Open Access

Patrick Hoher, Tim Baur, Johannes Reuter, Dennis Griesser, Felix Govaers, Wolfgang Koch

• In extended object tracking, random matrices are commonly used to filter the mean and covariance matrix from measurement data. However, the relation from mean and covariance matrix to the extension parameters can become challenging when a lidar sensor is used. To address this, we propose virtual measurement models to estimate those parameters iteratively by adapting them, until the statistical moments of the measurements they would cause, match the random matrix result. While previous work has focused on 2D shapes, this paper extends the methodology to encompass 3D shapes such as cones, ellipsoids and rectangular cuboids. Additionally, we introduce a classification method based on Chamfer distances for identifying the best-fitting shape when the object’s shape is unknown. Our approach is evaluated through simulation studies and with real lidar data from maritime scenarios. The results indicate that a cone is the best representation for sailing boats, while ellipsoids are optimal for motorboats.