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Robust Kalman tracking and smoothing with propagating and non-propagating outliers

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  • Peter Ruckdeschel
  • Bernhard Spangl
  • Daria Pupashenko

Abstract

A common situation in filtering where classical Kalman filtering does not perform particularly well is tracking in the presence of propagating outliers. This calls for robustness understood in a distributional sense, i.e.; we enlarge the distribution assumptions made in the ideal model by suitable neighborhoods. Based on optimality results for distributional-robust Kalman filtering from Ruckdeschel (Ansätze zur Robustifizierung des Kalman-Filters, vol 64, 2001 ; Optimally (distributional-)robust Kalman filtering, arXiv: 1004.3393, 2010a ), we propose new robust recursive filters and smoothers designed for this purpose as well as specialized versions for non-propagating outliers. We apply these procedures in the context of a GPS problem arising in the car industry. To better understand these filters, we study their behavior at stylized outlier patterns (for which they are not designed) and compare them to other approaches for the tracking problem. Finally, in a simulation study we discuss efficiency of our procedures in comparison to competitors. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Peter Ruckdeschel & Bernhard Spangl & Daria Pupashenko, 2014. "Robust Kalman tracking and smoothing with propagating and non-propagating outliers," Statistical Papers, Springer, vol. 55(1), pages 93-123, February.
    • Handle: RePEc:spr:stpapr:v:55:y:2014:i:1:p:93-123
    DOI: 10.1007/s00362-012-0496-4
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    References listed on IDEAS

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    1. R. H. Shumway & D. S. Stoffer, 1982. "An Approach To Time Series Smoothing And Forecasting Using The Em Algorithm," Journal of Time Series Analysis, Wiley Blackwell, vol. 3(4), pages 253-264, July.
    2. Ruckdeschel, Peter, 2000. "Robust Kalman filtering," SFB 373 Discussion Papers 2000,59, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    3. Birmiwal Kailash & Papantoni-Kazakos P., 1994. "Outlier Resistant Prediction For Stationary Processes," Statistics & Risk Modeling, De Gruyter, vol. 12(4), pages 395-428, April.
    4. Fried, Roland & Bernholt, Thorsten & Gather, Ursula, 2006. "Repeated median and hybrid filters," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2313-2338, May.
    5. Sarah Gelper & Roland Fried & Christophe Croux, 2010. "Robust forecasting with exponential and Holt-Winters smoothing," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(3), pages 285-300.
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    Cited by:

    1. Marczak, Martyna & Proietti, Tommaso & Grassi, Stefano, 2018. "A data-cleaning augmented Kalman filter for robust estimation of state space models," Econometrics and Statistics, Elsevier, vol. 5(C), pages 107-123.

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