Outlier-Insensitive Kalman Filtering Using NUV Priors

TL;DR

This paper introduces an outlier-insensitive Kalman filter that models potential outliers with unknown variance priors, estimating them online to improve robustness against corrupted observations while maintaining optimal performance on clean data.

Contribution

It proposes a novel outlier-insensitive Kalman filtering method using NUV priors and online variance estimation, combining EM and AM techniques for improved robustness and efficiency.

Findings

Outperforms existing algorithms in MSE on outlier-affected data

Reverts to classic KF performance on clean data

AM approach reduces runtime by 40% compared to EM

Abstract

The Kalman filter (KF) is a widely-used algorithm for tracking the latent state of a dynamical system from noisy observations. For systems that are well-described by linear Gaussian state space models, the KF minimizes the mean-squared error (MSE). However, in practice, observations are corrupted by outliers, severely impairing the KFs performance. In this work, an outlier-insensitive KF is proposed, where robustness is achieved by modeling each potential outlier as a normally distributed random variable with unknown variance (NUV). The NUVs variances are estimated online, using both expectation-maximization (EM) and alternating maximization (AM). The former was previously proposed for the task of smoothing with outliers and was adapted here to filtering, while both EM and AM obtained the same performance and outperformed the other algorithms, the AM approach is less complex and thus requires 40 percentage less run-time. Our empirical study demonstrates that the MSE of our proposed outlier-insensitive KF outperforms previously proposed algorithms, and that for data clean of outliers, it reverts to the classic KF, i.e., MSE optimality is preserved