Modeling Contour Measurements of Elliptical Extended Objects via Gaussian Spatial Distributions
Simon Steuernagel, Kolja Thormann, Marcus Baum · 2024
Many elliptical extended object tracking methods model the spatial distribution of the measurement sources on the object with a Gaussian distribution. With the help of moment matching, alternative spatial distributions of the measurement sources can be incorporated. For example, a uniform distribution on the surface leads to a constant scaling of the matching Gaussian distribution's covariance matrix. This work is concerned with measurement sources from the contour of an elliptical object. It is shown that for a circle with uniformly distributed measurement sources on the contour, a constant scalar factor is obtained. This scaling factor still holds for an ellipse when the contour points are stretched accordingly. If, however, the semi-axes are not equal and the distribution is uniform on the contour, individual scaling factors for each axis are required. These depend on the (unknown) ratio of semi-axis lengths, but it is shown that they can also be estimated online in a recursive filtering framework. The applicability of the results to extended object tracking are evaluated based on simulations, showing that by employing the correct scaling factors, the Random Matrix (RM) filter can accurately track an extended object given contour measurements.