Modeling Contour Measurements of Elliptical Extended Objects via Gaussian Spatial Distributions

Code for the paper "Modeling Contour Measurements of Elliptical Extended Objects via Gaussian Spatial Distributions" by Simon Steuernagel, Kolja Thormann, and Marcus Baum, published at the 2024 SDF Workshop.

Abstract: 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.

Furthermore, please consider having a look at the following closely related work:
Random Matrix-based Tracking of Rectangular Extended Objects with Contour Measurements
GitHub repository

where rectangular objects are considered.

Brief repository overview:

• Key scripts to run the conducted experiments can be found here
  • For the extended object tracking experiments, tracking_experiment.py generates all the key figures used in the paper
  • Numerical verification of the derived scaling factors is done here
  • Examples for the two sampling strategies can be generated using this script
• Implementations of the trackers can be found in this directory
  • For the random matrix tracker, the standard version with a fix (scalar) scaling factor can be found in this file
  • The version that adaptively determines the two scaling factors for the axis extends the standard RM tracker and can be found here