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Predictively-Oriented Kalman Filtering

NeurIPS 2026 · Probabilistic and scientific modeling › Uncertainty and Gaussian processes · approach: Sparse variational Gaussian processes · 0 citations (OpenAlex)

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Proposes PrO-Kalman filters, a hyper-parameter-free post-Bayesian filter that uses predictively oriented posteriors with Gaussian variational approximation and difference-of-convex optimisation to handle misspecified dynamics and measurement models.

Problem

Online filtering in nonlinear state-space models becomes overconfident when the dynamical model, measurement model, or both are misspecified.

Approach

Replaces the Bayesian log-likelihood loss with the predictively oriented loss -log∫p(y|x)q(x)dx, approximates the update with a Gaussian variational family, and solves it via difference-of-convex programming, yielding an EKF-like update that inflates covariance data-dependently under misspecification.

Key results

• On 2D tracking with outlier-only misspecification, WoLF-IMQ achieves the lowest positional MSE, while PrO-KF is preferred under systematic and maneuver misspecification.
• On Lorenz96, outlier-robust filters Wang-EKF and WoLF-MD underperform the standard EKF under systematic misspecification, whereas PrO is particularly beneficial.
• Calculations for PrO were reported to be 10-20x slower than the standard Kalman filter, but all experiments ran in a few minutes on a laptop.

Surprising findings

• Outlier-robust filters (Wang-EKF, WoLF-MD) can worsen performance relative to the standard EKF when the outliers are caused by state-space misspecification, because consecutive observations get rejected.

Limitations

• Wall-clock cost 10-20x slower than the standard Kalman filter.
• Theoretical properties (statistical efficiency, dimension dependence) are not well understood.
• Restricted to linear or linearised models with Gaussian variational approximation.

Experimental setup

Datasets: simulated constant-velocity tracking data simulated maneuvering object data simulated Lorenz96 data

Benchmarks: 2D object tracking (outlier, systematic, maneuver misspecification) Lorenz96 (d=60) with systematic misspecification

Metrics: mean squared error position error over time

Baselines: EKF iterated EKF Bernoulli filter (Wang) inverse-Wishart filter (Agamenoni) WoLF-IMQ WoLF-MD

Builds on: Kalman filter extended Kalman filter iterated extended Kalman filter weighted observation likelihood filter predictively oriented posteriors

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