多维观测的矩阵参数建模与加权最小二乘估计  

Matrix-Parameter Weighted Least-Squares Method for Multivariable Observations

作　　者：刘志平[1] 朱丹彤[1] 余航[1] 李思达[1] LIU Zhiping;ZHU Dantong;YU Hang;LI Sida(School of Environment Science and Spatial Informatics,China University of Mining and Technology,1 Daxue Road,Xuzhou 221116,China)

机构地区：[1]中国矿业大学环境与测绘学院,江苏省徐州市大学路1号221116

出　　处：《大地测量与地球动力学》2018年第8期862-867,共6页Journal of Geodesy and Geodynamics

基　　金：国家自然科学基金(41204011;41504032);国家重点研发计划(2016YFC0803103;2016YFB0502102);精密工程与工业测量国家测绘地理信息局重点实验室开放基金(PF2017-12)~~

摘　　要：针对常规向量参数法多维观测建模与平差效率低的问题,分析指出多维观测矩阵参数建模条件应满足不同观测维度的参数独立且个数相等特点(简称独立同构特征),进而利用该建模条件、Kronecker积运算性质和加权最小二乘原理提出矩阵参数建模与加权最小二乘估计方法。该方法顾及不同观测维互相关性,增大系数阵稠密度,降低法矩阵阶数,从而有效提高了建模与平差计算效率。空间直线和GPS站坐标时序模型计算结果均表明,向量参数法和矩阵参数法平差结果相同,但后者具有更高的存储与计算效率。Aiming at the low computational efficiency of the existing vector-parameter method for multivariable observations modeling and adjustment,we propose a matrix-parameter weighted leastsquares method for multivariable observations,using the equivalent transformation,Kronecker product techniques and weighted least-squares method.Considering cross-correlation of different dimensional observations,the proposed method reconstructs the vector-parameter as a matrix-parameter form that has parameter independence and isomorphism in the multivariable observations model.This reduces the dimension number of the normal matrix and increases matrix density of the coefficient matrix.Consequently,high computational efficiency can be achieved with the proposed method.The adjustment results of space linear model and IGS coordinate time series model show that both the new matrix-parameter method and the traditional vector-parameter method have the same estimation results,but the proposed method achieves higher computational efficiency.

关 键 词：多维观测模型 完全稠密矩阵 向量参数法 矩阵参数法 加权最小二乘估计 

分 类 号：P207[天文地球—测绘科学与技术]