Abstract
Global navigation satellite system (GNSS) velocity fields generally contain outliers due to environmental interference, local crustal activities, or strong seismic activities, which significantly affect the parameter estimation of the crustal deformation model. The robust M estimation can be used to improve the accuracy of the parameter estimation while retaining as much GNSS observation information as possible. The current robust estimation still uses the least-squares residuals instead of real errors as the initial values of the equivalent weight function and the breakdown point of parameters estimation is less than 50%. First, a new automatic selection strategy is proposed for quasi-accurate observations (observations that are reliable and do not have outliers but require confirmations) using quasi-accurate detection, and the outliers are roughly identified, almost independent of the breakdown point. Second, the variance of the unit weight of the estimate of real error of quasi-accurate observations is used as the initial variance factor and the estimate of real error of quasi-accurate observations is used as the initial value for the iterative calculation of the robust M estimation to accurately identify and detect large, medium, and small outliers. We evaluate the rigorousness of the least-squares estimation, conventional robust estimation, median method, and new algorithm from four perspectives using simulated GNSS velocity fields, i.e., model parameter estimation, variance factor, distribution of the observation weights, and accuracy of forward deformation fields. The new algorithm effectively eliminates outliers and estimates the model parameters. When outliers are below 50%, the robustness of the new algorithm is better than that of the other three. When the proportion of outliers is higher than 50% (60%, 70%, and 80%), the other three algorithms break down, while the new algorithm yields better parameter estimates with an increasing breakdown point.
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Data availability
Original GNSS horizontal velocities can be obtained from Yu et al., (2019), which are available from the authors upon reasonable request. https://doi.org/10.1016/j.asr.2018.10.001
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Acknowledgments
This work is sponsored by the National Natural Science Foundation of China (42090055,42174006,41674001), National Key Research and Development Program of China (2018YFC1503604), the Opening fund of State Key Laboratory of Geohazard Prevention and Geoenvironment Protection of Chengdu University of Technology (SKLGP2021K022), Selection Research Projects of Scientific and Technological Activities for overseas students in Shaanxi Province (13), the Fundamental Research Funds for the Central Universities, CHD (300102261404), Science and technology innovation project of Shaanxi Bureau of surveying, mapping and geographic information (SCK2020-03), Natural Science Basic Research Plan in Shaanxi Province of China (2019JM-202). We also express our thanks to the Editor and three anonymous reviewers for their constructive comments and suggestions that improved the manuscript.
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W.Q. and Q.Z. conceived and designed the research; H.C, Y.G, and W.Q performed the experiments; W.Q, H.C, Q.Z, Q.W, and M.H analyzed and interpreted the results. All the authors participated in writing and editing the manuscript.
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Qu, W., Chen, H., Zhang, Q. et al. A robust estimation algorithm for the increasing breakdown point based on quasi-accurate detection and its application to parameter estimation of the GNSS crustal deformation model. J Geod 95, 125 (2021). https://doi.org/10.1007/s00190-021-01574-w
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DOI: https://doi.org/10.1007/s00190-021-01574-w