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摘要: 本文研究多个传感器测量非线性系统时的分布式无迹Kalman滤波器(Unscented Kalman filter, UKF)的设计问题.借助离散多智能体系统有限时间平均一致算法的思想, 针对无向通信和有向通信网络分别设计了两种不同的滤波算法.对于无向连通的通信拓扑, 利用节点存储的一致性算法的迭代值构造差向量, 由该差向量构成的Hankel矩阵的核来得到分布式无迹Kalman滤波器, 并通过利用误差协方差矩阵的逆来构造Lyapunov函数, 基于随机稳定性引理证明了该有限时间一致无迹Kalman滤波器的稳定性.对于有向强连通的通信拓扑, 结合比率一致和Hankal矩阵的核来设计分布式无迹Kalman滤波器, 该滤波器的稳定性与无向通信拓扑的滤波器相同.最后, 通过仿真例子来验证所提滤波器的跟踪效果.
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关键词:
- 一致Kalman滤波器 /
- 无迹Kalman滤波器 /
- 有限时间一致 /
- Hankel矩阵
Abstract: This paper investigates how to design the distributed unscented Kalman filter (UKF) for nonlinear system in sensor networks. With the aid of finite-time average consensus for discrete-time multi-agent systems, we present unscented Kalman filters for undirected and directed communication topologies, respectively. For the undirected communication case, the distributed unscented Kalman filter is computed by the kernels of some Hankel matrices. The components of these Hankel matrices are the difference values of this node0s current and past consensus iteration values. The stability of this filter is further proved via the Lyapunov function and the stochastic stability theory. For the strongly connected directed communication case, a distributed unscented Kalman filter is designed through combining ratio consensus and Hankel matrix. Finally, the tracking performance of these two filters are verified by the simulation examples.-
Key words:
- Consensus Kalman filter /
- unscented Kalman filter (UKF) /
- finite-time consensus /
- Hankel matrix
1) 本文责任编委 诸兵 -
图 1 6个传感器构成的无向与有向通信图
Fig. 1 Undirected and directed communication topologies of 6 sensors
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