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 single beacon, we obtain the observability conditions in relation 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 analysis 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.%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.
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