  In this paper, we focus on the statistical filtering problem in dynamical
models with jumps. When a particular application relies on physical properties
which are modeled by linear and Gaussian probability density functions with
jumps, an usualmethod consists in approximating the optimal Bayesian estimate
(in the sense of the Minimum Mean Square Error (MMSE)) in a linear and Gaussian
Jump Markov State Space System (JMSS). Practical solutions include algorithms
based on numerical approximations or based on Sequential Monte Carlo (SMC)
methods. In this paper, we propose a class of alternative methods which
consists in building statistical models which share the same physical
properties of interest but in which the computation of the optimal MMSE
estimate can be done at a computational cost which is linear in the number of
observations.
