重复观测平差的一种新算法

A Kind of New Adjustment Method about Repetition Surveying

计算单位权中误差,采用^σ0=±√VTPV/r是不严格的,因为它把VTPV与VTPV的平均值混为一谈。为此,有学者基于χ2统计量,按每次平差所得的VTPV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。

^σ0=±√VTPV/r isn't strict to calculate mean square error of unit weight because it confuses VTPV and average of. So,based on statistical variable χ2,some scholar proposed a sort of new method according to adjustment value VTPV 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.