Research map / Probabilistic and scientific modeling / Uncertainty and Gaussian processes
Outlier-robust Kalman Filtering through Generalised Bayes
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Proposes WoLF, a generalised-Bayes weighted-likelihood update for Kalman, extended and ensemble Kalman filters that down-weights outlier measurements, giving closed-form robust filtering at Kalman-filter cost.
Problem
Online Bayesian filtering in state-space models is corrupted by outlier measurements and misspecified measurement models, while existing robust filters are iterative (VB) or require many particles, making them slow.
Approach
Replace the measurement log-likelihood in the Bayesian update with a data-dependent weighted log-likelihood (weight W^2 from the innovation, e.g. IMQ or Mahalanobis thresholding), within generalised Bayes; for Gaussian likelihoods this stays conjugate, so the update is closed-form and provably outlier-robust (bounded posterior influence function).
Key results
- On 2D tracking, WoLF-IMQ and WoLF-MD estimate the true state more closely than KF and other robust baselines, at about 1.0x KF running time versus 2.0x-5.3x for Wang et al. and Agamennoni et al.
- On corrupted UCI MLP regression, WoLF variants are the only methods in the lower-left quadrant, i.e. lower RMedSE and lower running time than online gradient descent (Adam)
- On Lorenz96 with outliers, WoLF-hard and WoLF-soft are more robust to the threshold c than the Huberised EnKF
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use WoLF-IMQ instead of the KF | KF · 2D tracking, Student observations | state estimation error | Helped |
| Use WoLF-MD instead of the KF | KF · 2D tracking, Student observations | state estimation error | Helped |
| Use WoLF-IMQ instead of the KF | KF · 2D tracking, mixture observations | state estimation error | Helped |
| Use WoLF-MD instead of the KF | KF · 2D tracking, mixture observations | state estimation error | Helped |
| Use WoLF-IMQ instead of OGD | Online MLP regression on corrupted UCI datasets · Corrupted UCI datasets | RMedSE | Helped |
| Use WoLF-IMQ instead of OGD | Online MLP regression on corrupted UCI datasets · Corrupted UCI datasets | running time per step | Helped |
| Use WoLF-MD instead of OGD | Online MLP regression on corrupted UCI datasets · Corrupted UCI datasets | RMedSE | Helped |
| Use WoLF-MD instead of OGD | Online MLP regression on corrupted UCI datasets · Corrupted UCI datasets | running time per step | Helped |
| Use WoLF-Hard instead of Huberised EnKF | EnKF · Lorenz96 | in-state RMSE | No clear effect |
| Use WoLF-Hard or WoLF-Soft rather than Huberised EnKF when varying threshold c | EnKF · Lorenz96 | in-state RMSE | Helped |
Surprising findings
- The WoLF-MD heavy tail on the mixture-observation tracking variant (lowest median error but largest tail)
Limitations
- Not robust to outliers in the state process
- Assumes known measurement covariance R_t and known dynamics covariance Q_t
- Assumes a unimodal (Gaussian) posterior
Experimental setup
Datasets: UCI regression datasets (corrupted with uniform outliers) simulated 2D tracking data simulated Lorenz96 data
Benchmarks: 2D object tracking RMSE UCI regression RMedSE Lorenz96 in-state RMSE
Metrics: scaled RMSE median prediction RMSE (RMedSE) relative running time in-state RMSE L_t
Baselines: Bernoulli KF (Wang et al.) inverse-Wishart filter (Agamennoni et al.) Huberised EnKF standard KF/EKF/EnKF Adam-based online gradient descent
Builds on: Kalman filter extended Kalman filter ensemble Kalman filter generalised Bayes Huberised Kalman filtering
Closest papers by meaning
- Predictively-Oriented Kalman Filtering (NeurIPS 2026 · similarity 0.90)
- Implicit Maximum a Posteriori Filtering via Adaptive Optimization (ICLR 2024 · similarity 0.88)
- Generalised Bayesian Filtering via Sequential Monte Carlo (NeurIPS 2020 · similarity 0.87)
- Outlier Robust Mean Estimation with Subgaussian Rates via Stability (NeurIPS 2020 · similarity 0.86)
- The Kernel Kalman Rule — Efficient Nonparametric Inference with Recursive Least Squares (AAAI 2017 · similarity 0.86)
- Nonlinear Filtering with Brenier Optimal Transport Maps (ICML 2024 · similarity 0.85)
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