High-order moment Bayesian state estimation of nonlinear Markov jump system.

To deal with problem of complexity in state distribution, a recursive state estimator with high-order moment component form of a nonlinear Markov jump system (MJS) with state variable non-Gaussian. The nonlinear MJS is transformed into a nonlinear deterministic system with high-order moment component form by means of cumulant generating function. Based on the transformed single-mode nonlinear deterministic system, a recursive state estimation in Bayesian framework is given to estimate the error of the state with high-order moment component form. To describe the non-Gaussian state distribution, the generalized Gaussian distribution (GGD) is used which introduces the high-order moment information compared with the first- and second-order information, mean and variance in Gaussian distribution (GD). With the help of high-order moment information such as the skewness and kurtosis in the GGD, the performance of state estimation will be much more precise. The numerical example in the simulation part shows the performance of the state estimation and the comparison of errors in different moment, which demonstrate the effectiveness.