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

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.