Robust Mahalanobis bundle adjustment for laser tracker multi-station measurement

Ying-gang GUO; Wen-bin ZHAO; Guan-yu ZHANG; Hao YANG

doi:10.37188/OPE.20202809.2046

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Robust Mahalanobis bundle adjustment for laser tracker multi-station measurement

Micro/Nano Technology and Fine Mechanics | 更新时间：2020-09-28

- Robust Mahalanobis bundle adjustment for laser tracker multi-station measurement
- Optics and Precision Engineering Vol. 28, Issue 9, Pages: 2046-2055(2020)
- 作者机构：
  
  1.战略支援部队信息工程大学, 河南郑州 450001
  2.中国科学院上海高等研究院, 上海 201800
- 作者简介：
- 基金信息：
- DOI：10.37188/OPE.20202809.2046
  CLC： P258
- Received：13 April 2020，
  
  Revised：18 June 2020，
  
  Accepted：18 June 2020，
  
  Published：25 September 2020
- 稿件说明：
移动端阅览
Ying-gang GUO, Wen-bin ZHAO, Guan-yu ZHANG, et al. Robust Mahalanobis bundle adjustment for laser tracker multi-station measurement[J]. Optics and precision engineering, 2020, 28(9): 2046-2055.
DOI：

Ying-gang GUO, Wen-bin ZHAO, Guan-yu ZHANG, et al. Robust Mahalanobis bundle adjustment for laser tracker multi-station measurement[J]. Optics and precision engineering, 2020, 28(9): 2046-2055. DOI： 10.37188/OPE.20202809.2046.

摘要

为了提高激光跟踪仪多测站测量数据平差结果的精度，研究了抗差马氏光束法平差模型。在传统光束法平差（TBA）模型的基础上，引入马氏距离，将平差准则由原来的“使观测值改正数加权平方和最小”改造为“使观测值到加权平均值的马氏距离平方和最小”，并在计算加权平均坐标时对粗差观测值进行剔除，建立了抗差马氏光束法平差（RMBA）模型。仿真试验中，用MATLAB模拟了4个测站观测12个控制点的观测值，结果表明RMBA模型的解算结果优于TBA、文献[

]方法和SA软件的解算结果，与仿真坐标的偏差均方根为0.031 mm。在模拟观测值中加入粗差后，RMBA模型表现出了优良的抗差性。实测试验中，以上海光源实验大厅100 m范围内4个测站观测42个控制点的数据为例，SA软件的平差结果的点位中误差为0.05 mm，RMBA解算结果与SA结果的三维坐标偏差均方根为0.07 mm。结果表明：RMBA模型具有一定的抗差性，坐标解算精度优于TBA模型和文献[

]方法，与SA软件的解算精度在同一量级。

Abstract

A robust Mahalanobis bundle adjustment (RMBA) model was developed to improve the adjustment precision of a laser tracker multi-station measurement. In a traditional bundle adjustment (TBA) model

by introducing the Mahalanobis distance

the adjustment criterion

"minimize the weighted sum of squares of the observed corrections

" was transformed to "minimize the sum of squares of Mahalanobis distances from the observations to the weighted average." Gross errors were eliminated in the calculation of the weighted average coordinates

and then

the RMBA model was developed. Observations from four survey stations to 12 control points were simulated using MATLAB. Experimental results show that the RMBA model is better than the TBA model[

]. and Spatial Analyzer (SA) software. The root mean square (RMS) of the deviation from the calculated coordinates to the simulated coordinates was 0.031 mm. The RMBA model was resistant when a gross error was added to the observed values. The data measurement was carried out in the experimental hall of Shanghai Synchrotron Radiation Facility. The observations from four survey stations to 42 control points

which were distributed over a length of approximately 100 m

were used as an example. The mean square error of the coordinates of SA was 0.05 mm. The RMS of the three-dimensional deviation from the RMBA results to the SA results was 0.07 mm. The RMBA model could resist gross error to some degree. Its coordinate calculation precision was almost equal to that of SA and superior to that of the TBA model and that in[

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