Tune the Motion Model for a car

[elvout]

The 2D probability density plot for the simple Motion Model is roughly circular since the model assumes a diff-drive robot. However, for a car, d_x, d_y, d_theta are all linked since the wheels aren't completely independent. A car is more likely to have errors in the forward direction (x-axis) rather than the lateral direction (y-axis).

We can create a better motion model for the car by reshaping the probability density plot.

Intuitively, the variance for the x-axis error should be larger than the variance for the y-axis error.

Relevant slides.