Solution for GNSS height anomaly fitting of mining area based on robust TLS
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Global navigation satellite system (GNSS) height solutions of mining area are readily contaminated by outliers because of the special geological environment. Additionally, GNSS height anomaly fitting model is a type of errors-in-variables model, and the traditional solution for parameter estimation does not account for error in the coefficient matrix. To solve these two problems, this paper presents a solution of the robust total least squares estimation for GNSS height anomaly fitting of mining area. Different from the traditional solution for robust estimation, an algorithm is established employing median method to obtain stable parameter values under the condition that observation data are highly contaminated. Employing Lagrange function and weight function, an iterative algorithm for the parameter estimation of GNSS anomaly fitting model is proposed, and the algorithm is verified using real data of mining area. The numerical results show that the proposed solution obtains stable parameter values when observation data are highly contaminated by outliers and demonstrate that the proposed algorithm is more accurate than traditional solutions for robust estimation.
KeywordsErrors-in-variables model Total least squares Robust estimation Median method Height anomaly of mining area
The authors would like to thank the reviewers and the editor. This research was supported by the National Natural Science Foundation of China (41601501; 41271135), Natural Science Found for Colleges and Universities of Jiangsu Province (16KJD420001) and Huaian Key Laboratory of Geographic Information Technology and Applications (HAP201405).
- Dongfang L, Jianjun Z, Yingchun S et al (2016) Construction method of regularization by singular value decomposition of design matrix. Acta Geod Cartogr Sin 45(8):883–889Google Scholar
- Heiskanen WA, Moritz H (1967) Physical geodesy. W H Freeman and Company, San FranciscoGoogle Scholar
- Jiangwen Z (1989) Classic theory of errors and robust estimation. Acta Geod Cartogr Sin 18(2):115–120Google Scholar
- Ling Y, Yunzhong S, Lizhi L (2011) Equivalent weight robust estimation method based on median parameter estimates. Acta Geod Cartogr Sin 40(1):28–32Google Scholar
- Mahboub V, Amiri-Simkooei AR, Sharifi MA (2013) Iteratively reweighted total least squares: a robust estimation in error-in-variables models. Surv Rev 45(329):92–99Google Scholar
- Peter JH (1981) Robust statistics. Wiley, HobokenGoogle Scholar
- Schaffrin B, Uzun S (2011) Error-in-variables for mobile mapping algorithms in the presence of outliers. Arch Photogramm Cartogr Remote Sens 22:377–387Google Scholar
- Schaffrin B, Lee I, Choi Y et al (2006) Total least squares (TLS) for geodetic straight-line and plane adjustment. Bull Geod Sc Aff 65:141–168Google Scholar
- Xuming G, Jicang W (2012) Generalized regularization to ill-posed total least squares problem. Acta Geod Cartogr Sin 41(3):372–377Google Scholar
- Xunqiang G, Zhilin L (2014) A robust weighted total least squares method. Acta Geod Cartogr Sin 43(9):888–894Google Scholar