摘要
首先分析了法方程稳定性对平差解算结果的影响。为减弱法方程对平差解算结果的影响,采用矩阵分解方法直接对系数矩阵进行矩阵分解,以求解最小二乘最小范数解替代原来最小二乘的法矩阵求逆运算,从而克服法方程求逆造成的解算稳定性差和病态性问题。实验分析结果表明基于矩阵分解的平差解算精度和可靠性较优。
The effect of the normal equation stability on adjustment results is analyzed based on the least squares algorithm.In order to weaken this influence,the matrix decomposition method is used to obtain the least squares minimum norm solution instead of the least squares solution.By this way,the ill-posed and unstable problem of solution caused by normal equation solution can be solved.The experiment results show that the solution precision and reliability of this new method is better.
出处
《海洋测绘》
2014年第5期20-23,共4页
Hydrographic Surveying and Charting
基金
国家自然科学基金(41374042)
关键词
法方程
矩阵QR分解
SVD分解
最小二乘
normal equation
matrix QR decomposition
singular value decomposition
least squares
