总体最小二乘联合平差  

Total Least Squares Joint Adjustment

作　　者：王乐洋[1,2,3] 余航[1] 

机构地区：[1]东华理工大学测绘工程学院,江西南昌330013 [2]流域生态与地理环境监测国家测绘地理信息局重点实验室,江西南昌330013 [3]江西省数字国土重点实验室,江西南昌330013

出　　处：《武汉大学学报（信息科学版）》2016年第12期1683-1689,共7页Geomatics and Information Science of Wuhan University

基　　金：国家自然科学基金(41204003;41664001);江西省教育厅科技基金(GJJ150595;KJLD12077;KJLD14049);流域生态与地理环境监测国家测绘地理信息局重点实验室开放基金(WE2015005);对地观测技术国家测绘地理信息局重点实验室项目(K201502);测绘地理信息公益性行业科研专项(201512026);东华理工大学博士科研启动基金(DHBK201113);东华理工大学研究生创新专项(DHYC-2015005);江西省杰出青年人才资助计划项目;国家重点研发计划(2016YFB0501405)~~

摘　　要：提出了将总体最小二乘方法应用于联合平差的模型,推导了附有相对权比的总体最小二乘联合平差方法。采用了多种方案来确定相对权比的大小。以参数估值与真值的差值范数作为评价指标,分析比较了单一数据总体最小二乘平差和两类数据总体最小二乘联合平差的模拟算例;通过给各类数据加入不同大小的随机噪声,分析了判别函数最小化法中随机噪声大小对确定相对权比的影响。模拟算例表明,平差结果的质量与相对权比的选取有关;当先验信息准确时,验前单位权方差法的结果最好,而当先验信息不准确时,判别函数为∑n_1i=1|V1_i|+∑n_2j=1|V2_j|及∑n_1i=1|V1_i|+∑n_2j=1|V2_j|/(1+X^TX)法均能取得有效的平差的判别函数最小化结果。The Total Least Squares（TLS）method is applied to joint adjustment.An algorithm for total least squares joint adjustment with a weight scaling factor is derived.The weight scaling factor is the key to deal with joint adjustment,and methods for determining the weight scaling factor are discussed.The difference norm between the estimated and true values is used to evaluate the TLS joint adjustment simulation.The influence of different noises on the weight scaling factor is also analyzed for two simulated examples.The results show that the estimated values is related to the weight scaling factor.When priori information is accurate,the prior unit weight variance method performs the best,and when priori information is inaccurate,the minimum discriminate function method with ∑n_1i=1｜V1_i｜＋∑n_2j=1｜V2_j｜ and ∑n_1i=1｜V1_i｜＋∑n_2j=1｜V2_j｜/（1＋X^TX） as its discriminate function can achieve effective results.

关 键 词：联合平差 相对权比 总体最小二乘 验前单位权方差法 判别函数最小化法 

分 类 号：P207[天文地球—测绘科学与技术]