Kalman filtering approximations in triplet Markov Gaussian switching models

We consider a general triplet Markov Gaussian linear system (X, R, Y), where X is hidden continuous, R is hidden discrete, and Y is observed continuous. Exact Kalman filter (KF) is not workable and two approximations are considered in the paper. The classical one consists of particle filtering, which is a new extension of the classical method we propose. Another new method we propose consists of replacing the model by a simpler one, in which (R, Y) is Markovian and in which exact KF can be performed. We show the interest of our method via experiments.