Review of current GPS methodologies for producing accurate time series and their error sources

Removal of the common mode error (CME) is a routine procedure in postprocessing regional GPS network observations, which is commonly performed using principal component analysis (PCA). PCA decomposes a network time series into a group of modes, where each mode comprises a common temporal function and corresponding spatial response based on second-order statistics (variance and covariance). However, the probability distribution function of a GPS time series is non-Gaussian; therefore, the largest variances do not correspond to the meaningful axes, and the PCA-derived components may not have an obvious physical meaning. In this study, the CME was assumed statistically independent of other errors, and it was extracted using independent component analysis (ICA), which involves higher-order statistics. First, the ICA performance was tested using a simulated example and compared with PCA and stacking methods. The existence of strong local effects on some stations causes significant large spatial responses and, therefore, a strategy based on median and interquartile range statistics was proposed to identify abnormal sites. After discarding abnormal sites, two indices based on the analysis of the spatial responses of all sites in each independent component (east, north, and vertical) were used to define the CME quantitatively. Continuous GPS coordinate time series spanning $$\sim $$
 4.5 years obtained from 259 stations of the Tectonic and Environmental Observation Network of Mainland China (CMONOC II) were analyzed using both PCA and ICA methods and their results compared. The results suggest that PCA is susceptible to deriving an artificial spatial structure, whereas ICA separates the CME from other errors reliably. Our results demonstrate that the spatial characteristics of the CME for CMONOC II are not uniform for the east, north, and vertical components, but have an obvious north–south or east–west distribution. After discarding 84 abnormal sites and performing spatiotemporal filtering using ICA, an average reduction in scatter of 6.3% was achieved for all three components.

Spatiotemporal filtering for regional GPS network in China using independent component analysis

Characteristics of daily position time series from January 2001 to August 2007 at 12 GPS stations in the Hong Kong GPS fiducial network are investigated. A spatial filtering algorithm based on principal component analysis is employed to remove the common mode errors from the daily position time series. The noise characteristics of the filtered position time series are assessed by the method of maximum likelihood estimation. Contributions from atmospheric, nontidal oceanic, snow and soil moisture mass loading are evaluated. The results indicate that spatial filtering is an effective way to improve the precision of GPS position time series. The common mode errors have strong seasonal variations. The about 3 mm annual vertical variation of the common mode errors can be explained by the joint contribution of the seasonal surface mass redistributions. After removing these surface mass loading effects, the residual common mode errors are highly related to the higher-order ionospheric effects. The noise in the filtered position time series can be described as a combination of variable white noise and flicker noise. The velocity uncertainties are about 2~6 times larger if only variable white noise is assumed. The maximum relative horizontal velocity between the sites is 1.5 mm/yr, which indicates some local fault activities. In addition, there are obvious 1~2 mm local seasonal signals in the filtered position time series of some of the sites. The residual scatters of all filtered time series also show strong seasonal characteristics.

香港GPS基准站坐标序列特征分析 = Characteristics of daily position time series from the Hong Kong GPS fiducial network

Global navigation satellite system (GNSS) datasets suffer from common mode error (CME) and other unmodeled errors. To decrease the noise level in GNSS positioning, we propose a new data-driven adaptive multiscale denoising method in this paper. Both synthetic and real-world long-term GNSS datasets were employed to assess the performance of the proposed method, and its results were compared with those of stacking filtering, principal component analysis (PCA) and the recently developed multiscale multiway PCA. It is found that the proposed method can significantly eliminate the high-frequency white noise and remove the low-frequency CME. Furthermore, the proposed method is more precise for denoising GNSS signals than the other denoising methods. For example, in the real-world example, our method reduces the mean standard deviation of the north, east and vertical components from 1.54 to 0.26, 1.64 to 0.21 and 4.80 to 0.72 mm, respectively. Noise analysis indicates that for the original signals, a combination of power-law plus white noise model can be identified as the best noise model. For the filtered time series using our method, the generalized Gauss–Markov model is the best noise model with the spectral indices close to − 3, indicating that flicker walk noise can be identified. Moreover, the common mode error in the unfiltered time series is significantly reduced by the proposed method. After filtering with our method, a combination of power-law plus white noise model is the best noise model for the CMEs in the study region.

