加权整体最小二乘在激光跟踪仪转站中的应用

李丽娟; 赵延辉; 林雪竹

doi:10.3788/OPE.20152309.2570

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加权整体最小二乘在激光跟踪仪转站中的应用

微纳技术与精密机械 | 更新时间：2020-08-12

- 加权整体最小二乘在激光跟踪仪转站中的应用
- Application of WTLS in coordinate transformation of laser tracker
- 光学精密工程 2015年23卷第9期页码：2570-2577
- 作者机构：
  
  1. 长春理工大学光电工程学院,吉林长春,130022
  2. 长春理工大学机电工程学院,吉林长春,130022
- 作者简介：
- 基金信息：
  
  国家863高技术研究发展计划资助项目(No.2013xx0406)()
- DOI：10.3788/OPE.20152309.2570
  中图分类号： TH744.5
- 收稿日期：2015-01-20，
  
  修回日期：2015-02-27，
  
  纸质出版日期：2015-09-25
- 稿件说明：
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李丽娟, 赵延辉, 林雪竹. 加权整体最小二乘在激光跟踪仪转站中的应用[J]. 光学精密工程, 2015,23(9): 2570-2577

LI Li-juan, ZHAO Yan-hui, LIN Xue-zhu. Application of WTLS in coordinate transformation of laser tracker[J]. Editorial Office of Optics and Precision Engineering, 2015,23(9): 2570-2577
李丽娟, 赵延辉, 林雪竹. 加权整体最小二乘在激光跟踪仪转站中的应用[J]. 光学精密工程, 2015,23(9): 2570-2577 DOI： 10.3788/OPE.20152309.2570.

LI Li-juan, ZHAO Yan-hui, LIN Xue-zhu. Application of WTLS in coordinate transformation of laser tracker[J]. Editorial Office of Optics and Precision Engineering, 2015,23(9): 2570-2577 DOI： 10.3788/OPE.20152309.2570.

摘要

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。

Abstract

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.

关键词

Keywords

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