Effects of Navigation Errors on Geo-Registered Point Clouds in Building Navigation

We have a robot that uses a 2D LIDAR to navigate around a building. The coordinates of the four corners of the building are defined in a local East-North frame, which are (0 0)m, (0 10)m, (10 10)m and (10 0)m respectively. The robot is equipped with a low-cost GPS receiver and a low-cost IMU.The GPS-IMU navigation system may have errors in position, velocity and orientation.

The robot started from (0,0), moved along the outside walls of the building and returned to (0,0). The robot recorded the point cloud returned from the walls, and combined them with the navigation solution to form a geo-registered point cloud. Without error in the navigation system, this point cloud should represent the actual location and shape of the building.

It seems you're asking for sketches of the geo-registered point clouds under different navigation error scenarios. However, I'm unable to provide sketches directly. I can describe how the geo-registered point cloud would look under each scenario:

1. Navigation Error: Position Bias of 5 m (East Direction)

2. • The velocity bias causes a constant northward drift in the robot's trajectory.

   • Over time (assuming continuous movement around the building), this will result in points being geo-registered higher (north) than their actual positions.
3. • Points recorded on the south side of the building will appear lower than their actual positions due to the cumulative southward bias.