A Gaussian Integral Filter with Multivariate Laplace Process Noise

TL;DR

This paper presents the Gaussian integral filter (GIF), a novel approach derived as the limit of the Gaussian sum filter, effectively modeling multivariate Laplace process noise for maneuvering target tracking with improved accuracy and comparable computational cost.

Contribution

The paper introduces the Gaussian integral filter (GIF) as a new filtering method for multivariate Laplace process noise, demonstrating superior accuracy over the UKF in target tracking applications.

Findings

GIF requires 1.4 times the resources of UKF

GIF achieves up to 11 times smaller errors

UKF diverges in complex scenarios

Abstract

This paper introduces the concept of the Gaussian integral filter (GIF), the limit of the Gaussian sum filter (GSF) for when the number of mixands tends to infinity. The GIF is obtained via a combination of GSF, quadrature, and interpolation. While it is a very general concept, in this paper the GIF is used to represent multiviariate Laplace (ML) distributions defining the process noise when tracking a maneuvering target. The filter is first applied to a linear three-dimensional toy problem, and then to a maneuvering target tracking problem in Earth orbit. For the more complex maneuvering target tracking problem, the filter requires only 1.4 times the computational resources of an unscented Kalman filter (UKF), while having errors up to 11 times smaller. For the same problem, the UKF slowly diverges.