A new best fitting Gaussian performance measure for jump Markov systems

We consider the problem of estimator performance prediction in stochastic systems with Markov switching dynamical models. Following Hernandez et al, a new best-fitting Gaussian performance measure (BFG-PM) for jump Markov systems is proposed. The new BFG-PM matches the moments of the state transition density of the Markov switching system and the approximate uni-modal system. The new BFG-PM has a state-dependent process noise covariance matrix, hence its recursive computation is carried out via a new formulation of the Cramer-Rao bound for nonlinear filtering with state dependent noise statistics. The paper presents two numerical examples where the existing BFG-PM and the new BFG-PM are compared against the error performance of a typical state estimator for jump Markov systems.