Distributed recursive filter for 2-D Markov jump systems with stochastic communication protocol and nonlinearities

This paper investigates the distributed filtering for a class of two-dimensional Markov jump parameter systems with communication protocols and nonlinearity. The system is described by the FM-II model and the random communication protocol is characterized by a set of mutually uncorrelated random processes with known probability distributions, which determines the transmission order of each sensor data. The objective is to develop a recursive distributed filter for the two-dimensional systems. Firstly, an upper bound of the local estimation error variance is established through the mathematical induction method and the stochastic analysis approach. Then, by the complete mean square method, the filter gains are derived by optimizing the upper bound of the estimation error variance. Subsequently, a distributed filter based on covariance intersection (CI) fusion algorithm is developed, which exhibits higher accuracy and reliability. Finally, a numerical example is provided to demonstrate that the fusion estimator exhibits higher estimation accuracy compared to the local one.