Acta Geodaetica et Cartographica Sinica ›› 2017, Vol. 46 ›› Issue (11): 1795-1801.doi: 10.11947/j.AGCS.2017.20170004

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

YAO Yibin1,2,3, XIONG Zhaohui1, ZHANG Bao1, ZHANG Liang1, KONG Jian4   

  1. 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:2017-01-03 Revised:2017-08-18 Online:2017-11-20 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)

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

CLC Number: