# A Methodology to Model the Rain and Fog Effect on the Performance of Automotive LiDAR Sensors
## 3 Related Work and Introduction of a Novel Approach  
The influence of rain and fog on the LiDAR signal is well-described in the literature. For example, [PERSON] et al. [7] proposed a mathematical model to predict the influence of rain on the received power and range reduction. Afterward, they investigated the impact of the LiDAR performance degradation caused by rain on an obstacle-detection algorithm. [PERSON] et al. [8] described the signal attenuation and decrease in the maximum detection range of LiDAR sensors operating both at 905 nm and 1500 nm due to the effects of rain and fog. In addition, they have shown that the LiDAR sensors at 905 nm are less sensitive to environmental conditions than the ones at 1500 nm. [PERSON] et al. [9] used the Mie scattering theory to model the influence of the effect of rain, fog, and snow on the performance of LiDAR sensors. Their signal attenuation model results show good agreement with the real measurements, but they do not quantify the attenuation of the LiDAR signals. Furthermore, they show a reduction in the maximum detection range of LiDAR sensors once the rain rate increases up to 18 mm/h. [PERSON] et al. [10] also modeled the LiDAR signal attenuation caused by raindrops using the Mie scattering theory. They used the rain distribution of three regions to show that the LiDAR signal attenuation varies according to rain distribution characteristics. The LiDAR sensor model by [PERSON] et al. [11] considers the LiDAR signal attenuation caused by rain, fog, snow, and haze. [PERSON] et al. [12] extended the work of [11] and modeled the unwanted raw detections (false positives) due to raindrops. They verified their model intuitively by comparing it with the data obtained during uncontrolled outdoor measurements. In Ref. [13], the authors have developed a model to predict and quantify the LiDAR signal attenuation due to raindrops. The simulation results matched well with the real measurements, with a deviation of less than 7.5%. [PERSON] et al. [14; 15] introduced a noise model that adds unwanted raw detections (false positives) to the real LiDAR data based on the hit ratio. The hit ratio determines whether the laser beam hits the raindrop or not. If the hit ratio value exceeds the selected threshold, a false positive scan point will be added to the real point clouds. One drawback, however, of this approach is that it is computationally expensive. They verified their modeling approach by comparing real point clouds modified by the noise models with the points obtained under rainy conditions. The intensity values of the false positive scan points are set empirically because no internal information about the LiDAR hardware is available. [PERSON] et al. [16] proposed a probabilistic extension of the LiDAR equation to quantify the unwanted raw detection by LiDAR sensors due to raindrops. They combined the probabilistic models' parameters for rain distribution with the Mie scattering theory and the LiDAR detection theory in the Monte Carlo Simulation. However, they did not verify their model by comparing it with real measurements. In Ref. [17], the authors proposed a real-time LiDAR sensor model that considers the beam propagation characteristics and rain noise based on a probabilistic rain model developed in [16]. Their sensor model uses an unreal engine's ray casting module, providing the LiDAR point clouds. The sensor model is not validated by the measurements of the real LiDAR sensor. [PERSON] et al. [18] introduced a physics-based simulation approach to add the effect of rain, fog, and snow on the real point clouds obtained under normal weather conditions. Their results show that the LiDAR-based detector performance improved once they trained with the LiDAR data obtained under normal and adverse weather conditions. [PERSON] et al. [19] simulated the effect of fog on the real LiDAR sensor point clouds and used the obtained foggy data to train the LiDAR-based detector to improve its detection accuracy.