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.

中文翻译：

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用方向和轴长度参数化的椭圆扩展对象估计的融合

本文考虑跟踪由中心、方向和半轴参数化的椭圆扩展目标。本文的重点在于通过处理此参数化中的模糊性和均方误差的不明确含义来融合扩展目标估计，例如来自多个传感器。为此，我们基于两个新概念引入了一种用于椭圆范围估计和融合的新贝叶斯框架：1) 称为随机椭圆密度的椭圆概率密度函数，它结合了椭圆参数化带来的歧义，以及 2) 最小均值 Gaussian Wasserstein (MMGW) 估计，对于平方高斯 Wasserstein (GW) 距离而言是最佳的 - 椭圆上的合适距离度量。我们开发了用于椭圆融合和近似 MMGW 估计的实用算法。介绍了不同的实现，例如基于蒙特卡罗模拟的实现，并与最先进的方法进行了比较，突出了针对 GW 距离定制的估计器的好处。