Outlier-Insensitive Kalman Filtering Using NUV Priors

• URL: http://arxiv.org/abs/2210.06083v1
• Date: Wed, 12 Oct 2022 11:00:13 GMT
• Title: Outlier-Insensitive Kalman Filtering Using NUV Priors
• Authors: Shunit Truzman, Guy Revach, Nir Shlezinger, and Itzik Klein
• Abstract summary: In practice, observations are corrupted by outliers, severely impairing the Kalman filter (KF)s performance. In this work, an outlier-insensitive KF is proposed, where 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 robustness (AM)
• Score: 24.413595920205907
• License: http://creativecommons.org/licenses/by/4.0/
• 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

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