Variational-Based Nonlinear Bayesian Filtering with Biased Observations

TL;DR

This paper introduces a novel variational Bayesian filter designed to detect and mitigate measurement biases in nonlinear dynamical systems, improving robustness over traditional Kalman filters.

Contribution

It proposes the Bias Detecting and Mitigating (BDM) filter that models biases within the state-space and integrates bias detection into the recursive filtering process.

Findings

The BDM filter outperforms Kalman filters in the presence of biases.

Simulations show improved robustness to both temporary and persistent biases.

The method does not rely on external bias detectors.

Abstract

State estimation of dynamical systems is crucial for providing new decision-making and system automation information in different applications. However, the assumptions on the standard computational models for sensor measurements can be violated in practice due to different types of data abnormalities such as outliers and biases. In this work, we focus on the occurrence of measurement biases and propose a robust filter for their detection and mitigation during state estimation of nonlinear dynamical systems. We model the presence of bias in each dimension within the generative structure of the state-space models. Subsequently, employing the theory of Variational Bayes and general Gaussian filtering, we devise a recursive filter which we call the Bias Detecting and Mitigating (BDM) filter. As the error detection mechanism is embedded within the filter structure its dependence on any external detector is obviated. Simulations verify the performance gains of the proposed BDM filter compared to similar Kalman filtering-based approaches in terms of robustness to temporary and persistent bias presence.