时变拓扑卫星集群分布式自主相对导航方法

针对时变拓扑卫星集群的相对导航需求，提出了基于图论的时变拓扑分布式一致性无迹卡尔曼滤波算法。首先给出了固定拓扑卫星集群的相对运动方程、测角测距测量模型和无迹卡尔曼滤波算法，然后考虑测角失效时相对导航系统不可观或弱可观的问题，结合矢量环一致性约束，构造了一致性无迹卡尔曼滤波算法，以提高系统的可观度；在此基础上，针对时变拓扑卫星集群，以滤波精度为优化指标，在图论的基础上利用Dijkstra算法对卫星集群的时变拓扑结构进行重构，并将重构后的拓扑结构应用于卫星集群相对导航。仿真结果表明所提算法能有效改善不完备测量带来的模糊轨道问题，并且能够实现实时的拓扑重构，以满足时变拓扑星群的相对导航精度要求。

Distributed Autonomous Relative Navigation Method for Satellite Cluster with Time varying Topology

A graph theory based distributed consensus unscented Kalman filter algorithm is proposed to perform the relative navigation for satellite cluster with time varying topology. Firstly, the equations of relative motion, the angle range measurement model, and the Unscented Kalman Filter algorithm are given for the satellite cluster with fixed topology. Further, the issue of non observability or weak observability is considered when the optical angle measurement fails, then the consensus unscented Kalman filter is constructed by introducing the vector ring consensus constraint to improve the observability of the relative navigation system. On this basis, the Dijkstra algorithm is improved by taking the filtering accuracy as the optimization criterion to reconstruct the real time topology of the cluster system. Finally, the reconstructed topology is applied to the relative navigation of cluster satellites. The numerical simulations demonstrate that the proposed algorithm can effectively alleviate the ambiguous orbits problem caused by range only measurements and reconstruct real time topology to improve the relative navigation accuracy.