scholarly journals Analysis of Noise and Velocity in GNSS EPN-Repro 2 Time Series

2021 ◽  
Vol 13 (14) ◽  
pp. 2783
Author(s):  
Sorin Nistor ◽  
Norbert-Szabolcs Suba ◽  
Kamil Maciuk ◽  
Jacek Kudrys ◽  
Eduard Ilie Nastase ◽  
...  

This study evaluates the EUREF Permanent Network (EPN) station position time series of approximately 200 GNSS stations subject to the Repro 2 reprocessing campaign in order to characterize the dominant types of noise and amplitude and their impact on estimated velocity values and associated uncertainties. The visual inspection on how different noise model represents the analysed data was done using the power spectral density of the residuals and the estimated noise model and it is coherent with the calculated Allan deviation (ADEV)-white and flicker noise. The velocities resulted from the dominant noise model are compared to the velocity obtained by using the Median Interannual Difference Adjusted for Skewness (MIDAS). The results show that only 3 stations present a dominant random walk noise model compared to flicker and powerlaw noise model for the horizontal and vertical components. We concluded that the velocities for the horizontal and vertical component show similar values in the case of MIDAS and maximum likelihood estimation (MLE), but we also found that the associated uncertainties from MIDAS are higher compared to the uncertainties from MLE. Additionally, we concluded that there is a spatial correlation in noise amplitude, and also regarding the differences in velocity uncertainties for the Up component.

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
M. A. Goudarzi ◽  
M. Cocard ◽  
R. Santerre

AbstractWe analyzed the noise characteristics of 112 continuously operating GPS stations in eastern North America using the Spectral Analysis and the Maximum Likelihood Estimation (MLE) methods. Results of both methods show that the combination ofwhite plus flicker noise is the best model for describing the stochastic part of the position time series. We explored this further using the MLE in the time domain by testing noise models of (a) powerlaw, (b)white, (c)white plus flicker, (d)white plus randomwalk, and (e) white plus flicker plus random-walk. The results show that amplitudes of all noise models are smallest in the north direction and largest in the vertical direction. While amplitudes of white noise model in (c–e) are almost equal across the study area, they are prevailed by the flicker and Random-walk noise for all directions. Assuming flicker noise model increases uncertainties of the estimated velocities by a factor of 5–38 compared to the white noise model.


2021 ◽  
Vol 13 (22) ◽  
pp. 4534
Author(s):  
Xiaoxing He ◽  
Machiel Simon Bos ◽  
Jean-Philippe Montillet ◽  
Rui Fernandes ◽  
Tim Melbourne ◽  
...  

The noise in position time series of 568 GPS (Global Position System) stations across North America with an observation span of ten years has been investigated using solutions from two processing centers, namely, the Pacific Northwest Geodetic Array (PANGA) and New Mexico Tech (NMT). It is well known that in the frequency domain, the noise exhibits a power-law behavior with a spectral index of around −1. By fitting various noise models to the observations and selecting the most likely one, we demonstrate that the spectral index in some regions flattens to zero at long periods while in other regions it is closer to −2. This has a significant impact on the estimated linear rate since flattening of the power spectral density roughly halves the uncertainty of the estimated tectonic rate while random walk doubles it. Our noise model selection is based on the highest log-likelihood value, and the Akaike and Bayesian Information Criteria to reduce the probability of over selecting noise models with many parameters. Finally, the noise in position time series also depends on the stability of the monument on which the GPS antenna is installed. We corroborate previous results that deep-drilled brace monuments produce smaller uncertainties than concrete piers. However, if at each site the optimal noise model is used, the differences become smaller due to the fact that many concrete piers are located in tectonic/seismic quiet areas. Thus, for the predicted performance of a new GPS network, not only the type of monument but also the noise properties of the region need to be taken into account.


2021 ◽  
Author(s):  
David Howe

Statistical imputation is a field of study that attempts to fill missing data. It is commonly applied to population statistics whose data have no correlation with running time. For a time series, data is typically analyzed using the autocorrelation function (ACF), the Fourier transform to estimate power spectral densities (PSD), the Allan deviation (ADEV), trend extensions, and basically any analysis that depends on uniform time indexes. We explain the rationale for an imputation algorithm that fills gaps in a time series by applying a backward, inverted replica of adjacent live data. To illustrate, four intentional massive gaps that exceed 100% of the original time series are recovered. The L(f) PSD with imputation applied to the gaps is nearly indistinguishable from the original. Also, the confidence of ADEV with imputation falls within 90% of the original ADEV with mixtures of power-law noises. The algorithm in Python is included for those wishing to try it.


