选权拟合法解的特性探讨  

Investigation on the Characteristics of the Fitting Method by Selection of Parameter Weights

作　　者：王爱生[1] 欧吉坤[2] 阳仁贵[2] 

机构地区：[1]徐州师范大学测绘学院,徐州市上海路101号221116 [2]中国科学院测量与地球物理研究所动力大地测量学重点实验室,武汉市徐东大街340号430077

出　　处：《武汉大学学报（信息科学版）》2011年第7期835-838,共4页Geomatics and Information Science of Wuhan University

基　　金：国家自然科学基金资助项目(40874011;40874009);徐州师范大学科研基金资助项目(09XLR18)

摘　　要：选权拟合法是解决大地测量中的不适定问题的一种方法,是对吉洪诺夫正则化方法的改造。在推导一般正则化解的偏差计算公式并回顾了选权拟合法的基本原理和公式的基础上,推导了选权拟合法解的一个重要性质:只要被约束的部分参数估值无偏,其余的也无偏;该性质说明利用选权拟合进行参数估计的结果是有条件无偏的。这个不同于一般正则化解的重要特性可以用于设计加快GPS短基线快速定位双差模糊度解算策略。恰当利用选权拟合法,用实测数据算例分析了GPS基线分量的先验信息的偏差大小对模糊度解算的影响。The fitting method of selection of parameter weights is an approach to solve the ill-posed problem of geodesy,which is the reform of the Tikhonov regularization algorithm.The general formula that is used to compute the bias of the regularization resolution is deduced and the basic principles and theory of the fitting method of selection of parameter weights are introduced firstly.And then an important property is derived： the other parameters are also unbiased if the constrained partial parameters are unbiased.It indicates the result that is estimated by applying the fitting method of selection of parameter weights is conditional unbiased.This important property is different from that of the general regularization method and can be used to speed up the resolution of the double differential ambiguities in the fast positioning of GPS short baselines.Some experiments were adopted to analyze the impacts of three dimension baseline components on the resolution of the ambiguities.

关 键 词：正则化 选权拟合法 病态问题 模糊度解算 

分 类 号：P207[天文地球—测绘科学与技术] P228.41