中文摘要：

导航问题是发展自主水下航行器（Autonomous Underwater Vehicle，AUV）所面临的难题之一。针对单信标测距导航方法中的系统可观测性问题，文章通过建立AUV的三维运动学模型，利用线性时变系统的局部可观测性理论得到了导航系统关于AUV三维运动路径的可观测性条件，在此条件下实现了对AUV运动位置的在线估计。仿真结果表明，对于满足导航系统可测观性的运动路径，AUV的位置估计具有良好的收敛性和定位精度。

英文摘要：

Precise navigation is one of the most important challenges for developing an autonomous underwater vehicle （AUV）. Aiming at the observability of the underwater navigation system for range measurement with a beacon, we obtain the observability conditions in relation single to three-dimensional trajectories of AUV through the kinematic model of AUV and the local observability theory of a linear time-varying system. Subsection 1.3 explains mathematically in some detail the observability conditions ; eqs. （ 11 ） and （ 12 ） are particularly worth paying attention to. Section 2 utilizes the extended Kalman filtering navigation algorithm to implement the online estimation of the position of the AUV under the observability conditions. Section 3 simulates the estimation of the AUV＇ s position ; the simulation results, given in Figs. 4 and 5, and their analysis show preliminarily that our observability anal- ysis method can effectively do the real-time data updating for the underwater navigation system, reduce its complexity, thus estimating the AUV＇ s position with good convergence and positioning accuracy under the condition that the three-dimensional trajectories of AUV are observable.