附加一次和二次等式约束的Partial-EIV模型及相应算法  

Partial Errors-in-Variables Model with Linear and Quadratic Equality Constraints and Corresponding Algorithm

作　　者：韩杰 张松林 HAN Jie;ZHANG Songlin(College of Surveying and Geo-Informatics,Tongji University,Shanghai 200092,China)

机构地区：[1]同济大学测绘与地理信息学院

出　　处：《测绘科学技术学报》2019年第1期17-22,27,共7页Journal of Geomatics Science and Technology

基　　金：国家重点研发计划项目(2017YFB0502700);现代工程测量国家测绘地理信息局重点实验室开放课题项目(TJES1802)

摘　　要：研究了附加一次和二次等式约束的Partial-EIV模型,推导了加权整体最小二乘估计准则下相应的计算公式,并讨论了仅附加一次等式约束的Partial-EIV模型和仅附加二次等式约束的Partial-EIV模型。通过正交线性回归和平面坐标转换两个算例进行实验,将新算法与已有的附加等式约束的EIV模型的方法进行了对比,发现文中方法计算效率更高,且适用于结构化EIV模型的求解。In this paper,a Partial-EIV model with linear and quadratic equality constraints is studied and the corresponding formulas under the weighted total least squares criterion is derived.The Partial-EIV model with only linear equality constraints,and only quadratic equality constraints are discussed as well.Two experiments of orthogonal linear regression and plane coordinate transformation are carried out.The results show that the proposed method is more efficient,and can get consistent results with the existing algorithms of equality-constrained EIV model.The results also show that the proposed method is suitable for structured EIV problems.

关 键 词：整体最小二乘 Partial-EIV模型 等式约束 正交线性回归 平面坐标转换 

分 类 号：P223[天文地球—大地测量学与测量工程]