High-Order Moment Recursive State Estimation of Markov Jump Linear Systems

Abstract

A high-order moment recursive state estimator is designed to achieve the minimum mean square error estimation of a Markov jump linear system (MJLS) whose state distribution obeys a generalized Gaussian distribution (GGD). The operation properties of the cumulant generating function are explored to transform the stochastic MJLS into a high-order component form. Based on the transformed high-order moment deterministic system, a Kalman filter is applied to estimate the high-order moment information of the state variable, such as the skewness and kurtosis of the GGD. This method allows for the estimation of the Gaussian distribution, such as the two special cases, mean and variance. A comparison with the existing results of the mean error estimation demonstrates the higher estimation accuracy for the simulation. The application of the proposed method to economic and power systems demonstrates its effectiveness and advantages.

Keywords

• Markov jump linear systems
• high-order moment estimation
• Kalman filter
• cumulant generating function