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Objectives: Global navigation satellite system (GNSS) coordinate time series provide important data support for the study of crustal movement and deformation, and plate tectonics. Due to the noise caused by various external factors, the GNSS coordinate time series cannot reflect the real motion information of the station well. To effectively reduce the noise in the GNSS time series, we adopted a noise-reduction method combining genetic algorithm (GA) and variational mode decomposition (VMD-GA-VMD). Methods: First, the genetic algorithm was used to optimize VMD parameters, and the envelope entropy of the input signal was used as the fitness function of the genetic algorithm to find the optimal VMD parameter combination suitable for the signal. According to the optimized parameters, the signal was decomposed by VMD to obtain a series of modal components. Then we calculated the multi-scale permutation entropy (MPE) of each component and then regarded the MPE as the criterion of the noise component. Finally, according to the MPE, the noise components were identified and removed, and the remaining components were reconstructed to obtain the noise-reduced signal. In this paper, the noise reduction effect of GAVMD was analyzed through the example of noise reduction of analog signal and observation data, and compared with wavelet denoising (WD) and empirical mode decomposition (EMD) methods. Results: The experiment results show that: (1) The noise reduction results from the analog signals show that WD and EMD have the incomplete and excessive troubles on the noise reduction, respectively. However, GA-VMD can effectively eliminate noise and retain effective signals. From the evaluation index, compared with WD and EMD, the signal-to-noise ratio were increased by 5.18 dB and 2.91 dB, the correlation coefficient by 0.05 and 0.02, respectively, when using GA-VMD. (2) For the complex observation, we used the noise and velocity uncertainty as accuracy indicators to evaluate the noise reduction effects of the three methods. The results show that WD can only extract a part of the white noise, while EMD and GA-VMD can completely remove the white noise. GA-VMD can reduce the flicker noise to the range of 0 to 6 mm/a0.25. For the velocity uncertainty, the average gain rates of GA-VMD relative to the WD and EMD are 69% and 15.33%, respectively. GA-VMD has an average correction rate of 79.89% and 84.46% for the velocity uncertainty and flicker noise of GNSS coordinate time series. Conclusions: Therefore, GA-VMD is the most effective one among the three noise reduction methods, which can effectively reduce the noise in the GNSS time series and improve its accuracy. However, in this paper, we only discussed the effect of GA on VMD parameter optimization without comparing it with other methods. Hence, it will be the key for studying the advantages and shortcomings of those optimization algorithms in the selection of VMD, and improving the accuracy on the GNSS time series in the future. [ABSTRACT FROM AUTHOR]

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Objectives: The position time series of global navigation satellite system (GNSS) contain rich tectonic and non-tectonic deformation information, and the complex components are difficult to accurately model and effectively separate non-tectonic information. It is very important to remove the non-tectonic de‐ formation information for the accurate and effective application of the observation data. Methods: Empirical mode decomposition （EMD） is an adaptive time-frequency processing method to correct the period term of time series at 24 GNSS continuous stations and 2 mobile stations in Sichuan Province and Yunnan Province. Results: The results show that the correction of the period term is necessary, and the EMD method can ex‐ tract the different frequency and amplitude period components adaptively according to its own characteristics of signal at each station. Compared with the original time series, the average root mean square error after correction is reduced significantly in N, E and U directions. And EMD method is more accurate and effective than harmonic model modification. We use the modified continuous station time series to simulate the mobile observations, and find that relatively reliable motion velocities can be obtained after an observation period of 5 ‐6 years. The stability and reliability of EMD method are verified by correcting the period term of the mobile station with the actual continuous observation station at a close distance. Conclusions: This paper provides a reference and theoretical basis for the implementation of mobile GNSS observation and the correction of observation data. [ABSTRACT FROM AUTHOR]

Objectives: North China is an important social and economic area in China but suffers from severe surface deformation. Monitoring the surface displacement effectively and timely can provide data basis for understanding the deformation mechanism and predicting disasters. However, the surface vertical displacement in North China shows significant seasonal fluctuations. Hence, this paper aims to analyze the spatiotemporal feature of seasonal vertical displacement and determine the driving sources. Methods: Firstly, the vertical time series of 20 global navigation satellite system (GNSS) stations from January 2011 to November 2019 are decomposed by independent component analysis. Secondly, the first six independent components (ICs) are derived and compared with the vertical displacements caused by environmental loadings. Results: The results show that GNSS-IC1 presents obvious annual variation, as well as a relative uniform spatial response, which is highly consistent with the displacement time series derived from atmospheric loading, and the average correlation coefficient at all stations is 0.60. GNSS-IC2 and GNSS-IC3 are both the mixed signals constrained by annual and intra-annual periods, while the spatial responses reflect locally clustered characteristics, which corresponds to the distribution of water resources in North China. After combining GNSS-IC2 and GNSS-IC3 as GNSS-IC2/3, the average correlation coefficient between GNSS-IC2/3 and the hydrological loading displacement time series at all stations is 0.50. Conclusions: The temporal component of each IC is generally less clustered by different time cycles and the spatial response shows distinct localized characteristics. Atmospheric and hydrological loadings are the primary driving sources of seasonal vertical displacement in North China. However, the seasonal displacements induced by other effects, including non-tide ocean loading and thermal expansion effect of bedrock and observation pillar, are not extracted and need further analysis. [ABSTRACT FROM AUTHOR]

In order to effectively extract useful information from time series of the global naviga- tion satellite system(GNSS) sites, and improve the modeling accuracy of coordinate time series, this paper proposes a nonlinear motion modeling method combining wavelet decomposition and singular spectrum analysis. Experiments were carried out using global positioning system(GPS) vertical coordinate time series of 11 stations around the world from 1999 to 2018. Methods: Firstly, the coordinate time series is decom-posed into different scales by wavelet decomposition.And then the singular spectrum analysis(SSA) is per- formed on the high-frequency part and the low -frequency part of each layer. Finally, combine the fitting value that is the fitting coordinate time series, and the fitting effect of the new method was evaluated. Results: The results show that, compared with the simple singular spectrum analysis method, the new method can extract useful information such as trend and period more accurately from the limited scale of the time series with noise. And reduce the partial period items in the singular spectrum analysis method to some extent, for example, the seasonal period item and the monthly period item are regarded as the probability of noise rejec- tion, and the modeling accuracy is improved by 26%. Conclusions: The purpose is to propose a nonlinear motion modeling method based on wavelet decomposition and singular spectrum analysis, so as to improve the modeling accuracy of coordinate time series. [ABSTRACT FROM AUTHOR]