2020 ◽  
Author(s):  
Alvaro Santamaría-Gómez ◽  
Jim Ray

<p><em>Chameleonic: readily changing color or other attributes.</em></p><p><em>Chameleon: a lizard that changes skin color to match what surrounds it so that it cannot be seen.</em></p><p>The error spectrum of decadal long GPS position time series is typically represented by a combination of flicker (pink) noise at long periods and white noise at short periods. It is known that when fitting a linear trend to the series, part of the flicker noise at the longest observed period will be absorbed by the trend. Here, using real and synthetic GPS position series, we show how the error spectrum is even more altered by the position discontinuities that populate the series. The fitted position offsets at the discontinuity epochs absorb a significant portion of the power spectrum at periods longer than the separation between the discontinuity epochs. The resulting error spectrum is flattened at long periods and this implies that:</p><ul><li>the estimated content of colored noise is biased low and can even apparently change its color towards whiter noise, i.e. the true noise color is not observable due to the discontinuities,</li> <li>the red (random walk) noise , most probably present in the series in small quantity, becomes undetectable even if long series are used,</li> <li>the pink (flicker) noise is not the best color noise to represent the error spectrum in long series containing discontinuities,</li> <li>the colored noise content cannot be compared between series with different sets of discontinuities.</li> </ul><p>These findings need to be considered when comparing the noise levels between series from different solutions, networks or monuments. In particular, and contrary to a recently published recommendation, station operators should make every effort to avoid adding new discontinuities into their station time series if reliable velocity estimates are expected.</p>


Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3353 ◽  
Author(s):  
Xiaoning Su ◽  
Guojie Meng ◽  
Haili Sun ◽  
Weiwei Wu

The Crustal Movement Observation Network of China (CMONOC) has begun receiving BeiDou Navigation Satellite System (BDS) observations since 2015, and accumulated more than 2.5 years of data. BDS observations has been widely applied in many fields, and long-term continuous data provide a new strategy for the study of crustal deformation in China. This paper focuses on the evaluation of BDS positioning performance and its potential application on crustal deformation in CMONOC. According to the comparative analysis on multipath delay (MPD) and signal to noise ratio (SNR) between BDS and GPS data, the data quality of BDS is at the same level with GPS measurements in COMONC. The spatial distribution of BDS positioning accuracy evaluated as the root mean square (RMS) of daily residual position time series on horizontal component is latitude-dependent, declining with the increasing of station latitude, while the vertical one is randomly distributed in China. The mean RMS of BDS position residual time series is 7 mm and 22 mm on horizontal and vertical components, respectively, and annual periodicity in position time series can be identified by BDS data. In view of the accuracy of BDS positioning, there are no systematic differences between GPS and BDS results. Based on time series analysis with data volume being 2.5 years, the noise characteristics of BDS daily position time series is time-correlated and corresponding noise is white plus flicker noise model, and the derived mean RMS of the BDS velocities is 1.2, 1.5, and 4.1 mm/year on north, east, and up components, respectively. The imperfect performance of BDS positioning relative to GPS is likely attributed to the relatively low accuracy of BDS ephemeris, and the sparse amount of MEO satellites distribution in the BDS constellation. It is expectable to study crustal deformation in CMONOC by BDS with the gradual maturity of its constellation and the accumulation of observations.


2021 ◽  
Author(s):  
Kevin Gobron ◽  
Paul Rebischung ◽  
Olivier de Viron ◽  
Michel Van Camp ◽  
Alain Demoulin

