Optimal Tikhonov Regularization Matrix and Its Application in GNSS Ambiguity Resolution

BIAN Shaofeng; WU Zemin

doi:10.13203/j.whugis20160474

Volume 44 Issue 3

Mar. 2019

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Geomatics and Information Science of Wuhan University > 2019 > 44(3): 334-339. > DOI: 10.13203/j.whugis20160474

BIAN Shaofeng, WU Zemin. Optimal Tikhonov Regularization Matrix and Its Application in GNSS Ambiguity Resolution[J]. Geomatics and Information Science of Wuhan University, 2019, 44(3): 334-339. DOI: 10.13203/j.whugis20160474

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Optimal Tikhonov Regularization Matrix and Its Application in GNSS Ambiguity Resolution

BIAN Shaofeng^1,,
WU Zemin^{1, 2, ,}

1.
Department of Navigation Engineering, Naval University of Engineering, Wuhan 430033, China
2.
Unit 91919, Huanggang 438000, China

Funds:

The National Natural Science Foundation of China 41504029

The National Natural Science Foundation of China 41631072

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Author Bio:
BIAN Shaofeng, PhD, professor, specializes in GNSS precise positioning, gravity aided navigation and map projection transformation. E-mail: sfbian@sina.com
Corresponding author:
WU Zemin, PhD, engineer. E-mail:wzm_hust@sina.com
Received Date: October 17, 2016
Published Date: March 04, 2019

Graphical Abstract

Abstract

Abstract

This contribution can be mainly divided into 3 aspects:(1) Based on Bayesian theory, unknown parameters are treated as random varies and their non-informative prior distribution function is introduced. Mathematical analysis is carried out to drive the optimal Tikhonov regularization matrix in the sense of minimizing the mean square error (MSE) of the solutions. (2) Combining the efficient truncated singular value decomposition (eTSVD), a new regularization method is proposed. (3) Global Navigation Satellite System(GNSS) ambiguity resolution application of the new method is discussed. Least squares (LS) estimation, ridge estimation of L curve and the new algorithm are compared by a group of GNSS ambiguity resolution experiments. The results show that the MSE of the new algorithm is slightly smaller than ridge estimation of L curve and much smaller than LS, however, the computational cost of the new algorithm is slightly more than LS but much less than ridge estimation of L curve.
- ill-posed problem,
- Tikhonov regularization,
- Bayesian statistical theory,
- GNSS,
- ambiguity resolution

