限制GPS边长综合投影变形加权尺度比算法

A weighted scaling-ratio algorithm for reducing the integrated GPS side length projection deformation

高斯投影变形量是一个以至中央子午线距离为自变量的二次幂函数,其投影后的边长变形量沿横向呈二次曲线变化,理论上,横向不同位置的尺度比不一样,采用常规算数方法求定的平均尺度比一般情况下并不能理想地代表测区的整体尺度。尺度比计算时应顾及参与计算实测边长的高斯投影变形量及横向的最优代表范围,通过综合考虑高斯投影变形因素的影响来确定各个边长参与尺度比计算的权重。为了保持平差后GPS网的相对构型,以减少平差约束条件,宜将求定的加权尺度残差采用高程抵偿投影的方法予以处理。

The Gauss projection deformation is a quadratic power function with the distance to central meridian as an independent variable.The length deformation after projection is a quadratic curve along the lateral direction.In theory,the horizontal scale is different in different positions.Generally the average scale with conventional arithmetic methods cannot represent the total scale of the surveying area ideally.When it comes to the calculation of scale,the Gauss projection deformation of the actual side length and the optimal representative scope in lateral direction should be considered.Weight of each participated side length in the scale calculation should be determined by comprehensive consideration of the influence on Gauss projection deformation factors.In order to maintain the relative configuration of GPS network after adjustment and to reduce the constraints on adjustment,it is appropriate to deal with the weighted scaling-ratio residuals with the method of height compensation projection.