球体图像视觉伺服由于不变视觉特征的设计可获得良好的运动解耦特性，但球 体特征雅可比矩阵的计算依赖于若干未知三维参数，即被观测目标点的三维投影距离． 针 对球体图像视觉伺服特征雅可比矩阵未知三维参数的在线估计问题，文中提出了一种结 合线性时变系统持续激励引理的投影距离非线性观测算法． 首先结合统一投影模型对球 体特征运动学进行分析，然后根据持续激励引理设计系统状态的在线更新法则，在已知摄 像机运动及目标图像特征的情况下实现对未知三维投影距离的在线观测，并对观测器稳 定性进行了分析． 试验结果表明，该算法可有效实现对三维投影距离的在线估计，与基于 深度观测的间接估计方法相比具有更优的估计精度及观测动态特性，能有效地提高球体 图像视觉伺服控制的动态收敛特性． 

Due to the design of invariant visual features，spherical image-based visual servoing (IBVS) can obtain good motion decoupling characteristics． But calculation of feature Jacobian matrix depends on unknown 3D distance of each observed target point． For the problem of online estimating the unknown 3D parameters in spherical IBVS， a nonlinear projective distance observation algorithm is proposed with persistency of excitation (PE) lemma． In this paper，kinematics of spherical features is firstly analysed with the unified projection model; then，an update law of states of vision system is designed with PE lemma，online observation of 3D distances is realized by exploiting the known camera motion and the measured image features． Furthermore， stability analysis of the observer is proposed． Simulative results show that the proposed algorithm can effectively realize the online estimation of 3D distances，and has a better estimation accuracy and dynamic characteristics compared with the indirect estimation method based on depth observation． Meanwhile， the dynamic convergence characteristics of spherical IBVS control can be effectively improved．