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[1]	Tikhonov A N. Regularization of Ill-Posed Problems[J]. Dokl Akad Nauk SSSR, 1963, 151(1):49-52 http://d.old.wanfangdata.com.cn/OAPaper/oai_doaj-articles_eae560fae48c249b50ae0ce63aa285d9
[2]	Tikhonov A N. Solution of Incorrectly Formulated Problems and the Regularization Method[J]. Dokl Akad Nauk SSSR, 1963, 151(3):501-504
[3]	Hoerl A E, Kennard R W. Ridge Regression:Bia-sed Estimation for Non-orthogonal Problems[J]. Technometrics, 1970, 12:55-67 doi: 10.1080/00401706.1970.10488634
[4]	Xu P L, Rummel R. A Simulation Study of Smoothness Methods in Recovery of Regional Gra-vity Fields[J]. Geophys J Int, 1994, 117:472-486 doi: 10.1111/gji.1994.117.issue-2
[5]	Shen Y Z, Xu P L, Li B F. Bias-Corrected Regulari-zed Solution to Inverse Ill-Posed Models[J]. J Geod, 2012, 86:597-608 doi: 10.1007/s00190-012-0542-y
[6]	游扬声, 王新洲, 刘星.广义岭估计的直接解法[J].武汉大学学报·信息科学版, 2002, 27(2):175-178 http://ch.whu.edu.cn/CN/abstract/abstract4940.shtml You Yangsheng, Wang Xinzhou, Liu Xing. Direct Solution to Generalized Ridge Estimate[J]. Geomatics and Information Science of Wuhan University, 2002, 27(2):175-178 http://ch.whu.edu.cn/CN/abstract/abstract4940.shtml
[7]	Hansen P C. Analysis of Discrete Ill-posed Problems by Means of the L-curve[J]. SIAM Review, 1992(1):561-580 http://www.emeraldinsight.com/servlet/linkout?suffix=b4&dbid=16&doi=10.1108%2F03321640110383933&key=10.1137%2F1034115
[8]	柳响林, Pavel Ditmar.基于B-spline和正则化算法的低轨卫星轨道平滑[J].地球物理学报, 2006, 49(1):99-105 doi: 10.3321/j.issn:0001-5733.2006.01.014 Liu Xianglin, Pavel D. Smoothing a Satellite Orbit on the Basis of B-spline and Regularization[J]. Chinese Journal of Geophysics, 2006, 49(1):99-105 doi: 10.3321/j.issn:0001-5733.2006.01.014
[9]	郭海涛, 张保明, 归庆明.广义岭估计在解算单线阵CCD卫星影像外方位元素中的应用[J].武汉大学学报·信息科学版, 2003, 28(4):444-447 http://ch.whu.edu.cn/CN/abstract/abstract4868.shtml Guo Haitao, Zhang Baoming, Gui Qingming. Application of Generalized Ridge Estimate to Computing the Exterior Orientation Elements of Satellite Linear Array Scanner Imagery[J]. Geomatics and Information Science of Wuhan University, 2003, 28(4):444-447 http://ch.whu.edu.cn/CN/abstract/abstract4868.shtml
[10]	Li B F, Shen Y Z, Feng Y M. Fast GNSS Ambi-guity Resolution as an Ill-Posed Problem[J]. J Geod, 2010, 84:683-698 doi: 10.1007/s00190-010-0403-5
[11]	Shen Y Z, Li B F. Regularized Solution to Fast GPS Ambiguity Resolution[J]. J Surv Eng, 2007, 133:168-172 doi: 10.1061/(ASCE)0733-9453(2007)133:4(168)
[12]	Gui Q M, Han S H. New Algorithm of GPS Rapid Positioning Based on Double-k-Type Ridge Estimation[J]. J Surv Eng, 2007, 133:67-72
[13]	王振杰, 欧吉坤, 柳林涛.一种解算病态问题的方法:两步解法[J].武汉大学学报·信息科学版, 2005, 30(9):821-824 http://ch.whu.edu.cn/CN/abstract/abstract2283.shtml Wang Zhenjie, Ou Jikun, Liu Lintao. A Method for Resolving Ill-Conditioned Problems:Two-Step Solution[J]. Geomatics and Information Science of Wuhan University, 2005, 30(9):821-824 http://ch.whu.edu.cn/CN/abstract/abstract2283.shtml
[14]	Zhu J, Ding X, Chen Y. Maximum-Likelihood Ambiguity Resolution Based on Bayesian Principle[J]. J Geod, 2001, 75:175-187 doi: 10.1007/s001900100167
[15]	Wu Z M, Bian S F. GNSS Integer Ambiguity Validation Based on Posterior Probability[J]. J Geod, 2015, 89:961-977 doi: 10.1007/s00190-015-0826-0
[16]	陈伟, 王子亭.传统正则化方法和Bayes统计理论之间的联系[J].河北理工大学学报(自然科学版), 2011, 33(3):104-106 doi: 10.3969/j.issn.1674-0262.2011.03.024 Chen Wei, Wang Ziting. The Relation Between the Traditional Regularization and the Bayesian Method[J]. Journal of Hebei Polytechnic University (Natural Science Edition), 2011, 33(3):104-106 doi: 10.3969/j.issn.1674-0262.2011.03.024
[17]	Teunisen P J G. The Success Rate and Precision of GPS Ambiguities[J]. J Geod, 2000, 74(3/4):321-326 doi: 10.1007-s001900050289/
[18]	Verhagen S, Teunissen P J G. The Ratio Test for Future GNSS Ambiguity Resolution[J]. GPS Solut, 2013, 17(4):535-548 doi: 10.1007/s10291-012-0299-z

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