# Outlier-Insensitive Kalman Filtering Using NUV Priors

arXiv: https://arxiv.org/abs/2210.06083 · HTML: https://mlsanity.com/paper/2210.06083/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 26 references that are in the map.
- First posted on arXiv 12 Oct 2022.

## Builds on (most cited first, 3 of 3)

- [KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics](https://mlsanity.com/paper/2107.10043/) (2021)
- [Generalized Kalman Smoothing: Modeling and Algorithms](https://mlsanity.com/paper/1609.06369/) (2016)
- [Uncertainty in Data-Driven Kalman Filtering for Partially Known State-Space Models](https://mlsanity.com/paper/2110.04738/) (2021)

## Built on by (most cited first, 1 of 1)

- [Outlier-Insensitive Kalman Filtering: Theory and Applications](https://mlsanity.com/paper/2309.09505/) (2023)

## Abstract (arXiv)

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