15. Converting Landmark Observations

Here is another example that might help your intuition.

Referring to the figures below:

Suppose the map coordinate system (grey lines) and the vehicle coordinate system (orange lines) are offset, as depicted below. If we know the location of the observation in vehicle coordinates (grey lines), we would need to rotate the entire system, observation included, -45 degrees to find it in map coordinates (grey lines), Once this rotation is done, we can easily see the location of the observation in map coordinates.

Particle (blue dot) in Map Frame (grey)

Particle (blue dot) in Vehicle Frame (orange)