International Journal of Control, Automation, and Systems

Institute of Control, Robotics and Systems (제어로봇시스템학회)
권호 표지

New Algorithm for Recursive Estimation in Linear Discrete-Time Systems with Unknown Parameters

  • Shin Vladimir (Department of Mechatronics, Gwangju Institute of Science and Technology) ;
  • Ahn Jun-Il (Department of Mechatronics, Gwangju Institute of Science and Technology) ;
  • Kim Du-Yong (Department of Mechatronics, Gwangju Institute of Science and Technology)
  • Published : 2006.08.01
Download PDF
⟨ Previous Next ⟩

Abstract

The problem of recursive filtering far linear discrete-time systems with uncertainties is considered. A new suboptimal filtering algorithm is herein proposed. It is based on the fusion formula, which represents an optimal mean-square linear combination of local Kalman estimates with weights depending on cross-covariances between local filtering errors. In contrast to the optimal weights, the suboptimal weights do not depend on current measurements, and thus the proposed algorithm can easily be implemented in real-time. High accuracy and efficiency of the suboptimal filtering algorithm are demonstrated on the following examples: damper harmonic oscillator motion and vehicle motion constrained to a plane.

Keywords

References

  1. K. Watanabe, Adaptive Estimation and Control: Partitioning Approach, Prentice-Hall, New York, 1991
  2. D. G. Lainiotis, 'Partitioning: A unifying framework for adaptive systems, I: Estimation,' Proc. of IEEE, vol. 64, pp. 1126-1142, 1976
  3. D. T. Magill, 'Optimal adaptive estimation of sampled stochastic processes,' IEEE Trans. on Automation Control, vol. 10, no. 4, pp. 434-439, 1965 https://doi.org/10.1109/TAC.1965.1098191
  4. P. S. Maybeck, Stochastic Models, Estimation, and Control, vol. 2, Academic, New York, 1982
  5. D. G. Lainiotis, 'Partitioned linear estimation algorithm: Discrete case,' IEEE Trans. on Automation Control, vol. 20, no. 3, pp. 255-257, 1975 https://doi.org/10.1109/TAC.1975.1100907
  6. H. W. Sorenson, Parameter Estimation, Marcel Dekker, New York, 1980
  7. J. C. Spall (ed.), Bayesian Analysis of Time Series and Dynamic Models, Marcel Dekker, New York, 1988
  8. C. K. Chui and G. Chen, Kalman Filtering with Real-Time Applications, Springer-Verlag, Berlin, Heidelberg, 1987
  9. R. F. Stengel, Optimal Control and Estimation, Diver Publications, Inc., New York, 1994
  10. F. L. Lewis, Optimal Estimation with an Introduction to Stochastic Control Theory, John Wiley & Sons, New York, 1986
  11. A. Gelb, Applied Optimal Estimation, The M.I.T Press, Massachusetts, 1974
  12. Y. Bar-Shalom, X. Rong Li, and T. Kirubarajan, Estimation with Applications to Tracking and Navigation, John Wiley & Sons, New York, 2001
  13. D. P. Malladi and J. L. Speyer, 'A new approach to multiple model adaptive estimation,' Proc. of Conference Decision & Control, San Diego, California, USA, pp. 3460-3467, 1997
  14. J. R. Vasquez and P. S. Maybeck, 'Enhanced motion and sizing of bank in moving-bank MMAE,' IEEE Trans. on Aerospace and Electronic Systems, vol. 40, no. 3, pp. 770-779, 2004 https://doi.org/10.1109/TAES.2004.1337453
  15. P. D. Hanlon, and P. S. Maybeck, 'Interrelationship of single-filter and multiple-model adaptive algorithms,' IEEE Trans. on Aerospace and Electronic Systems, vol. 34, no. 3, pp. 934-946 1998 https://doi.org/10.1109/7.705899
  16. D. W. Kyger and P. S. Maybeck, 'Reducing lag in virtual displays using multiple model adaptive estimation,' IEEE Trans. on Aerospace and Electronic Systems, vol. 34, no. 4, pp. 1237-1248, 1998 https://doi.org/10.1109/7.722711
  17. F. Wang and V. Balakrishnan, 'Robust adaptive Kalman filters for linear time-varying systems with stochastic parametric uncertainties,' Proc. of Conference Decision & Control, San Diego, California, USA, pp. 440-444, 1999
  18. G. Chen and C. K. Chui, 'A modified adaptive Kalman filter for real-time applications,' IEEE Trans. on Aerospace and Electronic Systems, vol. 27, no. 1, pp. 149-154, 1991 https://doi.org/10.1109/7.68157
  19. Y. Bar-Shalom and L. Campo, 'The effect of the common process noise on the two-sensor fusedtrack covariance,' IEEE Trans. on Aerospace and Electronic Systems, vol. 22, no. 11, pp. 803-805, 1986 https://doi.org/10.1109/TAES.1986.310815