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

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

2012-04-16

arxiv.org/abs/1204.3358v1

Mathematics

Statistics Theory

27 pages, 12 figures, 2 tables

Scientific paper

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[01,10], 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.

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