School of Surveying and Land Information Engineering, Henan Polytechnic University, Jiaozuo, 454000, China.
Collaborative Innovation Center of BDS Research Application, Zhengzhou, 450052, China.
Sci Rep. 2023 Mar 17;13(1):4454. doi: 10.1038/s41598-023-31635-3.
Because the traditional Cholesky decomposition algorithm still has some problems such as computational complexity and scattered structure among matrices when solving the GNSS ambiguity, it is the key problem to further improve the computational efficiency of the least squares ambiguity reduction correlation process in the carrier phase integer ambiguity solution. But the traditional matrix decomposition calculation is more complex and time-consuming, to improve the efficiency of the matrix decomposition, in this paper, the decomposition process of traditional matrix elements is divided into two steps: multiplication update and column reduction of square root calculation. The column reduction step is used to perform square root calculation and column division calculation, while the update step is used for the update task of multiplication. Based on the above ideas, the existing Cholesky decomposition algorithm is improved, and a column oriented Cholesky (C-Cholesky) algorithm is proposed to further improve the efficiency of matrix decomposition, so as to shorten the calculation time of integer ambiguity reduction correlation. The results show that this method is effective and superior, and can improve the data processing efficiency by about 12.34% on average without changing the integer ambiguity accuracy of the traditional Cholesky algorithm.
由于传统的 Cholesky 分解算法在解决 GNSS 模糊度时仍然存在计算复杂度和矩阵间结构分散等问题，因此进一步提高载波相位整周模糊度解算中最小二乘模糊度降相关过程的计算效率是关键问题。但传统的矩阵分解计算较为复杂和耗时，为提高矩阵分解的效率，本文将传统矩阵元素的分解过程分为乘法更新和平方根计算的列约简两步进行。列约简步用于进行平方根计算和列划分计算，而更新步用于乘法的更新任务。基于上述思路，对现有的 Cholesky 分解算法进行了改进，提出了一种面向列的 Cholesky（C-Cholesky）算法，进一步提高了矩阵分解的效率，从而缩短整数模糊度降相关的计算时间。结果表明，该方法有效且优越，在不改变传统 Cholesky 算法整数模糊度精度的情况下，平均可提高约 12.34%的数据处理效率。
