利用垂线偏差计算高程异常差法方程的快速构建方法

Fast Approach to Constructing Normal Equation During the Time of Calculating Height Anomaly Difference by Using Vertical Deflections

利用垂线偏差等重力格网数据平差计算高程异常差时,施加少量GPS/水准点进行控制,可以确定区域似大地水准面,但是采用传统方法在构造法方程时,需要对系数阵的每个元素逐一进行操作,并全部或者对角存储系数阵,具有计算速度慢、占用内存高等问题。为此提出了在平差解算中对系数阵先进行矩阵分块(操作单元为分块矩阵),再稀疏化处理(仅存非零元素),最后拼接的方法,实现了法方程阵的快速构建及解算。实验表明,相比于传统方法,该方法的计算效率提高了至少两个数量级,并且可快速解算传统方法在一般计算机上难以解算的平差问题,对于解算比较规则的格网数据平差问题具有一定的参考与借鉴意义。

Vertical deflections can be used tocalculate height anomaly differences,and determine a regional quasi-geoid under the control of GPS leveling points.But the existing typical methods used for structural equation,the elements in coefficient matrix need to be operated one by one,and all of the elements or those on a diagonal must be saved in internal memory for computing.This usually leads to low-speed processing and high-memory occupancy rates.In order to solve these problems,we propose a novel method in the form of a blocked matrix,then processes sparsely（only saving non-zero elements）,and finally integrates all the blocked matrixes.This blocked matrix is considered as operational unit in the further steps.Experiments show that：compared to the typical methods,the computation efficiency of our method has been improved at least 2orders of magnitudes,this makes our method can quickly solve an adjustment problem intractable by traditional methods of computer configuration.Therefore,our method has great reference value when resolving adjustment problems with regular gridded data.