违背不相关性假设对Triple Collocation方法精度的影响  

Investigating the Impact of Violations in Orthogonality and Zero Cross-Correlation Assumption upon the Accuracy of Triple Collocation Methods

作　　者：谈松林 王洁[1,2] 季静静 刘美丽 湛忠宇 刘淼 王丽荣[5] 胡晓东 TAN Songlin;WANG Jie;JI Jingjing;LIU Meili;ZHAN Zhongyu;LIU Miao;WANG Lirong;HU Xiaodong(School of Hydrology and Water Resources,Nanjing University of Information Science and Technology,Nanjing 210044,China;Key Laboratory of Hydrometeorological Disaster Mechanism and Warning of Ministry of Water Resources,Nanjing University of Information Science and Technology,Nanjing 210044,China;Nanjing Sub-Bureau of Hydrology and Water Resources Survey,Jiangsu Survey Bureau of Hydrology and Water Resources,Nanjing 210008,China;Jiangsu Survey Bureau of Hydrology and Water Resources,Nanjing 210029,China;Hebei Meteorological Disaster Defense and Environmental Meteorology Center,Shijiazhuang 050022,China;Nanjing Hydraulic Research Institute,Nanjing 210017,China)

机构地区：[1]南京信息工程大学,南京210044 [2]水利部水文气象灾害机理与预警重点实验室,南京210044 [3]江苏省水文水资源勘测局南京分局,南京210008 [4]江苏省水文水资源勘测局,南京210029 [5]河北省气象灾害防御和环境气象中心,石家庄050022 [6]江苏省水利科学研究院,南京210017

出　　处：《地球信息科学学报》2024年第3期591-603,共13页Journal of Geo-information Science

基　　金：国家自然科学基金项目(41877158);河北省省级科技计划资助项目(19275408D);江苏省水利科技项目(2020040)。

摘　　要：Triple Collocation(TC)方法是一种可以在未知真值情况下评估3个独立观测样本各自不确定性的方法,该方法使用的前提是误差形式假设与2组不相关性假设,但在实际使用中,这3条假设难以完全满足。其中2组不相关性假设经常面临较大的违背,并且无法得知这种假设违背对结果误差的影响。本文通过虚拟样本实验生成了多组不同程度违背不相关性假设的样本,以定量评估不同程度假设违背对结果误差的影响。结果表明,一般情况下,某一条不相关性假设的违背程度增加时,方法的结果误差会相应地呈线性或平方倍数增加;但当不相关性假设的违背处于某个特定关系时,TC方法结果的误差会突然大幅度增加,这种现象在以往的研究中并没有得到重视,后文将该现象简称为异常点。为了探求异常点出现的原因,本文从理论上推导出了违反不相关性假设与结果误差之间的关系,这种关系呈现为分式结构,而异常点的出现正是这种分式结构所致。异常点的存在影响了方法的稳定性。从差值形式的TC方法的角度来看,抑制异常点的关键在于如何更好地设计缩放系数。本文给出了2种抑制异常点的方法:(1)忽略加性偏差系数,使得缩放系数不受两组不相关性假设的影响;(2)限制缩放系数的上下限。根据实际数据分析,第2种改进方法优于第1种。第2种方法不仅保留了TC方法的准确性,而且有效地避免了异常点的出现。值得注意的是,在实际数据中,部分异常点会以负值形式出现并因计算结果不能为负而被剔除。在使用TC方法进行计算时,重复次数较少的情况下,可以不考虑异常点的影响。Triple Collocation(TC)is a technique for assessing the uncertainties of three samples individually without knowledge of the true values.This method is based on the assumptions of linearity,orthogonality,and zero cross-correlation.In practical use,these three assumptions are often difficult to achieve,particularly the orthogonality and zero cross-correlation assumptions,which often encounter significant violations.Moreover,we are uncertain about the impact of these assumption violations on the errors of the method's results.In this study,we simulated multiple sets of synthetic samples with varying degrees of two assumption violations to investigate the impact of assumption violations on the accuracy of the TC method.The results of synthetic samples experiment indicate that,in general,when there is an increase in the violation of orthogonality or zero cross-correlation assumptions,the error of the method's results increases linearly or quadratically.However,under certain specific conditions of assumption violation,there is a sudden and spike-like increase in the error of TC method results.This phenomenon is referred to as"outliers".To understand the origin of the outliers,we derived the complete mathematical relationship between the violation of assumptions and the errors of the results.This relationship exhibits a fractional structure rather than a linear one,contributing to the emergence of outliers.From the perspective of the difference notation,this fractional structure results from rescaling coefficients.Continuing to analyze this mathematical relationship,we can draw two conclusions.Firstly,merely ensuring the approximate independence of the three samples does not necessarily lead to improved method results.When the structural relationships among the three samples meet certain conditions,outliers emerge.Additionally,previous attempts at method improvement have aimed at overall reducing the sensitivity of this method to assumptions,neglecting the presence of outliers.Considering these factors,the key to suppre

关 键 词：Triple collocation 假设违背 异常点 遥感 数据同化 数据评估 数据不确定性分析 无实测数据 

分 类 号：P237[天文地球—摄影测量与遥感]