# Outlier-robust Kalman Filtering through Generalised Bayes

arXiv: https://arxiv.org/abs/2405.05646 · HTML: https://mlsanity.com/paper/2405.05646/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 69 references that are in the map.
- First posted on arXiv 9 May 2024.

## Builds on (most cited first, 28 of 28)

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [A General Framework for Updating Belief Distributions](https://mlsanity.com/paper/1306.6430/) (2013)
- [The Bayesian Learning Rule](https://mlsanity.com/paper/2107.04562/) (2021)
- [Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing It](https://mlsanity.com/paper/1412.3730/) (2014)
- [Concentration of tempered posteriors and of their variational approximations](https://mlsanity.com/paper/1706.09293/) (2017)
- [Minimum Stein Discrepancy Estimators](https://mlsanity.com/paper/1906.08283/) (2019)
- [Robust Generalised Bayesian Inference for Intractable Likelihoods](https://mlsanity.com/paper/2104.07359/) (2021)
- [Fast and Simple Natural-Gradient Variational Inference with Mixture of Exponential-family Approximations](https://mlsanity.com/paper/1906.02914/) (2019)
- [A Stein variational Newton method](https://mlsanity.com/paper/1806.03085/) (2018)
- [Assigning a value to a power likelihood in a general Bayesian model](https://mlsanity.com/paper/1701.08515/) (2017)
- [Martingale posterior distributions](https://mlsanity.com/paper/2103.15671/) (2021)
- [Robust Bayesian inference via coarsening](https://mlsanity.com/paper/1506.06101/) (2015)
- [Stein Point Markov Chain Monte Carlo](https://mlsanity.com/paper/1905.03673/) (2019)
- [Optimal Thinning of MCMC Output](https://mlsanity.com/paper/2005.03952/) (2020)
- [Online Natural Gradient as a Kalman Filter](https://mlsanity.com/paper/1703.00209/) (2017)
- [Low-rank extended Kalman filtering for online learning of neural networks from streaming data](https://mlsanity.com/paper/2305.19535/) (2023)
- [Doubly Robust Bayesian Inference for Non-Stationary Streaming Data with β-Divergences](https://mlsanity.com/paper/1806.02261/) (2018)
- [The Ensemble Kalman Filter: A Signal Processing Perspective](https://mlsanity.com/paper/1702.08061/) (2017)
- [Robust and Scalable Bayesian Online Changepoint Detection](https://mlsanity.com/paper/2302.04759/) (2023)
- [Efficient Online Bayesian Inference for Neural Bandits](https://mlsanity.com/paper/2112.00195/) (2021)
- [General Bayesian Loss Function Selection and the use of Improper Models](https://mlsanity.com/paper/2106.01214/) (2021)
- [Generalised Bayesian Inference for Discrete Intractable Likelihood](https://mlsanity.com/paper/2206.08420/) (2022)
- [Robust and Conjugate Gaussian Process Regression](https://mlsanity.com/paper/2311.00463/) (2023)
- [Robustifying likelihoods by optimistically re-weighting data](https://mlsanity.com/paper/2303.10525/) (2023)
- [The limited-memory recursive variational Gaussian approximation (L-RVGA)](https://mlsanity.com/paper/2303.14195/) (2023)
- [Implicit Maximum a Posteriori Filtering via Adaptive Optimization](https://mlsanity.com/paper/2311.10580/) (2023)
- [Robust Inference for State-Space Models with Skewed Measurement Noise](https://mlsanity.com/paper/1503.06606/) (2015)
- [Robust Bayesian Inference for Moving Horizon Estimation](https://mlsanity.com/paper/2210.02166/) (2022)

## Built on by (most cited first, 21 of 21)

- [On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph Learning](https://mlsanity.com/paper/2502.10818/) (2025)
- [Bayesian Online Natural Gradient (BONG)](https://mlsanity.com/paper/2405.19681/) (2024)
- [Robust and Conjugate Spatio-Temporal Gaussian Processes](https://mlsanity.com/paper/2502.02450/) (2025)
- [On the Robustness of Kernel Goodness-of-Fit Tests](https://mlsanity.com/paper/2408.05854/) (2024)
- [A unifying framework for generalised Bayesian online learning in non-stationary environments](https://mlsanity.com/paper/2411.10153/) (2024)
- [Martingale Posterior Neural Networks for Fast Sequential Decision Making](https://mlsanity.com/paper/2506.11898/) (2025)
- [Robust, Online, and Adaptive Decentralized Gaussian Processes](https://mlsanity.com/paper/2509.18011/) (2025)
- [Multi-Output Robust and Conjugate Gaussian Processes](https://mlsanity.com/paper/2510.26401/) (2025)
- [Bayesian Natural Gradient Fine-Tuning of CLIP Models via Kalman Filtering](https://mlsanity.com/paper/2511.01694/) (2025)
- [Robust Bayesian Optimisation with Unbounded Corruptions](https://mlsanity.com/paper/2511.15315/) (2025)
- [Tempering the Bayes Filter towards Improved Model-Based Estimation](https://mlsanity.com/paper/2512.02823/) (2025)
- [Outlier-robust Diffusion Posterior Sampling for Bayesian Inverse Problems](https://mlsanity.com/paper/2602.02045/) (2026)
- [A Predictive View on Streaming Hidden Markov Models](https://mlsanity.com/paper/2604.09208/) (2026)
- [One Filters All: A Generalist Filter for State Estimation](https://mlsanity.com/paper/2509.20051/) (2025)
- [A theoretical framework for M-posteriors: frequentist guarantees and robustness properties](https://mlsanity.com/paper/2510.01358/) (2025)
- [Prequential posteriors](https://mlsanity.com/paper/2511.17721/) (2025)
- [A Robust State Filter Against Unmodeled Process And Measurement Noise](https://mlsanity.com/paper/2511.19157/) (2025)
- [Active Bayesian Inference for Robust Control under Sensor False Data Injection Attacks](https://mlsanity.com/paper/2604.11410/) (2026)
- [AdaKoop: Efficient Modeling of Nonlinear Dynamics from Nonstationary Data Streams with Koopman Operator Regression](https://mlsanity.com/paper/2606.04930/) (2026)
- [Structured Noise Adaptation for Sequential Bayesian Filtering with Embedded Latent Transfer Operators](https://mlsanity.com/paper/2606.14195/) (2026)
- [Adversarial observations in probabilistic State-Space Models for robust Reinforcement Learning](https://mlsanity.com/paper/2606.20880/) (2026)

## Abstract (arXiv)

We derive a novel, provably robust, and closed-form Bayesian update rule for online filtering in state-space models in the presence of outliers and misspecified measurement models. Our method combines generalised Bayesian inference with filtering methods such as the extended and ensemble Kalman filter. We use the former to show robustness and the latter to ensure computational efficiency in the case of nonlinear models. Our method matches or outperforms other robust filtering methods (such as those based on variational Bayes) at a much lower computational cost. We show this empirically on a range of filtering problems with outlier measurements, such as object tracking, state estimation in high-dimensional chaotic systems, and online learning of neural networks.