Fusion of Elliptical Extended Object Estimates Parameterized with
Orientation and Axes Lengths
Abstract
This article considers the fusion of target estimates stemming from
multiple sensors, where the spatial extent of the targets is
incorporated. The target estimates are represented as ellipses
parameterized with center orientation and semi-axis lengths and width.
Here, the fusion faces challenges such as ambiguous parameterization and
an unclear meaning of the Euclidean distance between such estimates. We
introduce a novel Bayesian framework for random ellipses based on the
concept of a Minimum Mean Gaussian Wasserstein (MMGW) estimator. The
MMGW estimate is optimal with respect to the Gaussian Wasserstein (GW)
distance, which is a suitable distance metric for ellipses. We develop
practical algorithms to approximate the MMGW estimate of the fusion
result. The key idea is to approximate the GW distance with a modified
version of the Square Root (SR) distance. By this means, optimal
estimation and fusion can be performed based on the square root of the
elliptic shape matrices. We analyze different implementations using,
e.g., Monte Carlo methods, and evaluate them in simulated scenarios. An
extensive comparison with state-of-the-art methods highlights the
benefits of estimators tailored to the Gaussian Wasserstein distances.