<p>Over the past two decades, numerous studies demonstrated that the stochastic variability in GNSS position time series – often referred to as noise – is both temporally and spatially correlated. The time correlation of this stochastic variability can be well approximated by a linear combination of white noise and power-law stochastic processes with different amplitudes. Although acknowledged in many geodetic studies, the presence of such power-law processes in GNSS position time series remains largely unexplained. Considering that these power-law processes are the primary source of uncertainty for velocity estimates, it is crucial to identify their origin(s) and to try to reduce their influence on position time series.</p><p> </p><p>Using the Least-Squares Variance Component Estimation method, we analysed the influence of removing surface mass loading deformation on the stochastic properties of vertical land motion time series (VLMs). We used the position time series of over 10,000 globally distributed GNSS stations processed by the Nevada Geodetic Laboratory at the University of Nevada, Reno, and loading deformation time series computed by the Earth System Modelling (ESM) team at GFZ-Potsdam. Our results show that the values of stochastic parameters, namely, white noise amplitude, spectral index, and power-law noise amplitude, but also the spatial correlation, are systematically influenced by non-tidal atmospheric and oceanic loading deformation. The observed change in stochastic parameters often translates into a reduction of trend uncertainties, reaching up to -75% when non-tidal atmospheric and oceanic loading deformation is highest.</p>


Geosciences ◽  
2019 ◽  
Vol 9 (5) ◽  
pp. 233
Author(s):  
Tarmo Kall ◽  
Tõnis Oja ◽  
Karin Kollo ◽  
Aive Liibusk

The aim of this study was to estimate the noise properties, velocities, and their uncertainties from a time-series of selected (~9 years long) Estonian continuously operating Global Navigation Satellite System (GNSS) stations. Two software packages based on different processing methods, Gipsy–Oasis and Bernese, were used for daily coordinate calculations. Different methods and software (Tsview, Hector, and MIDAS) were used for coordinate time-series analysis. Outliers were removed using three different strategies. Six different stochastic noise models were used for trend estimation altogether with the analysis of the noise properties of the residual time-series with Hector. Obtained velocities were compared with different land uplift and glacial isostatic adjustment models (e.g., ICE-6G (VM5a), NKG2016LU, etc.). All compared solutions showed similar fit to the compared models. It was confirmed that the best fit to the time-series residuals were with the flicker noise plus white noise model (for the North and East component) and generalized Gauss–Markov model (for Up). Velocities from MIDAS, Tsview, and Hector solutions within the same time-series (Gipsy–Oasis or Bernese) agreed well but velocity uncertainties differed up to four times. The smallest uncertainties were obtained from Tsview; the MIDAS solution produced the most conservative values. Although the East and Up component velocities between Gipsy and Bernese solutions agreed well, the North component velocities were systematically shifted.


2019 ◽  
Vol 11 (4) ◽  
pp. 386 ◽  
Author(s):  
Wenhao Li ◽  
Fei Li ◽  
Shengkai Zhang ◽  
Jintao Lei ◽  
Qingchuan Zhang ◽  
...  

The common mode error (CME) and optimal noise model are the two most important factors affecting the accuracy of time series in regional Global Navigation Satellite System (GNSS) networks. Removing the CME and selecting the optimal noise model can effectively improve the accuracy of GNSS coordinate time series. The CME, a major source of error, is related to the spatiotemporal distribution; hence, its detrimental effects on time series can be effectively reduced through spatial filtering. Independent component analysis (ICA) is used to filter the time series recorded by 79 GPS stations in Antarctica from 2010 to 2018. After removing stations exhibiting strong local effects using their spatial responses, the filtering results of residual time series derived from principal component analysis (PCA) and ICA are compared and analyzed. The Akaike information criterion (AIC) is then used to determine the optimal noise model of the GPS time series before and after ICA/PCA filtering. The results show that ICA is superior to PCA regarding both the filter results and the consistency of the optimal noise model. In terms of the filtering results, ICA can extract multisource error signals. After ICA filtering, the root mean square (RMS) values of the residual time series are reduced by 14.45%, 8.97%, and 13.27% in the east (E), north (N), and vertical (U) components, respectively, and the associated speed uncertainties are reduced by 13.50%, 8.06% and 11.82%, respectively. Furthermore, different GNSS time series in Antarctica have different optimal noise models with different noise characteristics in different components. The main noise models are the white noise plus flicker noise (WN+FN) and white noise plus power law noise (WN+PN) models. Additionally, the spectrum index of most PN is close to that of FN. Finally, there are more stations with consistent optimal noise models after ICA filtering than there are after PCA filtering.


2001 ◽  
Vol 172 (2) ◽  
pp. 141-158 ◽  
Author(s):  
Eric Calais ◽  
Roger Bayer ◽  
Jean Chery ◽  
Fabrice Cotton ◽  
Erik Doerflinger ◽  
...  

