Kalman filter sensitivity with respect to parametric noises uncertainty

Nikola Madjarov; Ludmila Mihaylova

Kybernetika (1996)

  • Volume: 32, Issue: 3, page 307-322
  • ISSN: 0023-5954

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Madjarov, Nikola, and Mihaylova, Ludmila. "Kalman filter sensitivity with respect to parametric noises uncertainty." Kybernetika 32.3 (1996): 307-322. <http://eudml.org/doc/28668>.

@article{Madjarov1996,
author = {Madjarov, Nikola, Mihaylova, Ludmila},
journal = {Kybernetika},
keywords = {uncertain noise covariance; reduced sensitivity; self-tuning Kalman filter},
language = {eng},
number = {3},
pages = {307-322},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Kalman filter sensitivity with respect to parametric noises uncertainty},
url = {http://eudml.org/doc/28668},
volume = {32},
year = {1996},
}

TY - JOUR
AU - Madjarov, Nikola
AU - Mihaylova, Ludmila
TI - Kalman filter sensitivity with respect to parametric noises uncertainty
JO - Kybernetika
PY - 1996
PB - Institute of Information Theory and Automation AS CR
VL - 32
IS - 3
SP - 307
EP - 322
LA - eng
KW - uncertain noise covariance; reduced sensitivity; self-tuning Kalman filter
UR - http://eudml.org/doc/28668
ER -

