Fusion of Elliptical Extended Object Estimates Parameterized With Orientation and Axes Lengths

Kolja Thormann,Marcus Baum

doi:10.1109/taes.2021.3057651

Kolja Thormann, Marcus Baum

Open Access

https://doi.org/10.1109/taes.2021.3057651

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Abstract

This article considers the tracking of elliptical extended targets parameterized by center, orientation, and semiaxes. The focus of this article lies on the fusion of extended target estimates, e.g., from multiple sensors, by handling the ambiguities in this parameterization and the unclear meaning of the mean square error. For this purpose, we introduce a novel Bayesian framework for elliptic extent estimation and fusion based on two new concepts: 1) A probability density function for ellipses called random ellipse density which incorporates the ambiguities that come with the ellipse parameterization, and 2) the minimum mean Gaussian Wasserstein (MMGW) estimate, which is optimal with respect to the squared Gaussian Wasserstein (GW) distance-A suitable distance metric on ellipses. We develop practical algorithms for ellipse fusion and approximating the MMGW estimate. Different implementations, e.g., based on Monte Carlo simulation, are introduced and compared to state-of-the-art methods, highlighting the benefits of estimators tailored to the GW distance.

Highlights

In many modern tracking applications the resolution of the involved sensors is high enough to resolve the spatial extent of the targets
In this case, it can be seen how MC-Minimum Mean Gaussian Wasserstein (MMGW) is outperformed by Random Ellipse Density (RED)-MMGW, as the approximation of the transformed density as a Gaussian fails under the increased noise
Given the Kalman filter-based linear fusion and the shape mean as the state-of-the-art in fusion of elliptical estimates parameterized by orientation and semi-axes, we demonstrated that our method offers improvements of up to 40% with respect to the squared Gaussian Wasserstein (GW) distance

Summary

Introduction

In many modern tracking applications the resolution of the involved sensors is high enough to resolve the spatial extent of the targets. For this reason, Extended Object Tracking (EOT) methods that estimate both the shape and kinematic parameters of a target are becoming increasingly important [1], [2]. More detailed shapes are possible by modelling them as a combination of multiple random matrices [10] or using a Random Hypersurface Model (RHM). The latter describes star-convex shapes and was modeled by, e.g., Fourier coefficients [11], Gaussian processes [12]–[14], or splines [15], [16]

Methods

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Discussion

Conclusion