不完全观测信息下网络化离散随机系统多目标滤波研究

本项目研究不完全观测信息下网络化离散随机系统多目标滤波设计与算法性能分析问题。首先，建立刻画网络诱导现象、通信约束及拓扑结构的数学模型，对传感器网络通信受限现象进行具有实际意义的统计刻画；综合考虑传感器网络通信环境，建立合适的网络化离散随机系统模型。其次，分别研究不同噪声统计特性情形下系统滤波问题，考虑滤波误差方差约束和椭球约束目标，基于不完全观测信息设计新型分布式递推滤波器和集员滤波器，建立滤波增益设计方法和求解算法。然后，利用随机分析、稳定性理论，探讨所提滤波方法及算法的性能分析问题，给出滤波误差稳定性和有界性、滤波算法收敛性和复杂性的判别条件。进一步，基于滚动时域优化方法，构造滚动时域分布式滤波器，有效利用有限域内不完全观测信息，设计以滤波误差成本函数最小化为目标的约束非线性优化问题，提高滤波算法精度。本项目研究结果将丰富网络化离散随机系统滤波研究方法，促进滤波算法在实际问题中应用。

This project will address the problems of multi-objective filter design and algorithm performance analysis for networked discrete stochastic systems under incomplete observation information. The new mathematical models will be established to describe the network induced phenomena, communication constraints and topological structure, which are the statistical characterization with practical significance for the sensor network with communication limitation phenomenon. Considering the sensor network communication environment comprehensively, a suitable networked discrete stochastic system model will be established. Subsequently, the system filtering problems under different noise statistical characteristics are studied separately. Based on the incomplete observation information, the new distributed recursive filter and set-membership filter are designed by considering the targets of the filter error variance constraint and the ellipsoid constraint, and the methods of filtering gain design and solving algorithms are established. Then, by employing stochastic analysis and stability theory, the performance analyses of the proposed filtering method and algorithm are discussed, and the criteria for determining the stability and boundness of the filtering error, the convergence and complexity of the filtering algorithm are given. Furthermore, based on the moving horizon optimization method, the moving horizon distributed filter will be designed. By utilizing the incomplete observation information within finite horizon effectively, the constrained nonlinear optimization problem with the objective of minimizing the filter error cost function will be designed to improve the filtering algorithm accuracy. The research results of this project will enrich the filtering research methods of networked discrete stochastic systems and promote the application of filtering algorithms in practical problems.