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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.
Lidar sensors are widely used for environmental perception on autonomous robot vehicles (ARV). The field of view (FOV) of Lidar sensors can be reshaped by positioning plane mirrors in their vicinity. Mirror setups can especially improve the FOV for ground detection of ARVs with 2D-Lidar sensors. This paper presents an overview of several geometric designs and their strengths for certain vehicle types. Additionally, a new and easy-to-implement calibration procedure for setups of 2D-Lidar sensors with mirrors is presented to determine precise mirror orientations and positions, using a single flat calibration object with a pre-aligned simple fiducial marker. Measurement data from a prototype vehicle with a 2D-Lidar with a 2 m range using this new calibration procedure are presented. We show that the calibrated mirror orientations are accurate to less than 0.6° in this short range, which is a significant improvement over the orientation angles taken directly from the CAD. The accuracy of the point cloud data improved, and no significant decrease in distance noise was introduced. We deduced general guidelines for successful calibration setups using our method. In conclusion, a 2D-Lidar sensor and two plane mirrors calibrated with this method are a cost-effective and accurate way for robot engineers to improve the environmental perception of ARVs.