This paper considers the fusion of multiple estimates of a spatially extended object, where the object extent is modeled as an ellipse that is parameterized by the orientation and semi-axes lengths. For this purpose, we propose a novel systematic approach that employs a distance measure for ellipses, i.e., the Gaussian Wasserstein distance, as a cost function. We derive an explicit expression for the Minimium Mean Gaussian Wasserstein distance (MMGW) estimate. Based on the concept of a MMGW estimator, we develop efficient methods for the fusion of extended target estimates. The proposed fusion methods are evaluated in a simulated experiment and the benefits of the novel methods are discussed.
In @cite_26 , several metrics suitable for eot are discussed, including Intersection-over-Union @cite_6 , gw distance @cite_5 , and Hausdorff distance, e.g. @cite_18 . It is pointed out that decoupling of state parameters is one option, as, e.g., calculating the Euclidean distance between two states could be difficult to interpret if the state consists of parameters in different units, like meters and radians. It is also argued that for elliptic shapes, the gw distance seems to be suitable for obtaining a single scalar score to rate the distance regarding all state parameters.
@cite_5 @cite_18 @cite_26 @cite_6
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This paper formulates properties of similarity measures. We list a number of similarity measures, some of which are not well known (such as the Monge-Kantorovich metric), or newly introduced (reflection metric), and give a set constructions that have been used in the design of some similarity measures. The objective of extended object tracking is to simultaneously track a target object and estimate its shape. As a consequence, it becomes necessary to incorporate both location and shape errors in the performance assessment of extended object tracking methods. In this work, we highlight the difficulties of selecting a proper metric for this purpose and discuss currently used metrics from literature. Furthermore, we suggest the Gaussian Wasserstein metric for comparing elliptic shapes and illustrate its advantages. This paper considers tracking of extended targets using data from laser range sensors. Two types of extended target shapes are considered, rectangular and elliptical, and a method to compute predicted measurements and corresponding innovation covariances is suggested. The proposed method can easily be integrated into any tracking framework that relies on the use of an extended Kalman filter. Here, it is used together with a recently proposed Gaussian mixture probability hypothesis density (GM-PHD) filter for extended target tracking, which enables estimation of not only position, orientation, and size of the extended targets, but also estimation of extended target type (i.e. rectangular or elliptical). In both simulations and experiments using laser data, the versatility of the proposed tracking framework is shown. In addition, a simple measure to evaluate the extended target tracking results is suggested.