google Scholar 

  25. R. C. Younce and C. E. Rohrs, Identification with nonparametric uncertainty,IEEE Trans. Automat. Contr., vol. AC-37, 715–728, 1992.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Michigan Technological University, 49931, Houghton, Michigan

    Fahmida N. Chowdhury

Authors
  1. Fahmida N. Chowdhury
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chowdhury, F.N. Kalman filter with hypothesis testing: A tool for estimating uncertain parameters. Circuits Systems and Signal Process 15, 291–311 (1996). https://doi.org/10.1007/BF01182588

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01182588

Keywords

Search

Navigation