Abstract The kinematics of the present-day deformation in the western Alps is still poorly known, mostly because of a lack of direct measurements of block motion and internal deformation. Geodetic measurements have the potential to provide quantitative estimates of crustal strain and block motion in the Alps, but the low expected rates, close to the accuracy of the geodetic techniques, make such measurements challenging. Indeed, an analysis of 2.5 years of continuous GPS data at Torino (Italy), Grasse (France), and Zimmerwald (Switzerland), showed that the present-day differential motion across the western Alps does not exceed 3 mm/yr [Calais, 1999]. Continuous measurements performed at permanent GPS stations provide unique data sets for rigorously assessing crustal deformation in regions of low strain rates by reducing the amount of time necessary to detect a significant strain signal, minimizing systematic errors, providing continuous position time series, and possibly capturing co- and post-seismic motion. In 1997, we started the implementation of a network of permanent GPS stations in the western Alps and their surroundings (REGAL network). The REGAL network mostly operates dual frequency Ashtech Z12 CGRS GPS stations with choke-ring antennae. In most cases, the GPS antenna is installed on top of a 1.5 to 2.5 m high concrete pilar directly anchored into the bedrock. The data are currently downloaded once daily and sent to a data center located at Geosciences Azur, Sophia Antipolis where they are converted into RINEX format, quality checked, archived, and made available to users. Data are freely available in raw and RINEX format at http://kreiz.unice.fr/regal/. The GPS data from the REGAL network are routinely processed with the GAMIT software, together with 10 global IGS stations (KOSG, WZTR, NOTO, MATE, GRAZ, EBRE, VILL, CAGL, MEDI, UPAD) that serve as ties with the ITRF97. We also include the stations ZIMM, TORI, GRAS, TOUL, GENO, HFLK, OBER because of their tectonic interest. We obtain long term repeatabilities on the order of 2-3 mm for the horizontal components, 8-10 mm for the vertical component. Using a noise model that combines white and coloured noise (flicker noise, spectral index 1), we find uncertainties on the velocities ranging from 1 mm/yr for the oldest stations (ZIMM, GRAS, TOUL, TORI, SJDV) to 4-5 mm/yr for the most recently installed (CHAT, MTPL). Station velocities obtained in ITRF97 are rotated into a Eurasian reference by substracting the rigid rotation computed from ITRF97 velocities at 11 central European sites located away from major active tectonic structures (GOPE, JOZE, BOR1, LAMA, ZWEN, POTS, WETT, GRAZ, PENC, Effelsberg, ONSA). The resulting velocity field shows residual motions with respect to Eurasia lower than 3 mm/yr. We obtain at TORI, in the Po plain, a residual velocity of 2.3+ or -0.8 mm/yr to the SSW and a velocity of 1.9+ or -1.1 mm/yr at SJDV, on the Alpine foreland. These results indicate that the current kinematic boundary conditions across the western Alps are extensional, as also shown by the SJDV-TORI baseline time series. We obtain at MODA (internal zones) a residual velocity of 1.2+ or -1.2 mm/yr to the SSE. The MODA-FCLZ baseline show lengthening at a rate of 1.6+ or -0.8 mm/yr. These results are still marginally significant but suggest that the current deformation regime along the Lyon-Torino transect is extension, as also indicated by from recent seismotectonic data. It is in qualitative agreement with local geodetic measurements in the internal zones (Briancon area) but excludes more than 2.4 mm/yr of extension (FCLZ-MODA baseline, upper uncertainty limit at 95% confidence). Our results indicate a different tectonic regime in the southern part of the western Alps and Provence, with NW-SE to N-S compression. The GRAS-TORI baseline, for instance, shows shortening at a rate of 1.4+ or -1.0 mm/an. This result is consistent with seismotectonic data and local geodetic measurements in these areas. The Middle Durance fault zone, one of the main active faults in this area, is crossed by the GINA-MICH baseline, which shows shortening at a rate of 1.0+ or -0.8 mm/an. This result is only marginally significant, but confirms the upper bound of 2 mm/yr obtained from triangulation-GPS comparisons. The REGAL permanent GPS network has been operating since the end of 1997 for the oldest stations and will continue to be densified. Although they are still close to or within their associated uncertainties, preliminary results provide, for the first time, a direct estimate of crustal deformation across and within the western Alps.


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