基于变量投影法的自回归模型方差分量估计  

Variance Component Estimation of Autoregressive Model Based on Variable Projection Method

作　　者：吕志鹏 隋立芬[1] Lü Zhipeng;SUI Lifen(Institute of Geospatial Information,Information Engineering University,Zhengzhou 450001,China)

机构地区：[1]信息工程大学地理空间信息学院,河南郑州450001

出　　处：《武汉大学学报（信息科学版）》2020年第2期205-212,共8页Geomatics and Information Science of Wuhan University

基　　金：国家自然科学基金(41674016,41274016).

摘　　要：在自回归(autoregressive,AR)模型中,系数矩阵与观测向量中的随机误差同源。针对AR模型平差时观测权阵分配不合理、随机模型不准确的情况,采用变量投影法提取系数矩阵和观测向量构成的增广矩阵中的随机量,将变量误差(errors-in-variables,EIV)模型转化为非线性高斯-赫尔默特(Gauss-Helmert,GH)模型,利用非线性最小二乘理论得到一种结构总体最小二乘(structural total least squares,STLS)算法,并与最小二乘方差分量估计(least squares variance component estimation,LS-VCE)相结合推导出STLS问题的一种方差分量估计算法,将其应用到AR模型的方差分量估计。通过实测算例对算法有效性进行了验证,取得了与已有方法一致的结果。该算法观测权阵的构造十分简洁,同时也可用于协方差分量的估计。In the autoregressive(AR)model,random errors in the observation vector are homologous to those in the coefficient matrix.In view of the unreasonable distribution of the observation weight matrix and the inaccuracy of the random model,the random quantities in the augmented matrix consisting of the coefficient matrix and the observation vector are extracted by the variable projection method.Then,we transform the errors-in-variables(EIV)model into the nonlinear Gauss-Helmert(GH)model and propose a structural total least squares(STLS)algorithm by the nonlinear least squares adjustment theory.Combined with the least squares variance component estimation(LS-VCE)method,the variance component estimation method of STLS problem is derived.Furthermore,it is applied to the variance component estimation of the AR model.Through the real example,the effectiveness of proposed algorithm is verified.Meanwhile,the results are consistent with those of modified existing variance component estimation methods,but the construction of observation weight matrix is simple,it can also applied to the estimation of covariance factors.

关 键 词：自回归模型 方差分量估计 结构总体最小二乘 变量投影法 协方差分量 

分 类 号：P204[天文地球—测绘科学与技术] O212.1[理学—概率论与数理统计]