由于利用经典最小二乘原则对激光跟踪仪进行坐标转换时,系数矩阵中携带的随机测量误差会影响转站精度,故对激光跟踪仪的转站算法进行了研究。提出了基于线性EIV模型(Errors-in-Variables)和加权整体最小二乘法(WTLS)并利用间接平差形式迭代求解转站参数的方法;利用Matlab进行仿真分析并用API公司生产的激光跟踪仪进行实验。仿真结果显示WTLS法的单位权中误差的平均值和标准差分别为经典加权最小二乘法(WLS)的4/5和1/5;实验结果显示WTLS和WLS两种方法的单位权中误差分别为2.003 5 mm和2.225 3 mm;这些数据证明采用WTLS法的转站结果比WLS的精度更高且更稳定。该方法可为组建激光跟踪仪测量网络,优化网络布局奠定基础。

The coordinate transformation algorithm of a laser tracker was investigated to solve the problem that random measurement error from the coefficient matrix of classical least square algorithm influences on transformation precision. The linear Errors-in-Variables(EIV ) model and Weighted Total Least Square (WTLS) were put forward and the form of indirect adjustment was used to solve the parameters of coordinate transformation in iteration. Simulation experiments using Matlab and practical experiments with API laser tracker were performed. The simulation results indicate that the average value and the standard deviation of mean square error of unit weight of WTLS are 4/5 and 1/5 times of those of traditional Weighted Least Square(WLS) respectively. The results of practical experiments show that mean square errors of unit weight of WTLS and WLS are 2.003 5 mm and 2225 3 mm,respectively. These results verify that the WTLS achieves higher transformation precision and better stability than those of the WLS. Meanwhile,this method can provide the foundation for establishment of laser tracker measuring networks and optimization of network arrangement.