Variance Component Estimation of Autoregressive Model Based on Variable Projection Method

LÜ Zhipeng; SUI Lifen

doi:10.13203/j.whugis20180352

Volume 45 Issue 2

Feb. 2020

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Geomatics and Information Science of Wuhan University > 2020 > 45(2): 205-212. > DOI: 10.13203/j.whugis20180352

LÜ Zhipeng, SUI Lifen. Variance Component Estimation of Autoregressive Model Based on Variable Projection Method[J]. Geomatics and Information Science of Wuhan University, 2020, 45(2): 205-212. DOI: 10.13203/j.whugis20180352

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Variance Component Estimation of Autoregressive Model Based on Variable Projection Method

Institute of Geospatial Information, Information Engineering University, Zhengzhou 450001, China

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The National Natural Science Foundation of China 41674016

The National Natural Science Foundation of China 41274016

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Author Bio:
LÜ Zhipeng, PhD candidate, specializes in theories and methods of spatial geodetic data processing. E-mail:lvzhipeng1989@qq.com
Received Date: May 27, 2019
Published Date: February 04, 2020

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Abstract

Abstract

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.
- AR model,
- variance component estimation,
- STLS,
- variable projection method,
- covariance factor

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[1]	Van Loan S, Van Dewalle J. The Total Least-Squares Problem:Computational Aspects and Analysis[M]. Philadelphia:Society for Industrial and Applied Mathematics, 1991
[2]	刘经南, 曾文宪, 徐培亮.整体最小二乘估计的研究进展[J].武汉大学学报·信息科学版, 2013, 38(5):505-512 http://ch.whu.edu.cn/CN/abstract/abstract2641.shtml Liu Jingnan, Zeng Wenxian, Xu Peiliang. Overview of Total Least Squares Methods[J]. Geomatics and Information Science of Wuhan University, 2013, 38(5):505-512 http://ch.whu.edu.cn/CN/abstract/abstract2641.shtml
[3]	王乐洋, 许才军.总体最小二乘研究进展[J].武汉大学学报·信息科学版, 2013, 38(7):850-856 http://ch.whu.edu.cn/CN/abstract/abstract2703.shtml Wang Leyang, Xu Caijun. Progress in Total Least Squares[J]. Geomatics and Information Science of Wuhan University, 2013, 38(7):850-856 http://ch.whu.edu.cn/CN/abstract/abstract2703.shtml
[4]	Fang Xing. A Structured and Constrained Total Least-Squares Solution with Cross-Covariances[J]. Studia Geophysica et Geodaetica, 2014, 58(1):1-16 doi: 10.1007/s11200-012-0671-z
[5]	Rosen J B, Park H, Glick J. Total Least Norm Formulation and Solution for Structured Problems[J]. SIAM Journal on Matrix Analysis & Applications, 1996, 17(1):110-126 http://www.researchgate.net/publication/239061482_Total_Least_Norm_Formulation_and_Solution_for_Structured_Problems
[6]	Van Huffel S, Park H, Rosen J B. Formulation and Solution of Structured Total Least Norm Problems for Parameter Estimation[J]. IEEE Transactions on Signal Processing, 1996, 44(10):2464-2474 doi: 10.1109/78.539031
[7]	Markovsky I, Huffel S V. On Weighted Structured Total Least Squares[C]. International Conference on Large-Scale Scientific Computing, Sozopol, Bulgaria, 2005
[8]	Xu Peiliang, Liu Jiangnan, Shi Chuang. Total Least Squares Adjustment in Partial Errors-In-Variables Models:Algorithm and Statistical Analysis[J]. Journal of Geodesy, 2012, 86(8):661-675 doi: 10.1007/s00190-012-0552-9
[9]	王乐洋, 余航, 陈晓勇. Partial EIV模型的解法[J].测绘学报, 2016, 45(1):22-29 doi: 10.11947/j.AGCS.2016.20140560 Wang Leyang, Yu Hang, Chen Xiaoyong. An Algorithm for Partial EIV Model[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(1):22-29 doi: 10.11947/j.AGCS.2016.20140560
[10]	王乐洋, 许光煜, 温贵森.一种相关观测的Partial EIV模型求解方法[J].测绘学报, 2017, 46(8):44-53 http://d.old.wanfangdata.com.cn/Periodical/chxb201708007 Wang Leyang, Xu Guangyu, Wen Guisen. A Method for Partial EIV Model with Correlated Observations[J]. Acta Geodaetica et Cartographica Sinica, 2017, 46(8):44-53 http://d.old.wanfangdata.com.cn/Periodical/chxb201708007
[11]	Fang Xing. Weighted Total Least Squares:Necessary and Sufficient Conditions, Fixed and Random Parameters[J]. Journal of Geodesy, 2013, 87(8):733-749 doi: 10.1007/s00190-013-0643-2
