经纬仪交会精度的定量预测  

Quantitative forecasting of intersection precision for theodolite

作　　者：刘旨春[1,2] 郭立红[1] 关文翠[3] 邢忠宝[1] 

机构地区：[1]中国科学院长春光学精密机械与物理研究所,吉林长春130033 [2]中国科学院研究生院,北京100039 [3]北华大学物理学院,吉林吉林132013

出　　处：《光学精密工程》2008年第10期1822-1830,共9页Optics and Precision Engineering

基　　金：国家863高技术研究发展计划资助项目(No.2006AA703104)

摘　　要：推导并建立了一系列的公式，用于定量预测两经纬仪的交会精度。给出了用于目标三维位置估计的基本多传感器三角交会法的公式，同时利用各个测量误差的泰勒展开式导出了误差传播等式。在测量误差中引入高斯分布，建立了测量误差标准差和目标位置估计标准差之间的关系式，给出了交会精度随各单项误差传播系数的变化曲线图。实验结果表明：目标的x、y坐标的估计误差不受站址坐标中z坐标误差的影响，也不受测量高低角的影响，站址坐标中z项误差直接转移到目标的z坐标估计误差中。交会角为90。时，交会精度受经纬仪单项差的影响最小，交会角在20～60°时的误差传播系数为0．079。目标（x，y）坐标的交会精度依赖于经纬仪站址的测量精度、方位角的测量精度、经纬仪和目标的距离测量精度及两经纬仪的交会角；目标z坐标的精度依赖于经纬仪到目标的水平投影距离、经纬仪z坐标的测量精度和传感器高低角测量精度。最后，给出了一套等式和图形用于设计一个两经纬仪系统，使之满足具体的精度要求。本预测方法已成功应用于实际项目中传感器的选型和光学系统的参考设计。In order to forecast quantitatively the intersection precision of a theodolite, a series of functions were introduced to study the intersection precision measurement. The basic multi-sensor triangulation equations were used to estimate a 3D target position, and the error propagation equations were derived by Taglor extension from various measurement errors. Then, the concept of Gaussian measurement error was introduced to establish the relationship of the standard deviation of various measurement errors with the standard deviation of target 3D position estimation,and the plots of various error propagation coefficients were generated. The results indicate that the estimations of the x,y location errors are independent of any errors, either the sensor z position or the elevation angle in measurement. The errors x and y in the sensor position （x, y） depend only on the azimuth angles be-tween sensors, and not on the actual sensor （x, y） locations. The errors in the z component of a sensor position can translate directly into equivalent errors in the z component of target position estimation. The optimum geometry for a two-sensor system is in a 90° azimuth separation angle between the two sensors. The target （x, y） position estimation accuracy depends on the accuracies of sensor location measurement, the sensor azimuth pointing measurement and the sensor-to target range, also the sensor-to-sensor azimuth separation geometry. The target z position estimation accuracy depends on the sensor-to-target horizontal range, the sensor z location measurement accuracy and the sensor elevation angle measurement. Intersection errors is the smallest one when the intersection angle is 90°, and the error propogation coefficient is 0. 079 when 20°-60°. Finally a set of equations and graphs useful for designing a two-sensor system was designed to meet the requirement for a required accuracy specification.

关 键 词：经纬仪 交会测量 三角测量 三维位置估计 多传感器 误差传播 

分 类 号：TH761.1[机械工程—仪器科学与技术] TP391.4[机械工程—精密仪器及机械]