无定向点优化布局的多边交会测量精度分析

多边交会系统利于提高激光跟踪仪坐标测量精度，但测量精度易受测站布局和系统参数标定精度的影响。引入球心拟合的无定向点系统参数标定法，避免传统系统参数标定精度受定向点分布的影响，根据无定向点系统参数标定模型推导出多边交会的最佳测站布局——直角正三棱锥，从而保证多边交会测量精度。仿真结果表明，在5 m范围内，球心拟合的无定向点系统参数标定中误差为0.006 4 mm，最佳测站布局下多边交会的点位中误差为0.005 mm。经标准尺长度测量验证和四面体标准器坐标测量验证，优化后多边交会的长度测量中误差为0.003 6 mm，坐标测量中误差为0.005 3 mm。在无定向点系统参数标定和直角三棱锥布局下，激光跟踪仪多边交会能够实现微米级三维坐标测量。

Measurement Accuracy Analysis of Multilateral Method Based on Optimal Layout with Non-directional Point Calibration

  Objectives  The measuring accuracy of the multilateral method is affected by the station layout and the calibration errors of system parameters. The optimal station layout and new system parameters calibration method are investigated for optimizing the multilateral method.  Methods  A spherical center fitting method is introduced to calibrate station coordinates without enhanced reference points. Besides, according to the model error of the multilateral method, the optimal station layout is an equilateral rectangular triangular pyramid.  Results  In the range of 5 m, the root mean square error (RMSE) of system parameters calibration based on spherical center fitting method is less than 0.006 4 mm, and the RMSE of coordinate measurement of point inside the optimal station layout is less than 0.005 mm. Within the survey region of 5 m, the RMSE of length measurement is less than 0.003 6 mm using optimized multilateral method, and the RMSE of coordinate measurement of optimized multilateral method is less than 0.005 3 mm.  Conclusions  The optimized multilateral method can achieve high-precision coordinate measurement in a small region. The large-scale 3D coordinate measurement will be studied later using multilateral method.