[12]	Amiri-Simkooei A R, Jazaeri S. Weighted Total Least Squares Formulated by Standard Least Squares Theory[J]. Journal of Geodetic Science, 2012, 2(2):113-124 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=10.2478/v10156-011-0036-5
[13]	姚宜斌, 黄书华, 陈家君.求解自回归模型参数的整体最小二乘新方法[J].武汉大学学报·信息科学版, 2014, 39(12):1463-1466 http://ch.whu.edu.cn/CN/abstract/abstract3142.shtml Yao Yibin, Huang Shuhua, Chen Jiajun. A New Method of TLS to Solving the Autoregressive Model Parameter[J]. Geomatics and Information Science of Wuhan University, 2014, 39(12):1463-1466 http://ch.whu.edu.cn/CN/abstract/abstract3142.shtml
[14]	姚宜斌, 熊朝晖, 张豹, 等.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 Yao Yibin, Xiong Zhaohui, Zhang Bao, et al.A New Method to Solving AR Model Parameters Considering Random Errors of Design Matrix[J]. Acta Geodaetica et Cartographica Sinica, 2017, 46(11):1795-1801 doi: 10.11947/j.AGCS.2017.20170004
[15]	Teunissen P J G, Amiri-Simkooei A R. Least-Squares Variance Component Estimation[J]. Journal of Geodesy, 2008, 82(2):65-82 doi: 10.1007/s00190-007-0157-x
[16]	Amiri-Simkooei A R. Least-Squares Variance Component Estimation: Theory and GPS Applications[D]. Delft: Delft University of Technology, 2007
[17]	Amiri-Simkooei A R. Application of Least Squares Variance Component Estimation to Errors-In-Variables Models[J]. Journal of Geodesy, 2013, 87(10-12):935-944 doi: 10.1007/s00190-013-0658-8
[18]	Mahboub V. Variance Component Estimation in Errors-In-Variables Models and a Rigorous Total Least-Squares Approach[J]. Studia Geophysica et Geodaetica, 2014, 58(1):17-40 doi: 10.1007/s11200-013-1150-x
[19]	Xu Peiling, Liu Jingnan. Variance Components in Errors-In-Variables Models:Estimability, Stability and Bias Analysis[J]. Journal of Geodesy, 2014, 88(8):719-734 doi: 10.1007/s00190-014-0717-9
[20]	Wang Leyang, Xu Guangyu. Variance Component Estimation for Partial Errors-In-Variables Models[J]. Studia Geophysica et Geodaetica, 2016, 60(1):35-55 doi: 10.1007/s11200-014-0975-2
[21]	王乐洋, 许光煜, 陈晓勇.附有相对权比的PEIV模型总体最小二乘平差[J].武汉大学学报·信息科学版, 2017, 42(6):857-863 http://ch.whu.edu.cn/CN/abstract/abstract5764.shtml Wang Leyang, Xu Guangyu, Chen Xiaoyong. Total Least Squares Adjustment of Partial Errors-In-Variables Model with Weight Scaling Factor[J]. Geomatics and Information Science of Wuhan University, 2017, 42(6):857-863 http://ch.whu.edu.cn/CN/abstract/abstract5764.shtml
[22]	王乐洋, 温贵森.相关观测PEIV模型的最小二乘方差分量估计[J].测绘地理信息, 2018, 43(1):8-14 http://d.old.wanfangdata.com.cn/Periodical/chxxygc201801002 Wang Leyang, Wen Guisen. Least Squares Variance Components Estimation of PEIV Model with Correlated Observations[J]. Journal of Geomatics, 2018, 43(1):8-14 http://d.old.wanfangdata.com.cn/Periodical/chxxygc201801002
[23]	王乐洋, 温贵森. Partial EIV模型的非负最小二乘方差分量估计[J].测绘学报, 2017, 46(7):857-865 http://d.old.wanfangdata.com.cn/Periodical/chxb201707008 Wang Leyang, Wen Guisen. Non-negative Least Squares Variance Estimation of Partial EIV Model[J]. Acta Geodaetica et Cartographica Sinica, 2017, 46(7):857-865 http://d.old.wanfangdata.com.cn/Periodical/chxb201707008
[24]	Wang Leyang, Zhao Yingwen. Unscented Transformation with Scaled Symmetric Sampling Strategy for Precision Estimation of Total Least Squares[J]. Studia Geophysica et Geodaetica, 2017, 61(3):385-411 doi: 10.1007/s11200-016-1113-0
[25]	Wang Leyang, Zhao Yingwen. The Scaled Unscented Transformation for Nonlinear Error Propagation Accuracy, Sensitivity and Applications[J]. Journal of Surveying Engineering, 2018, 144(1):04017022 doi: 10.1061/(ASCE)SU.1943-5428.0000243
[26]	Wang Leyang, Zhao Yingwen. Second Order Approximating Function Method for Precision Estimation of Total Least Squares[J]. Journal of Surveying Engineering, 2019, 145(1):04018011 doi: 10.1061/(ASCE)SU.1943-5428.0000266
[27]	王新洲, 陶本藻, 邱卫宁, 等.高等测量平差[M].北京:测绘出版社, 2006 Wang Xinzhou, Tao Benzao, Qiu Weining, et al. Advanced Surveying Adjustment[M]. Beijing:Surveying and Mapping Press, 2006
[28]	Teunissen P J G. Nonlinear Least-Squares[J]. Manuscripta Geodaetica, 1990, 15(3):137-150 http://d.old.wanfangdata.com.cn/Periodical/gpxygpfx201411036

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