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

Bayes理论下具有随机事件触发机制的DDS-DNNS状态估计

Coast Guard Academy, Naval Aviation University, Yantai, 264001, China

Received: 21 April 2025

Abstract

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.

摘要

针对基于数据分发服务的分散式组网导航系统(decentralized networked navigation system based on DDS, DDS-DNNS)单定位节点状态估计问题, 考虑节点能量约束及传感器增益退化, 以Bayes理论为基础, 设计了具有随机事件触发机制(stochastic event-triggered, SET)的DDS-DNNS最小均方误差状态估计器。其中, SET机制通过比较是否传输测量值对应的后验估计的差异来决定测量值的重要程度。以此为基础, 选取Wasserstein距离作为度量来表示后验估计的差异, 并利用Wasserstein距离的性质及Bayes定理证明了后验估计是Gaussian的, 从而得到了估计器的类Kalman滤波递推形式以及SET机制的显式表达式。证明了估计器的预测误差协方差有界, 且上界和下界均收敛, 同时, 证明了平均信息传输率有界并推导得到了上界和下界的表达式。利用算例仿真演示了如何通过平均信息传输率的上界和下界确定调整矩阵, 模拟了SET机制中一阶矩信息和二阶矩信息对SET机制的影响, 同时采用比较实验验证了估计器的有效性。