适用于激光跟踪仪转站的改进平差方法  

Improved Adjustment Method Applied in Transformation of Laser Tracker

作　　者：罗涛 齐志军 王巍[1] 何晓业[1] Luo Tao;Qi Zhijun;Wang Wei;He Xiaoye(National Synchrotron Radiation Laboratory,University of Science and Technology of China,Hefei 230029,Anhui,China;School of Geodesy and Geomatics,Wuhan University,Wuhan 430079,Hubei,China;Institute of Advanced Science Facilities,Shenzhen(IASF),Shenzhen 518107,Guangdong,China)

机构地区：[1]中国科学技术大学国家同步辐射实验室,安徽合肥230029 [2]武汉大学测绘学院,湖北武汉430079 [3]深圳综合粒子设施研究院,广东深圳518107

出　　处：《中国激光》2024年第2期60-67,共8页Chinese Journal of Lasers

基　　金：中国科学技术大学重要方向项目培育基金(WK2310000085)。

摘　　要：激光跟踪仪的转站误差直接影响数据质量。最小二乘(LS)方法只考虑观测向量误差,加权总体最小二乘(WTLS)方法忽略转站模型的特点,两种算法均存在一些不足。针对激光跟踪仪坐标转换模型的特点,提出了结构约束总体最小二乘(SCTLS)方法。该方法能够顾及坐标观测值的相关性,提取误差矩阵的特殊结构,从而保证相同元素的改正数是一致的。同时对待估参数附加限制条件,保证旋转矩阵具有正交性。使用拉格朗日乘数法严密推导算法的求解步骤,给出了精度评定的公式。仿真结果显示SCTLS法的估计参数偏差小于WTLS法,准确性更高;采用合肥光源控制网中的实测数据计算,验证SCTLS法的精度更高。与LS和WTLS算法相比,所提算法更加严密,能够有效减小转站中的误差积累。Objective Due to the influence of object size and measurement environment,we usually use the laser tracker to measure at different positions and then fuse the observation data of different stations into the same coordinate system.The transformation error of the laser tracker directly affects the quality of the observation results,so it is significant to study the high-precision transformation adjustment method for the laser tracker.The traditional least squares(LS)method,as a widely used method,can only consider the error in the observation vector.This assumption does not satisfy the actual situation and the estimated parameters by LS are biased statistically.The existing weighted total least squares(WTLS)method can consider the random error in the coefficient matrix and observation vector at the same time.Although WTLS overcomes the shortcomings of the LS method,this method still has some problems.For example,the rotation matrix obtained by WTLS is not orthogonal and the error matrix by WTLS does not meet the structural characteristics.Methods To overcome the shortcomings of the existing methods,we propose a new improved adjustment method suitable for the transformation of laser tracker,which is called the structured constrained total least squares(SCTLS)method.This new method does not require any limitations for the statistical model and can take into account the correlation of coordinate observations.SCTLS uses a new structure matrix to describe the special structure corresponding to the error matrix so that the corrections of the same elements are consistent.At the same time,this method imposes restrictions on the parameters to be estimated to ensure the orthogonality of the rotation matrix.Because the transformation model is nonlinear,we use the Lagrange multiplier method to rigorously derive and give the iterative solutions of the algorithm in detail.Finally,the first-order accuracy of the parameters is evaluated.The proposed method is able to handle both similar and rigid coordinate transformations by cont

关 键 词：测量 激光跟踪仪 结构约束总体最小二乘 迭代算法 转站精度 

分 类 号：P207[天文地球—测绘科学与技术]