Can a Kalman Filter predict where the tracked object will be after colliding with a wall?

Question

I'm tracking an object moving within a fixed-size box using a standard 2D CV (constant velocity) dynamic model as it moves through free space in the center of the box. But when it hits the edges of the box, its movement is more complex. Billiard-ball mechanics would work as a first approximation, but that model seems quite different than the CV model and I'm not sure how to incorporate it into the update step of the Kalman filter.

Is bounded motion (object in a box) a good use case for Interacting Multiple Model (IMM) filters, combining both the CV and billiard models? If so, will such a filter predict future collisions if I ask it to predict several tens of time steps into the future? Or is there a way to alter the CV filter state variables when a collision occurs such that subsequent update and predict steps continue to track the motion of the object (albeit in its new, reflected direction)?

Answer 1

A Kalman filter is able to handle linear process functions only, so it probably won't be a good choice since billard-ball mechanics don't fit in that criterion.

For such a task I would probably try to use a particle filter (or recursive Monte-carlo) with a process variable (position, velocity). This is a common model used for robot navigation for ex. It will be able to predict several steps into the future adjusting the uncertainty depending on collisions and such.