On improving sensitivity of the Kalman filter
Kybernetika, Tome 38 (2002) no. 4, pp. 425-443 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The impact of additive outliers on a performance of the Kalman filter is discussed and less outlier-sensitive modification of the Kalman filter is proposed. The improved filter is then used to obtain an improved smoothing algorithm and an improved state-space model parameters estimation.
The impact of additive outliers on a performance of the Kalman filter is discussed and less outlier-sensitive modification of the Kalman filter is proposed. The improved filter is then used to obtain an improved smoothing algorithm and an improved state-space model parameters estimation.
Classification : 62M20, 65C60, 93B35, 93E11
Keywords: outliers; smoothing algorithm; parameters estimation
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     url = {http://geodesic.mathdoc.fr/item/KYB_2002_38_4_a2/}
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Franěk, Petr. On improving sensitivity of the Kalman filter. Kybernetika, Tome 38 (2002) no. 4, pp. 425-443. http://geodesic.mathdoc.fr/item/KYB_2002_38_4_a2/

[1] Anderson B. D. O., Moore J. B.: Optimal Filtering. Prentice–Hall, Englewood Cliffs, N. J. 1979 | Zbl

[2] Box G. E. P., Tiao G. C.: Bayesian Inference in Statistical Analysis. Addison–Wesley, London 1973 | MR | Zbl

[3] Cantarelis N., Johnston F. R.: On-line variance estimation for the steady state Bayesian forecasting model. J. Time Ser. Analysis 3 (1982), 225–234 | DOI | MR | Zbl

[4] Cipra T.: Some modifications of recursive time series methods. In: ROBUST ’96 – Collection of Discussion Papers, Union of the Czech Mathematicians and Physicists, Praha 1997

[5] Cipra T., Rubio A.: Kalman filter with a non-linear non-gaussian observation relation. Trabajos de Estadistica 6 (1991), 111–119 | DOI | Zbl

[6] Cipra T., Rubio, A., Canal J. L.: Robust smoothing and forecasting procedures. Central European J. Oper. Research 1 (1992), 41–56

[7] Durbin J., Koopman S. J.: Time series analysis of non-Gaussian observations based on state space models from both classical and Bayesian perspectives. J. Roy. Statist. Soc. 62 (2000), 3–56 | DOI | MR

[8] Franěk P.: Kalman Filter. KPMS Seminair Works Series, MFF UK, Praha 1999

[9] Hosking J. R. M., Pai J. S., Wu L. S.+ Y.: An algorithm for estimating parameters of state-space models. Statist. Probab. Letters 28 (1996), 99–106 | DOI | MR | Zbl

[10] Jazwinski A. H.: Stochastic Processes and Filtering Theory. Academic Press, New York 1972 | Zbl

[11] Kalman R. E.: A new approach to linear filtering and prediction problems. Trans. Amer. Soc. Mech. Eng. – J. Basic Eng. 82 (1960), 35–45 | DOI

[12] Kitagawa G.: Non-Gaussian state-space modelling of nonstationary time series. J. Amer. Statist. Assoc. 82 (1987), 1032–1050 | MR | Zbl

[13] Kitagawa G.: Self-organizing state-space model. J. Amer. Statist. Assoc. 93 (1998), 1203-1215 | DOI

[14] Künsch H. R.: State space and hidden Markov models. In: Complex Stochastic Systems (O. E. Barndorf-Nielsen, D. R. Cox, and C. Klüppelberg, eds.), Chapman & Hall / CRC, Boca Raton 2001, pp. 109–173 | MR | Zbl

[15] Masreliez C. J.: Approximate non-Gaussian filtering with linear state and observation relations. IEEE Trans. Automat. Control AC-20 (1975), 107–110 | DOI | Zbl

[16] Masreliez C. J., Martin R. D.: Robust Bayesian estimation for the linear model and robustifying the Kalman filter. IEEE Trans. Automat. Control AC-22 (1975), 361–371 | DOI | MR

[17] Meinhold R. J., Singpurwalla N. Z.: Robustification of the Kalman filter. J. Amer. Statist. Assoc. 84 (1989), 479–486 | DOI | MR

[18] Ruckdeschel P.: Ansätze zur Robustifizierung des Kalman-filters. Doctoral Thesis, Bayreuth University, Bayreuth 2001 | MR | Zbl

[19] Tanizaki H.: Nonlinear and non-Gaussian state estimation: A quasi-optimal estimator. Comm. Statist. – Theory Methods 29 (2000), 2805–2834 | DOI | MR | Zbl