Predictively-Oriented Kalman Filtering

2026-06-02

AI Summary

This work addresses the issue of overconfident filtering in nonlinear state-space models caused by misspecification in either the dynamics or observation model. To mitigate this, the authors propose a Prediction-oriented (PrO) online filtering approach that does not strictly rely on Bayes’ theorem but instead learns only when the overall model is correctly specified. By integrating a linear-Gaussian approximation, the method establishes an efficient iterative update mechanism, yielding a variant of the extended Kalman filter termed EKF-PrO. This framework requires no hyperparameters, is computationally efficient, and automatically adapts to model misspecification. Experimental results demonstrate that, across various scenarios involving both linear and nonlinear model misspecifications, EKF-PrO achieves substantially improved inference robustness while maintaining computational costs comparable to existing methods.

Abstract

This paper presents a post-Bayesian approach to online filtering in nonlinear state-space models, capable of avoiding over-confident inferences in settings where either the dynamical model, the measurement model, or both, could be misspecified. This is addressed using predictively oriented (PrO) posteriors, an emerging paradigm in which learning (i.e., posterior concentration) occurs if and only if the overall model is well-specified, without strict adherence to Bayes' theorem. As the characterisation of PrO posteriors is challenging, our main technical contribution is a fast approximate linear-Gaussian update procedure, analogous to an (iterated) extended Kalman filter. The methodology, which we call EKF-PrO, has no tunable hyper-parameters and has a computational cost comparable to that of existing filtering methods. Performance is empirically assessed on a range of linear and non-linear applications, in which the state-space model is systematically misspecified.

Problem

• Kalman filtering
• model misspecification
• predictive inference
• state-space models
• over-confident inference

Innovation

• Predictively-Oriented Posterior
• Kalman Filtering
• Model Misspecification
• Online Filtering
• Nonlinear State-Space Models