实参数与复参数混合域最小二乘平差方法  

Mixing Real-Valued and Complex-Valued Parameters Modeling and Least Squares Adjustment Method

作　　者：刘志平[1] 李思达[1] 朱丹彤[1] 余航[1] LIU Zhiping;LI Sida;ZHU Dantong;YU Hang(School of Environment Science and Spatial Informatics,China University of Mining and Technology,Xuzhou 221116,China)

机构地区：[1]中国矿业大学环境与测绘学院,江苏徐州221116

出　　处：《测绘科学技术学报》2017年第6期551-555,共5页Journal of Geomatics Science and Technology

基　　金：国家自然科学基金项目(41204011;41504032);国家重点研发计划资助项目(2016YFC0803103;2016YFB0502102);精密工程与工业测量国家测绘局重点实验室开放基金项目(PF2017-12)

摘　　要：针对平差问题同时含有实数域参数和复数域参数的情形,提出了实参与复参混合的测量平差建模思路,并导出了相应的混合域最小二乘平差方法。该方法统一概括了实最小二乘和复最小二乘方法,其估计过程包括两步:基于零空间算子的实参数平差估计和复数平差模型的复参数估计。通过等价变换将实数域投影变换模型、直接线性变换模型分别重构为相应的混合域平差模型,有效降低法方程求逆维数,从而提高建模和平差计算效率。应用结果及分析验证了本文所提方法的正确性和有效性。The mixing real-valued and complex-valued parameters modeling and the least squares adjustment method are presented in this paper.Both the real-valued least squares method and complex-valued least squares method are generalized by this novel adjustment method,and the adjustment process can be decomposed into two steps.The first step is the real-valued parameters estimation process by eliminating the complex-valued parameters using the null-space matrix operator,and the second step is the complex-valued parameters estimation process by substituting the real-valued parameter estimates for the original mixing model.Both real-valued projection transformation model and real-valued direct linear transformation model are respectively transformed into the equivalent mixing model including the real-valued and complex-valued parameters.Thus,the normal equation dimension of the equivalent mixing model can be reduced and the parameters estimation efficiency can be improved.Finally,the application results demonstrate the validity and reliability of the mixing least squares adjustment method.

关 键 词：实最小二乘 复最小二乘 混合域最小二乘 投影变换模型 直接线性变换模型 

分 类 号：P207[天文地球—测绘科学与技术]