Geodetic Institute, Leibniz Universität Hannover, Nienburger Str. 1, 30167 Hannover, Germany.
Sensors (Basel). 2018 Sep 5;18(9):2964. doi: 10.3390/s18092964.
For a trustworthy least-squares (LS) solution, a good description of the stochastic properties of the measurements is indispensable. For a terrestrial laser scanner (TLS), the range variance can be described by a power law function with respect to the intensity of the reflected signal. The power and scaling factors depend on the laser scanner under consideration, and could be accurately determined by means of calibrations in 1d mode or residual analysis of LS adjustment. However, such procedures complicate significantly the use of empirical intensity models (IM). The extent to which a point-wise weighting is suitable when the derived variance covariance matrix (VCM) is further used in a LS adjustment remains moreover questionable. Thanks to closed loop simulations, where both the true geometry and stochastic model are under control, we investigate how variations of the parameters of the IM affect the results of a LS adjustment. As a case study, we consider the determination of the Cartesian coordinates of the control points (CP) from a B-splines curve. We show that a constant variance can be assessed to all the points of an object having homogeneous properties, without affecting the a posteriori variance factor or the loss of efficiency of the LS solution. The results from a real case scenario highlight that the conclusions of the simulations stay valid even for more challenging geometries. A procedure to determine the range variance is proposed to simplify the computation of the VCM.
对于可靠的最小二乘法 (LS) 解，对测量的随机特性进行良好的描述是必不可少的。对于地面激光扫描仪 (TLS)，范围方差可以用反射信号强度的幂律函数来描述。幂和比例因子取决于所考虑的激光扫描仪，并可以通过 1d 模式下的校准或 LS 调整的残差分析来准确确定。然而，这些程序显著增加了经验强度模型 (IM) 的使用难度。在 LS 调整中进一步使用推导的方差协方差矩阵 (VCM) 时，逐点加权的程度仍然存在疑问。由于闭环模拟，其中真实几何形状和随机模型都在控制之中，我们研究了 IM 参数的变化如何影响 LS 调整的结果。作为案例研究，我们考虑从 B 样条曲线上确定控制点 (CP) 的笛卡尔坐标。我们表明，可以对具有均匀特性的物体的所有点评估恒定的方差，而不会影响后验方差因子或 LS 解的效率损失。实际案例场景的结果表明，模拟的结论即使对于更具挑战性的几何形状仍然有效。提出了一种确定范围方差的方法来简化 VCM 的计算。
