A new approach to linear estimation for Markov jump linear systems

This paper investigates the linear minimum mean square error estimation for the Markov jump linear system (MJLS). To derive the existence condition of such estimator, we first transform the MJLS into a linear system with multiplicative noises; and then the system is converted into an averaged one just with addition noises by using the fictitious noise technique. The existence condition is established based on the novel transformation, and different kinds of estimators including predictor, filter and smoother are proposed via the projection formula. Compared with the augmented approach, the computational cost is reduced. And the estimators have the same dimensions as the original system.