A stochastic physical simulation framework to quantify the effect of rainfall on automotive lidar

The performance of environment perceiving sensors such as e.g. lidar, radar, camera and ultrasonic sensors is safety critical for automated driving vehicles. Therefore, one has to assess the sensors' performance to assure the automated driving system's safety. The performance of these sensors is however to some degree sensitive towards adverse weather conditions. A challenge is to quantify the effect of adverse weather conditions on the sensor's performance early in the development of an automated driving system. This challenge is addressed in this work for lidar sensors. The lidar equation was previously employed in this context to derive estimates of a lidar's maximum range in different weather conditions. In this work, we present a stochastic simulation framework based on a probabilistic extension of the lidar equation, to quantify the effect of adverse rainfall conditions on a lidar's raw detection performance. To this end, we combine basic probabilistic models for key rainfall parameters with Mie theory and the theory of signal detection in a Monte Carlo simulation framework. This allows to analyze and optimize a sensor's design early in the sensor development, when physical testing is not yet possible. A challenge not addressed in this work is to include the effect of road spray water on the lidar's performance. Combining the effect of other noise sources with the presented framework in a ray tracer is an opportunity for realistic physical lidar simulations and would allow to virtually estimate the performance of a lidar's object detection and tracking performance. Such simulations could contribute to verify the safety of automated driving functionalities.