一种相关观测的Partial EIV模型求解方法

摘要

As an extended form of the errors-in-variables(EIV) model, partial errors-in-variables(Partial EIV) model has more advantages than the previous one, such as regular structure, simple solving method, which make it has a wide range of applications.Considering the situation that the correlation between the observations and elements in coefficient matrix is not taken into account in the existed algorithms derived from Partial EIV model, the non-repetitive random elements in the augmented matrix consisting of observation vector and coefficient matrix are extracted to build a more suitable partial EIV model.Based on this model, the special assumptions are extended to the general case where the observations are correlated, a new weighted total least squares(WTLS)algorithms is derived when the observations and elements in coefficient matrix are heteroscedastic and correlated.Through two examples, the algorithm proposed in this paper and the existed algorithms which consider the correlation of the observation in EIV model are compared and analyzed.Research shows that these algorithms can improve the calculation efficiency and more general, especially for the situation that coefficient matrix consists of constant elements and repeated elements.%Partial errors-in-variables(Partial-EIV)模型作为EIV模型的扩展形式,其构造方式更有规律,解算方法更为简便,能有效应用于实际情况.针对已有Partial EIV模型方法未考虑观测向量和系数矩阵存在相关性这一情况,通过提取观测向量和系数矩阵组成的增广矩阵中非重复出现的随机元素,构建更具一般适用性的Partial EIV模型,在该模型的基础上,将特殊假定条件扩展到不限定观测数据相关性的一般情况,详细推导了观测向量和系数矩阵元素相关且不等精度情况下的加权总体最小二乘方法,通过算例试验,并与目前已有的解决EIV模型相关观测情况下的方法进行了比较分析,研究表明本文方法可以提高计算效率,更具一般性,特别是对于观测向量和系数矩阵中存在常数元素和重复元素的情况.