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

TL;DR

This paper develops robust Kalman filters and smoothers capable of handling propagating and non-propagating outliers, improving tracking accuracy in noisy, outlier-prone environments such as GPS-based vehicle tracking.

Contribution

It introduces new distributionally robust recursive filters and smoothers, extending classical Kalman filtering to better handle outliers, with specialized versions for different outlier types.

Findings

Robust filters outperform classical Kalman filters in outlier scenarios.

Specialized filters effectively handle non-propagating outliers.

Simulation results show improved efficiency over existing methods.

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[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.