References

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  1. V. Angelova N. Christov, P. Petkov, Perturbation and numerical analysis of Kalman filters, Automatics & Informatics (1993), 5/6, 19-20 (in Bulgarian). (1993) 
  2. K. Birmiwal, J. Shen, Optimal robust filtering, Statist. Decisions 11 (1993), 101-119. (1993) Zbl0790.62089MR1238479
  3. B. Carew, P. Bélanger, Identification of optimum filter steady-state gain for systems with unknown noise covariances, IEEE Trans. Automat. Control 18 (1973), 6, 582-587. (1973) MR0441498
  4. P. Gahinet, A. Laub, Computable bounds for the sensitivity of algebraic Riccati equation, SIAM J. Control Optim. 28 (1990), 6, 1461-1480. (1990) MR1075213
  5. R. E. Griffin, A. P. Sage, Large and small scale sensitivity analysis of optimum estimation algorithms, IEEE Trans. Automat. Control 13 (1968), 4, 320-329. (1968) MR0249176
  6. R. E. Griffin, A. P. Sage, Sensitivity analysis of discrete filtering and smoothing algorithms, AIAA J. 7 (1969), 10, 1890-1897. (1969) Zbl0193.15701
  7. N. S. Gritsenko, al, Adaptive estimation: a survey, Zarubezhnaya Radioelectronica (1983), 7, 3-27 and (1985), 3, 3-26 (in Russian). (1983) 
  8. A. H. Jazwinski, Stochastic Processes and Filtering Theory, Academic Press, New York 1970. (1970) Zbl0203.50101
  9. R. E. Kalman, A new approach to linear filtering and prediction problems, Trans. ASME, J. Basic Engrg. 82D (1960), 34-45. (1960) 
  10. C. Kenney, G. Hewer, The sensitivity of the algebraic and differential Riccati equations, SIAM J. Control Optim. 28 (1990), 1, 50-69. (1990) Zbl0695.65025MR1035972
  11. B. Kovačević Ž. Durović, S. Glavaški, On robust Kalman filtering, Internat. J. Control 56 (1992), 3, 547-562. (1992) MR1181998
  12. D. G. Lainiotis, F. L. Sims, Sensitivity analysis of discrete Kalman filters, Internat. J. Control 12 (1970), 4, 657-669. (1970) Zbl0199.49204
  13. N. Madjarov, L. Mihaylova, Sensitivity analysis of linear optimal stochastic observers, In: Proc. of the IEEE Internat. Conf. on Systems, Man and Cybernetics, Systems Engineering in the Service of Humans. Le Touquet, France 1993, pp. 482-487. (1993) 
  14. N. Madjarov, L. Mihaylova, Sensitivity of Kalman filters, Automatics & Informatics (1993), 1/2, 1-18 (in Bulgarian). (1993) Zbl0825.93814
  15. N. Madjarov, L. Mihaylova, Kalman filters under stochastic uncertainty, In: Proc. of the Tenth Internat. Conf. on Systems Engineering, Coventry 1994, 756-763. (1994) 
  16. C. J. Masreliez, R. D. Martin, Robust Bayesian estimation for the linear model and robustifying the Kalman filter, IEEE Trans. Automat. Control 22 (1977), 3, 361-371. (1977) Zbl0354.93054MR0453124
  17. A. I. Matasov, The Kalman-Bucy filter accuracy in the guaranteed parameter estimation problem with uncertain statistics, IEEE Trans. Automat. Control 39 (1994), 3, 635-639. (1994) Zbl0815.93081MR1268311
  18. V. Mathews, Z. Xie, A stochastic gradient adaptive filter with gradient adaptive step size, IEEE Trans. Sign. Process. 41 (1993), 6, 2075-2087. (1993) Zbl0775.93269
  19. R. K. Mehra, Approaches to adaptive filtering, IEEE Trans. Automat. Control 11 (1972), 5, 693-698. (1972) Zbl0261.93036MR0441510
  20. A. Moghaddamjoo, Approaches to adaptive Kalman filtering: a survey, Control Theory and Adv. Tech. 5 (1989), 1, 1-18. (1989) MR0991227
  21. J. M. Morris, The Kalman filter: A robust estimator for some classes of linear quadratic problems, IEEE Trans. Inform. Theory 22 (1976), 5, 526-534. (1976) Zbl0336.93037MR0419040
  22. T. Nishimura, Modeling errors in Kalman filters, In: Theory and Application of Kalman Filtering (C.T. Leondes, ed.), Chapter 4, 1970, AGARDograph No. 139. (1970) 
  23. M. Ogarkov, Methods for Statistical Estimation of Random Processes Parameters, Energoatomizdat, Moscow 1990 (in Russian). (1990) MR1192134
  24. R. V. Patel, M. Toda, Bounds on performance of non stationary continuous-time filters under modeling uncertainty, Automatica 20 (1984), 1, 117-120. (1984) 
  25. S. Sangsuk-Iam, T. Bullok, Analysis of continuous-time Kalman filtering under incorrect noise covariances, Automatica 24 (1988), 5, 659-669. (1988) MR0966690
  26. S. Sangsuk-Iam, T. Bullok, Analysis of discrete-time Kalman filtering under incorrect noise covariances, IEEE Trans. Automat. Control 35 (1990), 12, 1304-1308. (1990) MR1078143
  27. L. L. Scharf, D. L. Alspach, On stochastic approximation and an adaptive Kalman filter, In: Proc. of the IEEE Decision and Control Conference, 1972, pp. 253-257. (1972) 
  28. N. K. Sinha, Adaptive Kalman filtering using stochastic approximation, Electr. Letters 9 (1973), 819, 177-178. (1973) 
  29. N. K. Sinha, A. Tom, Adaptive state estimation systems with unknown noise covariances, Internat. J. Systems Sci. 8 (1977), 4, 377-384. (1977) 
  30. D. A. Stratton, R. F. Stengel, Robust Kalman filter design for predictive wind shear detection, IEEE Trans. Aerospace Electron. Systems 29 (1993), 4, 1185-1193. (1993) 
  31. M. Toda, R. V. Patel, Bounds on estimation errors of discrete-time filters under modeling uncertainty, IEEE Trans. Automat. Control 26 (1980), 6, 1115-1121. (1980) Zbl0485.93068MR0601493
  32. Ya. Z. Tsypkin, Foundations of Informational Identification Theory, Nauka, Moscow 1984 (in Russian). (1984) MR0783831
  33. W. Vetter, Matrix calculus operations and Taylor expansions, SIAM Rev. 15 (1973), 2, 352-369. (1973) Zbl0254.65033MR0340513
  34. L. Xie, Y. Soh, Robust Kalman filtering for uncertain systems, Systems Control Lett. 22 (1994), 123-129. (1994) Zbl0792.93118MR1261851

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