Kalman filter can accommodate time varying system matrices. Equations to run the filter are the same and it preserves its optimality under linear gaussian model.
My question is the following:
Can the evolution of time varying system matrices be stochastic? In some references I seem to read between the lines that they should evolve deterministically. Does it mean that the entire filter breaks or do we simply lose optimality by making them stochastic?
For reference, please peek at section 3.2 of the following paper:
A similar comment is in Harvey's book on Kalman Filter.