现场双经纬仪三维坐标测量系统

分析了经纬仪透视投影模型以及双经纬仪三维坐标测量模型。采用线性与非线性相结合的方法来求解双经纬仪坐标测量系统的参数,首先由8个以上空间点在两台经纬仪投影平面内对应的投影坐标计算出本质矩阵E,通过本质矩阵E的奇异值分解以及空间绝对距离的约束采用线性方法求出右经纬仪的投影矩阵,然后建立包含空间点在两台经纬仪投影平面内投影点固有约束以及空间点三维坐标在内的目标函数,并以线性方法求出的参数为初值,采用非线性优化的方法求解最优测量系统的参数。该方法保证了求解参数为全局最优,且求解速度快。试验结果表明,该方法切实可行。

THREE-DIMENSIONAL COORDINATE MEASURING SYSTEM WITH BINO-THEODOLITES ON SITE

The perspective projection model of the theodolite is analyzed and the mathematical model of the three-dimensional coordinates measuring system with bino-theodolites(TCMSBT) is analyzed. A new method, involving a direct linear solution and an iterative nonlinear solution, to determine all the geometrical parameters of the TCMSBT is proposed. Firstly, essential matrix E can be determined from 8 or more point correspondences in two projective planes of bino-theodolites and on the basis of absolute distance constraint, the projective matrix of the right theodolite can be determined by the singular value decomposition of E with closed-form method. Secondly, taking the parameters obtained in the first step as an initial guess, all the accurate geometrical parameters of the TCMSBT are estimated by nonlinear minimization of the cost function relative to the distance error affected by the measurement errors for the three coordinates of the space point and the co-planarity errors which two projective points and two observed centers of the bino-theodolites should follow. The two-steps procedures to determine the geometrical parameters permit a rapid estimation considerably reducing the number of iterations, moreover, the convergence is nearly guaranteed due to the linear guess obtained in the first step. It shows that this method is practical by experiments.