Efficient Gaussian Mixture Filters based on Transition Density Approximation

TL;DR

This paper introduces a novel approach to Gaussian mixture filtering for nonlinear systems by approximating transition densities with axis-aligned Gaussian mixtures, maintaining a constant number of components and balancing accuracy with computational efficiency.

Contribution

It proposes two methods for approximating transition densities that prevent exponential growth of mixture components, simplifying computation in Gaussian mixture filters.

Findings

Automatic component count stabilization in filters

Trade-off control between accuracy and complexity

Reduction in computational load for nonlinear filtering

Abstract

Gaussian mixture filters for nonlinear systems usually rely on severe approximations when calculating mixtures in the prediction and filtering step. Thus, offline approximations of noise densities by Gaussian mixture densities to reduce the approximation error have been proposed. This results in exponential growth in the number of components, requiring ongoing component reduction, which is computationally complex. In this paper, the key idea is to approximate the true transition density by an axis-aligned Gaussian mixture, where two different approaches are derived. These approximations automatically ensure a constant number of components in the posterior densities without the need for explicit reduction. In addition, they allow a trade-off between estimation quality and computational complexity.