顾及设计矩阵误差的AR模型新解法

姚宜斌; 熊朝晖; 张豹; 张良; 孔建

doi:10.11947/j.AGCS.2017.20170004

测绘学报 >

2017 , Vol. 46 >Issue 11: 1795 - 1801

DOI: https://doi.org/10.11947/j.AGCS.2017.20170004

大地测量学与导航

顾及设计矩阵误差的AR模型新解法

姚宜斌 ,
熊朝晖 ,
张豹 ,
张良 ,
孔建

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1. 武汉大学测绘学院, 湖北武汉 430079;
2. 武汉大学地球空间环境与大地测量教育部重点实验室, 湖北武汉 430079;
3. 地球空间信息技术协同创新中心, 湖北武汉 430079;
4. 武汉大学中国南极测绘研究中心, 湖北武汉 430079

姚宜斌(1976-),男,教授,主要从事测量数据处理理论与方法、GNSS空间环境学研究。E-mail:ybyao@sgg.whu.edu.cn

收稿日期: 2017-01-03

修回日期: 2017-08-18

网络出版日期: 2017-12-05

基金资助

国家自然科学基金（41274022；41574028）；湖北省杰出青年科学基金（2015CFA036）

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A New Method to Solving AR Model Parameters Considering Random Errors of Design Matrix

YAO Yibin ,
XIONG Zhaohui ,
ZHANG Bao ,
ZHANG Liang ,
KONG Jian

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1. School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China;
2. Key Laboratory of Geospace Environment and Geodesy, Ministry of Education, Wuhan University, Wuhan 430079, China;
3. Collaborative Innovation Center for Geospatial Technology, Wuhan 430079, China;
4. Chinese Antarctic Center of Surveying and Mapping, Wuhan 430079, China

Received date: 2017-01-03

Revised date: 2017-08-18

Online published: 2017-12-05

Supported by

The General Program of National Natural Science Foundation of China (Nos. 41274022; 41574028); Natural Science Foundation for Distinguished Young Scholars of Hubei Province of China (No. 2015CFA036)

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摘要

在自回归模型求解中，设计矩阵和观测值均存在误差，传统的最小二乘法不能很好地解决这一问题。本文提出了一种顾及设计矩阵误差的AR模型新解法，通过引入虚拟观测值，使观测向量与设计矩阵不仅同源而且带误差的元素个数相同，然后通过对观测方程进行等价变换巧妙实现了在最小二乘框架下求解自回归问题。利用模拟数据及实测数据分别对新算法进行了内符合精度检验，并利用实测数据对新算法进行外符合精度检验，结果表明新算法得到的结果显著优于奇异值分解（singular value decomposition，SVD）解法及传统最小二乘解法，验证了算法的精度和有效性。

关键词： AR模型; 设计矩阵误差; 整体最小二乘; 虚拟观测值; 奇异值分解

本文引用格式

姚宜斌 , 熊朝晖 , 张豹 , 张良 , 孔建 . 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 . DOI: 10.11947/j.AGCS.2017.20170004

Abstract

The ordinary least square method could not solve the problem that the error exist both in design matrix and observation vector while compute parameter values of AR model. In this article, a new method is proposed which consider the random errors of design matrix. The source of design matrix and observation vector is same and the amount of parameters contain error can be equal by introducing virtual observation. Then, this problem could be solved under the framework of normal least square by equivalence transformation of observation equation. The result of this new method is superior to SVD method and normal least square method by simulation date and observation data which verify the feasibility and effectiveness of this method.

Key words： AR model; design matrix error; TLS; virtual observations; SVD method

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