复数域与实数域最小二乘平差的等价性研究

发布时间：2018-04-10 02:32

  本文选题：实最小二乘平差　切入点：复矩阵求逆　出处：《大地测量与地球动力学》2016年08期

【摘要】：针对等精度独立观测条件下的同一平差问题,从理论上证明复数域与实数域最小二乘平差结果的等价性,并指出复平差方法在函数模型表达上的简便特点。基于常用的图像几何校正多项式模型构造复数域多项式模型,并设计一阶和二阶多项式图像校正算例。结果表明,两种方法的平差结果完全相同,但复数域平差方法的参数维数和法矩阵阶数仅为实数域平差方法的一半。
[Abstract]:In view of the same adjustment problem under the condition of equal precision independent observation, the equivalence of the results of least square adjustment in complex field and real field is proved theoretically, and the simple characteristics of complex adjustment method in the expression of function model are pointed out.Based on the commonly used image geometric correction polynomial model, the complex domain polynomial model is constructed, and the first and second order polynomial image correction examples are designed.The results show that the adjustment results of the two methods are identical, but the parameter dimension and the normal matrix order of the complex domain adjustment method are only half of the real number domain adjustment method.
【作者单位】： 中国矿业大学国土环境与灾害监测国家测绘地理信息局重点实验室;
【基金】：国家自然科学基金(41204011,41504032) 大地测量与地球动力学国家重点实验室开放基金(SKLGED2014-3-2-E)~~
【分类号】：P207.2
，

本文编号：1729289