A New Perspective and Extension of the Gaussian Filter

TL;DR

This paper introduces the Feature Gaussian Filter (FGF), a generalized version of the Gaussian Filter that uses a nonlinear transformation of measurements, improving accuracy in nonlinear systems by relaxing belief restrictions.

Contribution

It presents a variational-inference-based analysis of Gaussian Filters and proposes the FGF, which enhances filtering performance in nonlinear observation models.

Findings

FGF outperforms standard GF in nonlinear systems

The approach maintains simplicity and efficiency

Numerical experiments validate the performance gains

Abstract

The Gaussian Filter (GF) is one of the most widely used filtering algorithms; instances are the Extended Kalman Filter, the Unscented Kalman Filter and the Divided Difference Filter. GFs represent the belief of the current state by a Gaussian with the mean being an affine function of the measurement. We show that this representation can be too restrictive to accurately capture the dependences in systems with nonlinear observation models, and we investigate how the GF can be generalized to alleviate this problem. To this end, we view the GF from a variational-inference perspective. We analyse how restrictions on the form of the belief can be relaxed while maintaining simplicity and efficiency. This analysis provides a basis for generalizations of the GF. We propose one such generalization which coincides with a GF using a virtual measurement, obtained by applying a nonlinear function to the actual measurement. Numerical experiments show that the proposed Feature Gaussian Filter (FGF) can have a substantial performance advantage over the standard GF for systems with nonlinear observation models.