A data-driven approach for denoising GNSS position time series

Many GPS time series contain offsets, sometimes nonsecular trends, and seasonal signals withtime-varying amplitudes due to several different types of geophysical phenomena. Therefore, the use ofnonsecular models to depict the real geophysical movement of GPS sites is better than a linear model. Inthis study, an enhanced singular spectrum analysis (SSA) method for fitting GPS time series and predictingits coordinates is proposed. Simulation results show that the root-mean-square (RMS) of differencesbetween the reconstructed and simulated signals is 1.7 mm; the RMS of the differences between thepredicted coordinates and simulated signal is about 3 mm for the first half 1.5 years of testing period anddecreases to 10 mm for the last half 1.5 years. Fitting results for three GPS time series are obtained usingmaximum likelihood estimation (MLE), which is used to fit the time series with a piecewise linear trend plusan annual/semiannual components, SSA, and state space model (SSM). Both SSA and SSM perform similarlyand better than the MLE in extracting the nonsecular trend and annual/semiannual components from theGPS time series. The prediction results from SSA have higher coefficients with raw time series and lowerpower of annual/semiannual in their residuals than that from MLE for two case studies. The differencesbetween the linear trend estimated by Plate Boundary Observatory and SSA nonsecular model for 16 GPStime series are all larger than 2 mm in up direction, which is not negligible for a high-accuracy terrestrialreference frame construction.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/2015JB012573

An enhanced singular spectrum analysis method for constructing nonsecular model of GPS site movement

Accuracy enhancement of GPS time series using principal component analysis and block spatial filtering

The global navigation satellite system (GNSS) has seen tremendous advances in measurement precision and accuracy, and it allows researchers to perform geodynamics and geophysics studies through the analysis of GNSS time series. Moreover, GNSS time series not only contain geophysical signals, but also unmodeled errors and other nuisance parameters, which affect the performance in the estimation of site coordinates and related parameters. As the number of globally distributed GNSS reference stations increases, GNSS time series analysis software should be developed with more flexible format support, better human–machine interaction, and with powerful noise reduction analysis. To meet this requirement, a new software named GNSS time series noise reduction software (GNSS-TS-NRS) was written in MATLAB and was developed. GNSS-TS-NRS allows users to perform noise reduction analysis and spatial filtering on common mode errors and to visualize GNSS position time series. The functions’ related theoretical background of GNSS-TS-NRS were introduced. Firstly, we showed the theoretical background algorithms of the noise reduction analysis (empirical mode decomposition (EMD), ensemble empirical mode decomposition (EEMD)). We also developed three improved algorithms based on EMD for noise reduction, and the results of the test example showed our proposed methods with better effect. Secondly, the spatial filtering model supported five algorithms on a separate common model error: The stacking filter method, weighted stacking filter method, correlation weighted superposition filtering method, distance weighted filtering method, and principal component analysis, as well as with batch processing. Finally, the developed software also enabled other functions, including outlier detection, correlation coefficient calculation, spectrum analysis, and distribution estimation. The main goal of the manuscript is to share the software with the scientific community to introduce new users to the GNSS time series noise reduction and application.

https://www.mdpi.com/2072-4292/12/21/3532/pdf

GNSS-TS-NRS: An Open-Source MATLAB-Based GNSS Time Series Noise Reduction Software

In the field of geomatics engineering and signal processing, observational data can bring a lot of information. However, the abnormal data (i.e. outliers) may be acquired due to human carelessness or limiting condition, causing interference to subsequent research. To solve this problem, outlier detection methods have been proposed to detect and remove outliers. Three common outlier detection methods (i.e. Z-score method, boxplot method and median absolute deviation method) in signal processing are introduced in this paper. A comparison of the three methods is conducted through experimental evaluation with two sets of experiments. The results of experiments show that the number of outliers detected with median absolute deviation method significantly outperform those of Z-score and boxplot methods. It shows that the median absolute deviation method can more effectively detect and remove outliers so that the more reliable and accuracy results can be obtained.

Tieding Lu

Papers

Accuracy enhancement of GPS time series using principal component analysis and block spatial filtering

GNSS-TS-NRS: An Open-Source MATLAB-Based GNSS Time Series Noise Reduction Software

Comparative Analysis of three outlier detection methods in univariate data sets

Evaluation of BDS and GPS RAIM availability based on data collected in June 2020

Progress of global ARAIM availability of BDS-2/BDS-3 with TGD and ISB