Spatial variations of stochastic noise properties of GNSS time series

2020 ◽  
Author(s):  
Rui Fernandes ◽  
Xiaoxing He ◽  
Jean-Philippe Montillet ◽  
Machiel Bos ◽  
Tim Melbourne ◽  
...  
Keyword(s):  
Time Series ◽  
North America ◽  
White Noise ◽  
Goodness Of Fit ◽  
Vertical Component ◽  
Noise Model ◽  
Cascadia Subduction Zone ◽  
Slow Slip Events ◽  
Trajectory Model ◽  
Gnss Time Series

<p>The analysis of daily position Global Navigation Satellite System (GNSS) time series provides information about various geophysical processes that are shaping the Earth’s crust. The goodness of fit of a trajectory model to these observations is an indication of our understanding of these phenomena. However, the fit also depends on the noise levels in the time series and in this study we investigate for 568 GNSS stations across North America the noise properties, its relation with the choice of trajectory model and if there exists a relationship with the type of monuments. We use the time series of two processing centers, namely the Central Washington University (CWU) and the New Mexico Tech (NMT), which process the data using two different complete processing strategies.</p><p>We demonstrate that mismodelling slow slip events within the geodetic time series increases the percentage of selecting the Random-Walk + Flicker + White noise (RW+FN+WN) as the optimal noise model for the horizontal components, especially when the Akaike Information Criterion is used. Furthermore, the analysis of the spatial distribution of the RW component (in the FN+WN+RW) around North America takes place at stations mostly localised around tectonic active areas such as the Cascadia subduction zone (Pacific Northwest) or the San Andreas fault (South California) and coastal areas. It is in these areas that most shallow and drilled-braced monuments are also located. Therefore, the comparison of monument type with observed noise level should also take into account its location which mostly has been neglected in previous studies. In addition, the General Gauss-Markov (GGM) with white noise (GGM+WN) is often selected for the Concrete Pier monument especially on the Up component which indicates that the very long time series are experiencing this flattening of the power spectrum at low frequency. Finally, the amplitude of the white noise is larger for the Roof-Top/Chimney (RTC) type than for the other monument’s types. With a varying seasonal signal computed using a Wiener filter, the results show that RTC monuments have larger values in the East and North components, whereas the deep-drilled brace monuments have larger values on the vertical component.</p>

scholarly journals Noise behavior in CGPS position time series: the eastern North America case study

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
M. A. Goudarzi ◽  
M. Cocard ◽  
R. Santerre
Keyword(s):  
Time Series ◽  
Random Walk ◽  
North America ◽  
White Noise ◽  
Flicker Noise ◽  
Noise Model ◽  
Eastern North America ◽  
Position Time Series ◽  
White Noise Model ◽  
Noise Models

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.

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 ◽  
...  
Keyword(s):  
Time Series ◽  
Visual Inspection ◽  
Flicker Noise ◽  
Vertical Component ◽  
Likelihood Estimation ◽  
Noise Model ◽  
Noise Amplitude ◽  
Allan Deviation ◽  
Power Spectral ◽  
Position Time Series

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.

Noise Modeling

2017 ◽  
Author(s):  
Richard McCleary ◽  
David McDowall ◽  
Bradley J. Bartos
Keyword(s):  
Time Series ◽  
White Noise ◽  
Autocorrelation Function ◽  
Model Building ◽  
Moving Average ◽  
Information Criteria ◽  
Noise Model ◽  
Adequate Model ◽  
Noise Modeling ◽  
Modeling Strategy

Chapter 3 introduces the Box-Jenkins AutoRegressive Integrated Moving Average (ARIMA) noise modeling strategy. The strategy begins with a test of the Normality assumption using a Kolomogov-Smirnov (KS) statistic. Non-Normal time series are transformed with a Box-Cox procedure is applied. A tentative ARIMA noise model is then identified from a sample AutoCorrelation function (ACF). If the sample ACF identifies a nonstationary model, the time series is differenced. Integer orders p and q of the underlying autoregressive and moving average structures are then identified from the ACF and partial autocorrelation function (PACF). Parameters of the tentative ARIMA noise model are estimated with maximum likelihood methods. If the estimates lie within the stationary-invertible bounds and are statistically significant, the residuals of the tentative model are diagnosed to determine whether the model’s residuals are not different than white noise. If the tentative model’s residuals satisfy this assumption, the statistically adequate model is accepted. Otherwise, the identification-estimation-diagnosis ARIMA noise model-building strategy continues iteratively until it yields a statistically adequate model. The Box-Jenkins ARIMA noise modeling strategy is illustrated with detailed analyses of twelve time series. The example analyses include non-Normal time series, stationary white noise, autoregressive and moving average time series, nonstationary time series, and seasonal time series. The time series models built in Chapter 3 are re-introduced in later chapters. Chapter 3 concludes with a discussion and demonstration of auxiliary modeling procedures that are not part of the Box-Jenkins strategy. These auxiliary procedures include the use of information criteria to compare models, unit root tests of stationarity, and co-integration.

scholarly journals Quantitative Evaluation of Environmental Loading Induced Displacement Products for Correcting GNSS Time Series in CMONOC

2020 ◽  
Vol 12 (4) ◽  
pp. 594 ◽  
Author(s):  
Li ◽  
Huang ◽  
Chen ◽  
Dam ◽  
Fok ◽  
...  
Keyword(s):  
Time Series ◽  
Mainland China ◽  
Vertical Component ◽  
Satellite System ◽  
Environmental Loading ◽  
Noise Characteristics ◽  
The Difference ◽  
Land Data Assimilation System ◽  
Global Navigation Satellite ◽  
Gnss Time Series

