Particle filter to get most likely trajectory

Question

I have implemented a Particle Filter to localise a robot. If i want to get the most likely set of paths, what would be the best way to do it?

I was wondering if taking the particle with the highest weight is a correct way to do it?

Answer 1

At first, each particle should track its paths. This can be done by adding a list of waypoints to each Particle. When you want to get the most likely path, you can take the path from the particle with the highest weight. This is not the same as taking the most likely position in each time step and aggregate them as the most likely path!

You can also use the weighted average values of all paths of the particles. This depends on what distribution you expect. When it has only one mode, this may give a more precise path. In contrast, if you expect a multimodal distribution (assume an obstacle, where half of the particles pass left and the other half pass right), the weighted average might give wrong results.

I would stick with the particle with the highest weight.