The Consideration of Formal Errors in Spatiotemporal Filtering Using Principal Component Analysis for Regional GNSS Position Time Series

Li, Weiwei; Shen, Yunzhong

doi:10.3390/rs10040534

Cited by 26 publications

(28 citation statements)

References 30 publications

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“…Considering that the temporal correlation is not provided in GNSS time series and the precision of observations is only related to noise, not the signal [50], the weight of time series is adjusted by multiplying the noise with a weight factor i p as follows ( 0,1 , 1)…”

Section: Weighted Wavelet Analysis By Considering Formal Errorsmentioning

confidence: 99%

“…2020, 12, 992 5 of 16 weight factor, for this reason the proposed approach is called weight wavelet analysis (WWA). In order to keep the total energy of the adjusted time series unchanged [50,51], the sum of the weights for all epochs should be equal to the number of epochs, i.e.,…”

Section: Weighted Wavelet Analysis By Considering Formal Errorsmentioning

confidence: 99%

“…Klos et al [18,48] employed reconstructed components of seventh and eighth levels based on wavelet decomposition (WD) to model the seasonal signals, which included annual and semi-annual signals, respectively.The traditional WA deals with a GNSS position time series without taking the formal errors into account. This is not reasonable because the precision of GNSS position time series varies from epoch to epoch [49][50][51]. Therefore, the formal errors, which are provided along with the position time series, should be considered when extracting signals using WA.…”

mentioning

confidence: 99%

“…The traditional WA deals with a GNSS position time series without taking the formal errors into account. This is not reasonable because the precision of GNSS position time series varies from epoch to epoch [49][50][51]. Therefore, the formal errors, which are provided along with the position time series, should be considered when extracting signals using WA.…”

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confidence: 99%

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Signal Extraction from GNSS Position Time Series Using Weighted Wavelet Analysis

Shen

Wang

2020

Remote Sensing

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The daily position time series derived by Global Navigation Satellite System (GNSS) contain nonlinear signals which are suitably extracted by using wavelet analysis. Considering formal errors are also provided in daily GNSS solutions, a weighted wavelet analysis is proposed in this contribution where the weight factors are constructed via the formal errors. The proposed approach is applied to process the position time series of 27 permanent stations from the Crustal Movement Observation Network of China (CMONOC), compared to traditional wavelet analysis. The results show that the proposed approach can extract more exact signals than traditional wavelet analysis, with the average error reductions are 13.24%, 13.53% and 9.35% in north, east and up coordinate components, respectively. The results from 500 simulations indicate that the signals extracted by proposed approach are closer to true signals than the traditional wavelet analysis.Remote Sens. 2020, 12, 992 2 of 16 filter (AWF) [28]. Wavelet analysis (WA) is one of the data-driven approaches to analyzing the non-linear time series. It was initially proposed by Morlet et al. [29,30] to analyze the seismic signals in geophysics and was popularized by Grossmann and Morlet [31] and Goupillaud et al. [32]. Nowadays, WA becomes a new mathematical approach and is widely applied in geodesy and geophysics [33,34], remote sensing [35,36] and hydrology [37,38]. Unlike the Fourier transform (FT) [39] which maps a time series from time domain to frequency domain, the wavelet transform (WT) can simultaneously describe the time-frequency characteristics of a time series, which is one of the most important properties of the wavelets [40]. As a time-frequency analysis method, the WT can decompose the time series into different components according to frequency, and then map the decomposed components at different scales to obtain the information of time series at different resolutions, which is named as multiresolution analysis (MRA) [41]. Due to its superior performance on signal processing, it has also been employed to analyze the GNSS position time series. For preprocessing of GNSS position time series, Wu et al. [42] proposed an improved 3σ method of outlier detection based on WA. Borghi et al. [43] introduced WT to detect discontinuity in GNSS position time series. For noise analysis, Kaczmarek and Kontny [44] identified the noise model using WA and demonstrated that the nature of noise did not depend on the method of modeling the time series. Wu et al. [45] proposed a wavelet-based hybrid approach to remove white noise and flicker noise originating from GNSS position time series. Li et al. [46] introduced a WT-based multiscale multiway principle component analysis (MSMPCA) to eliminate noise in high-rate GNSS data including high-frequency random noise, low-frequency errors and common mode error (CME). For signal analysis, Kaczmarek and Kontny [17] applied wavelet power spectrum analysis to position time series and found that annual signal is more significant than other pe...

