重复观测平差的一种新算法
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摘要
计算单位权中误差,采用■是不严格的,因为它把V~TPV与V~TPV的平均值混为一谈。为此,有学者基于χ~2统计量,按每次平差所得的V~TPV计算单位权中误差,精度有所提高。但是,该方法没有研究该单位权中误差与传统方法单位权中误差的理论关系。提出了一种新方法,推导了新旧方法的理论关系,并给出了模拟算例。结果表明:新方法的单位权方差是无偏估计,新旧方法单位权中误差近似相等(但含义不一致,数字近似相等),新方法单位权方差的方差大约是旧方法的1/m,故新方法更有利于单位权中误差或方差的准确计算;新方法未知数X的估值是无偏估计,新方法未知数X方差阵与旧方法近似相等,且新方法未知数X的相关计算等于或优于旧方法;模拟算例验证了新方法的可行性和有效性。
■ isn't strict to calculate mean square error of unit weight because it confuses V~TPV and average of. So,based on statistical variable χ~2,some scholar proposed a sort of new method according to adjustment value V~TPV of each time. The new method is better in precision,but it hasn't studied on the theoretical relationship of mean square error between the new method and the traditional method. This paper proposes a sort of new method,deducing the theoretical relationship between the traditional method and the new method,and giving a simulation example. The results showed that,variance of unit weight of the new method is unbiased variable, mean square errors of the traditional method and the new method are approximately equal but the meanings of mean square error are inconsistent,variance of variance of unit weight of the new method is about 1/m that of the traditional method. So,the new method is more conducive to accurately calculate mean square error or variance of unit weight. And also,the results showed that,the unknown X of the new method is unbiased variable,the variance matrix of the unknown X of the new method is approximately equal to that of the traditional method,and the correlation calculation of the unknown X of the new method is not lower than that of the traditional method. In addition,the results showed that the simulation example verified the feasibility and effectiveness of the new method.
■ isn't strict to calculate mean square error of unit weight because it confuses V~TPV and average of. So,based on statistical variable χ~2,some scholar proposed a sort of new method according to adjustment value V~TPV of each time. The new method is better in precision,but it hasn't studied on the theoretical relationship of mean square error between the new method and the traditional method. This paper proposes a sort of new method,deducing the theoretical relationship between the traditional method and the new method,and giving a simulation example. The results showed that,variance of unit weight of the new method is unbiased variable, mean square errors of the traditional method and the new method are approximately equal but the meanings of mean square error are inconsistent,variance of variance of unit weight of the new method is about 1/m that of the traditional method. So,the new method is more conducive to accurately calculate mean square error or variance of unit weight. And also,the results showed that,the unknown X of the new method is unbiased variable,the variance matrix of the unknown X of the new method is approximately equal to that of the traditional method,and the correlation calculation of the unknown X of the new method is not lower than that of the traditional method. In addition,the results showed that the simulation example verified the feasibility and effectiveness of the new method.
引文
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[19]陶武勇,鲁铁定,吴飞.求解GM(1,1)模型新总体最小二乘算法[J].测绘科学技术学报,2016,33(5):476-479.
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[3]崔希璋,於宗俦,陶本藻,等.广义测量平差(新版)[M].武汉:武汉大学出版社,2001.
[4]武汉大学测绘学院测量平差学科组.误差理论与测量平差基础(第二版)[M].武汉:武汉大学出版社,2009.
[5]陶本藻.自由网平差与变形分析[M].北京:测绘出版社,1984.
[6]陶本藻.测量数据处理的统计理论和方法[M].北京:测绘出版社,2007.
[7]宁津生,陈俊勇,李德仁,等.测绘学概论[M].武汉:武汉大学出版社,2004.
[8]李德仁,袁修孝.误差处理与可靠性理论[M].武汉:武汉大学出版社,2002.
[9]张正禄,黄全义,文鸿雁,等.工程的变形监测分析与预报[M].北京:测绘出版社,2007.
[10]康建松,黄瑶,吴志斌.悬索桥锚碇监测基准网的构建方法及稳定性分析[J].勘察科学技术,2009(1):13-16.
[11]范成成,张俊.基于最小二乘法的NAR模型及其在沉降预测中的应用[J].城市勘测,2019(1):161-164.
[12]兰汉东,郭锥.基于附加参数的跨海高程传递研究[J].铁道建筑技术,2018(10):16-21.
[13]姚宜斌,熊朝晖,张豹,等.顾及设计矩阵误差的AR模型新解法[J].测绘学报,2017,46(11):1795-1801.
[14]陶叶青,蔡安宁,杨娟.抗差总体最小二乘理论研究进展[J].河北北方学院学报(自然科学版),2018,34(1):58-62.
[15]陈良松,曾维荣. GPS高程拟合及精度分析[J].城市建设理论研究(电子版),2017(35):169-170.
[16]陶武勇,鲁铁定,吴飞,等.求解球面拟合的改进总体最小二乘算法[J].大地测量与地球动力学,2018,38(1):92-96.
[17]陈潇,侯金波,王鑫森.棱镜常数快速检测方法研究[J].测绘工程,2017,26(3):77-80.
[18]曾艳艳,朱照荣,杨伯钢,等.九参数法在不动产测绘空间基准中的应用[J].测绘科学,2016,41(12):270-272.
[19]陶武勇,鲁铁定,吴飞.求解GM(1,1)模型新总体最小二乘算法[J].测绘科学技术学报,2016,33(5):476-479.