Robust Kalman filter and its application in time series analysis

Tomáš Cipra; Ma.Rosario Romera Ayllón

Kybernetika (1991)

  • Volume: 27, Issue: 6, page 481-494
  • ISSN: 0023-5954

How to cite

top

Cipra, Tomáš, and Romera Ayllón, Ma.Rosario. "Robust Kalman filter and its application in time series analysis." Kybernetika 27.6 (1991): 481-494. <http://eudml.org/doc/27447>.

@article{Cipra1991,
author = {Cipra, Tomáš, Romera Ayllón, Ma.Rosario},
journal = {Kybernetika},
keywords = {time series analysis; robustification of Kalman filter; approximative recursive formulas; robust estimation; exact recursive formulas; steady model; AR(1) model; simulation study; strong consistency; autoregressive parameter},
language = {eng},
number = {6},
pages = {481-494},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Robust Kalman filter and its application in time series analysis},
url = {http://eudml.org/doc/27447},
volume = {27},
year = {1991},
}

TY - JOUR
AU - Cipra, Tomáš
AU - Romera Ayllón, Ma.Rosario
TI - Robust Kalman filter and its application in time series analysis
JO - Kybernetika
PY - 1991
PB - Institute of Information Theory and Automation AS CR
VL - 27
IS - 6
SP - 481
EP - 494
LA - eng
KW - time series analysis; robustification of Kalman filter; approximative recursive formulas; robust estimation; exact recursive formulas; steady model; AR(1) model; simulation study; strong consistency; autoregressive parameter
UR - http://eudml.org/doc/27447
ER -

References

top
  1. K. K. Aase, Recursive estimation in non-linear time series models of autoregressive type, J. Roy. Statist. Soc. Ser. B 45 (1983), 228-237. (1983) Zbl0524.62085MR0721750
  2. B. D. O. Anderson, J. B. Moore, Optimal Filtering, Prentice-Hall, Englewood Cliffs, New Jersey 1979. (1979) Zbl0688.93058
  3. A. E. Bryson, J. C. Ho, Applied Optimal Control, J. Wiley, New York 1975. (1975) MR0446628
  4. K. Campbell, Recursive computation of M-estimates for the parameters of a finite autoregressive process, Ann. Statist. 10 (1982), 442-453. (1982) Zbl0492.62076MR0653519
  5. J. E. Englund, Multivariate Recursive M-estimators of Location and Scatter for Dependent Sequences, Research Report, University of Lund and Lund Institute of Technology 1988. (1988) 
  6. A. A. Ershov, R. S. Liptser, Robust Kalman filter in discrete time, Automat. Remote Control 39 (1978), 359-367. (1978) Zbl0417.93070
  7. E. J. Hannan, Multiple Time Series, J. Wiley, New York 1970. (1970) Zbl0211.49804MR0279952
  8. P. J. Harrison, C. F. Stevens, Bayesian forecasting, J. Roy. Statist. Soc. Ser. B 38 (1976), 205-247. (1976) Zbl0349.62062MR0655429
  9. U. Holst, Convergence of a recursive stochastic algorithm with m-dependent observations, Scand. J. Statist. 7 (1980), 207-215. (1980) Zbl0455.62065MR0605992
  10. U. Hoist, Convergence of a recursive robust algorithm with strongly regular observations, Stochastic Process. Appl. 16 (1984), 305-320. (1984) MR0723851
  11. P. J. Huber, Robust Statistics, J. Wiley, New York 1981. (1981) Zbl0536.62025MR0606374
  12. R. D. Martin, Robust estimation for time series autoregressions, In: Robustness in Statistics (R. L. Launer and G. N. Wilkinson, eds.), Academic Press, New York 1979, pp. 147-176. (1979) 
  13. C. J. Masreliez, Approximate non-Gaussian filtering with linear state and observation relations, IEEE Trans. Automat. Control AC-20 (1975), 107-110. (1975) Zbl0298.93018
  14. C. J. Masreliez, R. D. Martin, Robust Bayesian estimation for the linear model and robustifying the Kalman filter, IEEE Trans. Automat. Control AC-22 (1977), 361 - 371. (1977) Zbl0354.93054MR0453124
  15. R. J. Meinhold, N. D. Singpurwalla, Robustification of Kalman filter models, J. Amer. Statist. Assoc. 84 (1989), 479-486. (1989) MR1010336
  16. M. Pantel, Adaptive Verfahren der stochastischen Approximation, Dissertation, Universitiit Essen 1979. (1979) 
  17. D. Peňa, J. Guttman, Optimal collapsing of mixture distributions in robust recursive estimation, Comm. Statist. Theory Methods 18 (1989), 817-833. (1989) MR1001623
  18. B. T. Polyak, Ya. Z. Tsypkin, Adaptive estimation algorithms: convergence, optimality, stability (in Russian), Avtomat. Telemekh. (1979), 3, 71-84. (1979) MR0544876
  19. B. T. Polyak, Ya. Z. Tsypkin, Optimal methods of estimation of autoregressive parameters under incomplete information (in Russian), Tekh. kibernet. (1983), 1, 118-126. (1983) MR0736269
  20. H. Robbins, D. Siegmund, A convergence theorem for non negative almost supermartingales and some applications, In: Optimizing Methods in Statistics (J. S. Rustagi, ed.), Academic Press, New York 1971, pp. 233 - 257. (1971) Zbl0286.60025MR0343355
  21. L. D. Servi, Y. C. Ho, Recursive estimation in the presence of uniformly distributed measurement noise, IEEE Trans. Automat. Control AC-26 (1981), 563-565. (1981) Zbl0475.93065MR0613583
  22. N. Stockinger, R. Dutter, Robust Time Series Analysis: A Survey, Supplement to Kybernetika vol. 23 (1987). (1987) Zbl0652.62088MR0921397
  23. Yu. Sh. Verulava, Convergence of a stochastic approximation algorithm for estimating an autoregressive parameter (in Russian), Avtomat. Telemekh. (1981), 7, 115-119. (1981) MR0647669

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.