Progressive Gaussian Filtering

TL;DR

This paper introduces a progressive Bayesian filtering method that continuously updates Gaussian approximations of the posterior using a system of differential equations, improving tracking performance in nonlinear estimation problems.

Contribution

It presents a novel progressive Gaussian filtering approach based on coupled density representation and differential equations for continuous posterior tracking.

Findings

Outperforms existing filters in nonlinear estimation benchmarks

Effectively tracks non-Gaussian posteriors with differential equation-based updates

Demonstrates improved accuracy in the cubic sensor problem

Abstract

In this paper, we propose a progressive Bayesian procedure, where the measurement information is continuously included into the given prior estimate (although we perform observations at discrete time steps). The key idea is to derive a system of ordinary first-order differential equations (ODE) by employing a new coupled density representation comprising a Gaussian density and its Dirac Mixture approximation. The ODE is used for continuously tracking the true non-Gaussian posterior by its best matching Gaussian approximation. The performance of the new filter is evaluated in comparison with state-of-the-art filters by means of a canonical benchmark example, the discrete-time cubic sensor problem.