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Section: Weighted Wavelet Analysis By Considering Formal Errorsmentioning

confidence: 99%

Section: Weighted Wavelet Analysis By Considering Formal Errorsmentioning

confidence: 99%

mentioning

confidence: 99%

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confidence: 99%

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Signal Extraction from GNSS Position Time Series Using Weighted Wavelet Analysis

Shen

Wang

2020

Remote Sensing

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“…We then evaluate the consistency between the environmental loading results and the reprocessed daily CMONOC GPS height time series [36][37][38][39][40][41][42]. Afterwards, we confirm and quantify the loss of velocity precision caused by environmental loading correction.…”

Section: Introductionmentioning

confidence: 99%

Influences of Environmental Loading Corrections on the Nonlinear Variations and Velocity Uncertainties for the Reprocessed Global Positioning System Height Time Series of the Crustal Movement Observation Network of China

Peng

Jiang

et al. 2018

Remote Sensing

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Mass redistribution of the atmosphere, oceans, and terrestrial water storage generates crustal displacements which can be predicted by environmental loading models and observed by the Global Positioning System (GPS). In this paper, daily height time series of 235 GPS stations derived from a homogeneously reprocessed Crustal Movement Observation Network of China (CMONOC) and corresponding loading displacements predicted by the Deutsche GeoForschungsZentrum (GFZ) are compared to assess the effects of loading corrections on the nonlinear variations of GPS time series. Results show that the average root mean square (RMS) of vertical displacements due to atmospheric, nontidal oceanic, hydrological, and their combined effects are 3.2, 0.6, 2.7, and 4.0 mm, respectively. Vertical annual signals of loading and GPS are consistent in amplitude but different in phase systematically. The average correlation coefficient between loading and GPS height time series is 0.6. RMS of the GPS height time series are reduced by 20% on average. Moreover, an investigation of 208 CMONOC stations with observing time spans of~4.6 years shows that environmental loading corrections lead to an overestimation of the GPS velocity uncertainty by about 1.4 times on average. Nevertheless, by using a common mode component filter through principal component analysis, the dilution of velocity precision due to environmental loading corrections can be compensated.

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A Wavelet-Based Outlier Detection and Noise Component Analysis for GNSS Position Time Series

Shen

2020

International Association of Geodesy Symposia

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Various signals of crustal deformation and mass loading deformation are contained in a GNSS position time series. However, a GNSS position time series is also polluted by outliers and various colored noise, which must be reasonably modelled before estimating deformation signals. Since temporal signals of the GNSS position time series are non-linear and complicated, we propose a wavelet-based approach for outlier detection, which first retrieves the temporal signals from the GNSS position time series by using wavelet analysis, and then detect outliers in the residual position time series by using the interquartile range. After the detected outliers are eliminated from the residual time series, the noise components, including white noise and flicker noise, are estimated by using MINQUE approach. Our proposed approach is used to process the real GNSS position time series of the Crustal Movement Observation Network of China (CMONOC) over the period spanning 1999–2018. The results demonstrate that our approach can detect the outliers more efficiently than the traditional approach, which retrieves the temporal signals by using a functional model with trend and periodic variations. As a result, the noise components estimated with our proposed approach are smaller than those with the traditional approach for the GNSS position time series of all CMONOC stations.

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The Consideration of Formal Errors in Spatiotemporal Filtering Using Principal Component Analysis for Regional GNSS Position Time Series

Cited by 26 publications

References 30 publications

Signal Extraction from GNSS Position Time Series Using Weighted Wavelet Analysis

Signal Extraction from GNSS Position Time Series Using Weighted Wavelet Analysis

Influences of Environmental Loading Corrections on the Nonlinear Variations and Velocity Uncertainties for the Reprocessed Global Positioning System Height Time Series of the Crustal Movement Observation Network of China

A Wavelet-Based Outlier Detection and Noise Component Analysis for GNSS Position Time Series

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