State estimation of DDS-DNNS with stochastic event-triggered mechanism under Bayes theory

Addressing the state estimation problem of a single positioning node in a decentralized networked navigation system based on data distribution service(DDS-DNNS), considering node energy constraints and sensor gain degradation, a minimum mean square error(MMSE) state estimator for DDS-DNNS with a stochastic event-triggered(SET) mechanism is designed based on Bayesian theory. The SET mechanism determines the importance of measurement values by comparing the differences in posterior estimates corresponding to the transmitted measurement values. Based on this, the Wasserstein distance is selected as a metric to represent the difference in posterior estimates. The properties of the Wasserstein distance and Bayes' theorem are utilized to prove that the posterior estimate is Gaussian, thereby obtaining the Kalman-like filter recursive form of the estimator and the explicit expression of the SET mechanism. Subsequently, it is proven that the prediction error covariance of the estimator is bounded, and both the upper and lower bounds converge. Meanwhile, it is demonstrated that the average information transmission rate is bounded, and the expressions for the upper and lower bounds are derived. Finally, a numerical simulation is conducted to illustrate how to determine the adjustment matrix through the upper and lower bounds of the average information transmission rate. The impact of first-order moment information and second-order moment information on the SET mechanism is simulated, and the effectiveness of the estimator is verified through comparative experiments.