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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.
Virtual measurement models (VMM) can be used to generate artificial measurements and emulate complex sensor models such as Lidar. The input of the VMM is an estimation and the output is the set of measurements this estimation would cause. A Kalman filter with extension estimation based on random matrices is used to filter mean and covariance of the real measurements. If these match the mean and covariance of the artificial measurements, then the given estimation is appropriate. The optimal input of the VMM is found using an adaptation algorithm. In this paper, the VMM approach is expanded for multi-extended object tracking where objects can be occluded and are only partially visible. The occlusion can be compensated if the extension estimation is performed for all objects together. The VMM now receives as input an estimation for the multi-object state and the output are the measurements that this multi-object state would cause.