Optics and Precision Engineering, Volume. 28, Issue 9, 2046(2020)

Robust Mahalanobis bundle adjustment for laser tracker multi-station measurement

GUO Ying-gang1,*... ZHAO Wen-bin2, LI Zong-chun1, ZHANG Guan-yu1 and YANG Hao1 |Show fewer author(s)
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  • 1[in Chinese]
  • 2[in Chinese]
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    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 [22]. 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 [22].

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    GUO Ying-gang, ZHAO Wen-bin, LI Zong-chun, ZHANG Guan-yu, YANG Hao. Robust Mahalanobis bundle adjustment for laser tracker multi-station measurement[J]. Optics and Precision Engineering, 2020, 28(9): 2046

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    Paper Information

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    Received: Apr. 13, 2020

    Accepted: --

    Published Online: Dec. 28, 2020

    The Author Email: Ying-gang GUO (fariel_gyg@163.com)

    DOI:10.37188/ope.20202809.2046

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