# Outlier-Insensitive Kalman Filtering: Theory and Applications

arXiv: https://arxiv.org/abs/2309.09505 · HTML: https://mlsanity.com/paper/2309.09505/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 50 references that are in the map.
- First posted on arXiv 18 Sep 2023.

## Builds on (most cited first, 6 of 6)

- [KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics](https://mlsanity.com/paper/2107.10043/) (2021)
- [RTSNet: Learning to Smooth in Partially Known State-Space Models (Preprint)](https://mlsanity.com/paper/2110.04717/) (2021)
- [Generalized Kalman Smoothing: Modeling and Algorithms](https://mlsanity.com/paper/1609.06369/) (2016)
- [Sparse/Robust Estimation and Kalman Smoothing with Nonsmooth Log-Concave Densities: Modeling, Computation, and Theory](https://mlsanity.com/paper/1301.4566/) (2013)
- [Outlier-Insensitive Kalman Filtering Using NUV Priors](https://mlsanity.com/paper/2210.06083/) (2022)
- [Robust Maximum Correntropy Kalman Filter](https://mlsanity.com/paper/2302.02694/) (2023)

## Abstract (arXiv)

State estimation of dynamical systems from noisy observations is a fundamental task in many applications. It is commonly addressed using the linear Kalman filter (KF), whose performance can significantly degrade in the presence of outliers in the observations, due to the sensitivity of its convex quadratic objective function. To mitigate such behavior, outlier detection algorithms can be applied. In this work, we propose a parameter-free algorithm which mitigates the harmful effect of outliers while requiring only a short iterative process of the standard update step of the KF. To that end, we model each potential outlier as a normal process with unknown variance and apply online estimation through either expectation maximization or alternating maximization algorithms. Simulations and field experiment evaluations demonstrate competitive performance of our method, showcasing its robustness to outliers in filtering scenarios compared to alternative algorithms.