Distributed estimation for multi-sensor networked stochastic uncertain systems with correlated noises under a general stochastic communication protocol

The distributed state estimation problem is studied for multi-sensor networked stochastic uncertain systems with correlated noises under a stochastic communication protocol (SCP). Random parameter matrices are utilized to describe the stochastic uncertainties within the system model. Given the limited channel bandwidth among sensor nodes, a general SCP is set to randomly select multiple components from the complete state prediction estimate for transmission. A set of random variables is introduced to indicate which combination of state prediction components is selected for transmission at each time step. In the case that the sensor node does not know which combination of state prediction components from each neighboring node is transmitted to it at each time step, a distributed Kalman-like recursive estimator structure that depends on the probability distributions of random variables is developed. Under this estimator structure, an optimal distributed estimation algorithm is presented based on the linear unbiased minimum variance criterion, which necessitates the computation of estimation error cross-covariance matrices between different nodes. To avert the computation of cross-covariance matrices, a suboptimal distributed estimation algorithm is also proposed, where optimal gains are achieved by minimizing the upper bound of estimation error covariance matrix at each node. In addition, the scalar parameters in the upper bound of the covariance matrix are optimized to obtain a minimum upper bound. Stability and steady-state properties of two distributed estimation algorithms are analyzed. Finally, the effectiveness of the presented algorithms is validated through a simulation example.