GaussianNoise.md

Gaussian noise

Robotec GPU Lidar (RGL) allows introducing Gaussian noise which models the naturally present noise of the physical devices.

Gaussian noise is described by the following formula:

It is parametrized by these two values:

• μ - mean value
• σ - standard deviation

Supported noise types

The following table presents concisely all kinds of Gaussian noise available in RGL. The next chapters describe them in greater detail.

Noise type	Visualization
Ray-based angular noise: Rotate rays around selected axis of the lidar This kind of noise intends to model the noise in lidar's rotational speed
Hitpoint-based angular noise Rotate hitpoints around selected axis of the lidar This is different than rotating rays! Think of the effect on hitpoints on surfaces near-parallel to the ray This kind of noise could model e.g. error in reading position of the rotated laser or sensor
Distance noise This kind of noise can model e.g. error in measuring time-of-flight

Ray-based angular noise

This type of noise applies angular noise to the rays before raycasting. When this type of noise is applied, points stay on the obstacle surface

Step	Visualization
Rays are provided by the user via RGL API
Angular noise is applied to rays
Raytracing is performed using noised rays. Hitpoints are produced
Hitpoints with ray-based noise are sent for further processing

Usage

Create GaussianNoiseAngularRayNode using API call rgl_node_gaussian_noise_angular_ray. Next, add this node to the RGL pipeline before RaytraceNode.

Parameter name	Type	Description
mean	float	Angular noise mean in radians
st_dev	float	Angular noise standard deviation in radians
axis	rgl_axis_t	Axis on which angular noise will be perform

Hitpoint-based angular noise

This type of noise adds angular noise to already computed hitpoints. In other words, it is a rotation of each hitpoint around LiDAR's origin. When this type of noise is applied, points may be no longer on the obstacle surface

Step	Visualization
Rays are provided by the user via RGL API
Raycasting is performed using user-provided rays. Hitpoints are produced
Hitpoints are rotated by the noise value
Hitpoints with hitpoint-based noise are sent for further processing

Usage

Create GaussianNoiseAngularHitpointNode using API call rgl_node_gaussian_noise_angular_hitpoint. Next, add this node to the RGL pipeline right after RaytraceNode.

Parameter name	Type	Description
mean	float	Angular noise mean in radians
st_dev	float	Angular noise standard deviation in radians
axis	rgl_axis_t	Axis on which angular noise will be perform

Distance noise

This kind of noise changes the distance between hitpoint and lidar's origin.

Standard deviation can depend (increase linearly) on the point's distance from the sensor origin.

Overall standard deviation of the distance error is computed as follows:

where

symbol	description
	computed distance standard deviation applied to hitpoints
	base value of distance standard deviation (configurable)
	current points distance from sensor origin
	rise of the standard deviation per 1 meter of distance (configurable)

Step	Visualization
Ray are provided by the user via RGL API
Raycasting is performed. Hitpoints are produced
Hitpoints distance is changed by noise value
Hitpoints with distance noise are sent for further processing

Usage

Create GaussianNoiseDistanceNode using API call rgl_node_gaussian_noise_distance. Next, add this node to the RGL pipeline right after RaytraceNode.

Parameter name	Type	Description
mean	float	Distance noise mean in meters
st_dev_base	float	Distance noise standard deviation base in meters. Represented as in Distance noise chapter
st_dev_rise_per_meter	float	Distance noise standard deviation rise per meter. Represented as in Distance noise chapter