Physics-based modeling of rain and snow effects in virtual LiDAR

A virtual LiDAR sensor comprising a one or more modules, the one or modules configured to:

• receive a point cloud model representing three-dimensional coordinates of objects as the objects would be sensed by a LiDAR sensor;
• generate a stochastic model of rainfall or snowfall;
• estimate a probability that a light source from the LiDAR sensor hits a raindrop or a snowflake based on the stochastic model, the probability P being determined using a stochastic formulation given by:
• P=((Ar/Aro)/(V/Vo))·(D/Do)·(πR2/Dm2),
• where Ar/Aro is a normalized drop arrival rate, V/Vo is a normalized drop velocity, D/Do is a normalized laser beam diameter, R is a droplet radius, and Dm is a length of a cubic volume in a direction parallel to the laser beam;
• identifying whether the estimated probability is above a threshold;
• and
• modify the received point cloud model to include effects induced by the modeled rainfall or snowfall in response to the estimated probability, including performing a physics-based calculation of reflection and backscatter of incident laser light interacting with a raindrop when the estimated probability is above the threshold, the physics-based calculation comprising determining an intensity after scattering i(j,p) according to:
• i(j,p)=(R2/r2)·i0·ε(j,p)D,
• where i0 is an incident intensity, r is a distance between the droplet and a LiDAR receiver, and ε(j,p)D is a scattering coefficient defined by ε(j,p)D=f(θ, m, p), with θ being a scattering angle, m being a refraction index, and p being a path such that the modification reflects the likelihood that light sourced from the LiDAR sensor encounters a raindrop or a snowflake.

A vehicle system comprising:

• a vehicle;
• a LiDAR sensor mounted to the vehicle, the LiDAR sensor configured to provide raw point cloud information;
• a virtual LiDAR sensor configured to receive the raw point cloud information and to generate a modified point cloud that incorporates simulated effects of precipitation, the virtual LiDAR sensor further configured to:
• generate a stochastic model of rainfall or snowfall;
• estimate a probability that a light source from the LiDAR sensor hits a raindrop or a snowflake based on the stochastic model, the probability P being determined using a stochastic formulation given by:
• P=((Ar/Aro)/(V/Vo))·(D/Do)·(πR2/Dm2),
• where Ar/Aro is a normalized drop arrival rate, V/Vo is a normalized drop velocity, D/Do is a normalized laser beam diameter, R is a droplet radius, and Dm is a length of a cubic volume in a direction parallel to the laser beam;
• identifying whether the estimated probability is above a threshold;
• and
• modify the received point cloud model to include effects induced by the modeled rainfall or snowfall in response to the estimated probability, including performing a physics-based calculation of reflection and backscatter of incident laser light interacting with a raindrop when the estimated probability is above the threshold, the physics-based calculation comprising determining an intensity after scattering i(j,p) according to:
• i(j,p)=(R2/r2)·i0·ε(j,p)D,
• where i0 is an incident intensity, r is a distance between the droplet and a LiDAR receiver, and ε(j,p)D is a scattering coefficient defined by ε(j,p)D=f(θ, m, p), with θ being a scattering angle, m being a refraction index, and p being a path, such that the modification reflects the likelihood that light sourced from the LiDAR sensor encounters a raindrop or a snowflake.