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.

Random matrices are used to filter the center of gravity (CoG) and the covariance matrix of measurements. However, these quantities do not always correspond directly to the position and the extent of the object, e.g. when a lidar sensor is used.In this paper, we propose a Gaussian processes regression model (GPRM) to predict the position and extension of the object from the filtered CoG and covariance matrix of the measurements. Training data for the GPRM are generated by a sampling method and a virtual measurement model (VMM). The VMM is a function that generates artificial measurements using ray tracing and allows us to obtain the CoG and covariance matrix that any object would cause. This enables the GPRM to be trained without real data but still be applied to real data due to the precise modeling in the VMM. The results show an accurate extension estimation as long as the reality behaves like the modeling and e.g. lidar measurements only occur on the side facing the sensor.