Mass redistribution within the Earth system deforms the surface elastically. Loading theory allows us to predict loading induced displacement anywhere on the Earth’s surface using environmental loading models, e.g., Global Land Data Assimilation System. In addition, different publicly available loading products are available. However, there are differences among those products and the differences among the combinations of loading models cannot be ignored when precisions of better than 1 cm are required. Many scholars have applied these loading corrections to Global Navigation Satellite System (GNSS) time series from mainland China without considering or discussing the differences between the available models. Evaluating the effects of different loading products over this region is of paramount importance for accurately removing the loading signal. In this study, we investigate the performance of these different publicly available loading products on the scatter of GNSS time series from the Crustal Movement Observation Network of China. We concentrate on five different continental water storage loading models, six different non-tidal atmospheric loading models, and five different non-tidal oceanic loading models. We also investigate all the different combinations of loading products. The results show that the difference in RMS reduction can reach 20% in the vertical component depending on the loading correction applied. We then discuss the performance of different loading combinations and their effects on the noise characteristics of GNSS height time series and horizontal velocities. The results show that the loading products from NASA may be the best choice for corrections in mainland China. This conclusion could serve as an important reference for loading products users in this region.

Accuracy of GNSS campaign site velocities with respect to ITRF14 solution

2020 ◽  
Author(s):  
Yener Turen ◽  
Dogan Ugur Sanli
Keyword(s):  
Time Series ◽  
White Noise ◽  
Vertical Component ◽  
Global Network ◽  
Global Studies ◽  
Time Series Analyses ◽  
Noise Error ◽  
Set Up ◽  
Continuous Gps ◽  
Gps Time Series

<p>In this study, we assess the accuracy of deformation rates produced from GNSS campaign measurements sampled in different frequencies. The ideal frequency of the sampling seems to be 1 measurement per month however it is usually found to be cumbersome. Alternatively the sampling was performed 3 measurements per year and time series analyses were carried out. We used the continuous GPS time series of JPL, NASA from a global network of the IGS to decimate the data down to 4 monthly synthetic GNSS campaign time series. Minimum data period was taken to be 4 years following the suggestions from the literature. Furthermore, the effect of antenna set-up errors in campaign measurements on the estimated trend was taken into account. The accuracy of deformation rates were then determined taking the site velocities from ITRF14 solution as the truth. The RMS of monthly velocities agreed pretty well with the white noise error from global studies given previously in the literature. The RMS of four monthly deformation rates for horizontal positioning were obtained to be 0.45 and 0.50 mm/yr for north and east components respectively whereas the accuracy of vertical deformation rates was found to be 1.73 mm/yr. This is slightly greater than the average level of the white noise error from a global solution previously produced, in which antenna set up errors were out of consideration. Antenna set up errors in campaign measurements modified the above error level to 0.75 and 0.70 mm/yr for the horizontal components north and east respectively whereas the accuracy of the vertical component was slightly shifted to 1.79 mm/yr.</p>

scholarly journals Methodological approach for the estimation of a new velocity model for continental Ecuador

2017 ◽  
Vol 9 (1) ◽  
Author(s):  
Marco P. Luna ◽  
Alejandra Staller ◽  
Theofilos Toulkeridis ◽  
Humberto Parra
Keyword(s):  
Time Series ◽  
Chaotic Behavior ◽  
Methodological Approach ◽  
Vertical Component ◽  
Velocity Model ◽  
Geostatistical Approach ◽  
The Mean ◽  
Gnss Network ◽  
Best Fit ◽  
Gnss Time Series

AbstractWe used 33 stations belonging of the Ecuador Continuous Monitoring GNSS Network (REGME) during the period 2008-2014, with aim to contribute with a methodological approach for the estimation of a new velocity model for Continental Ecuador. We used daily solutions to perform the analysis of GNSS time series, to obtain models of the series that best fit, taking into count the trend, seasonal variations and the type of noise. The sum of all these components represent the real-time series, and thus we can have a better estimation of the velocity parameter and its uncertainty.The velocities were calculated introducing the trend, seasonality and noise that were presented in each series into the overall model, which improved uncertainty by 12% and changed in magnitude up to 1.7 mm/yr and 2.5 mm/yr in the horizontal and vertical components, respectively, with respect to the initial velocities. The velocity field describes the crustal movement of the REGME stations in mainland Ecuador with uncertainty of 1 mm/yr and 2 mm/yr for the horizontal and vertical components, respectively. Finally, a velocity model has been developed using the kriging technique whose geostatistical approach has been based on the data to identify the spatial characteristics by examining the observations by peers. The mean square error (rms) of prediction obtained in this method is 1.78 mm/yr and 1.95 mm/yr in the east and north components, respectivaly. The vertical component could not be modeled due to its chaotic behavior.

scholarly journals Noise characteristics in Zenith Total Delay from homogeneously reprocessed GPS time series

2016 ◽  
Author(s):  
Anna Klos ◽  
Addisu Hunegnaw ◽  
Felix Norman Teferle ◽  
Kibrom Ebuy Abraha ◽  
Furqan Ahmed ◽  
...  
Keyword(s):  
Time Series ◽  
White Noise ◽  
Autoregressive Process ◽  
Noise Model ◽  
Total Delay ◽  
Tropical Zone ◽  
Climate Zones ◽  
Zenith Total Delay ◽  
Noise Characteristics ◽  
Gps Time Series

Abstract. Zenith Total Delay (ZTD) time series, derived from the re-processing of Global Positioning System (GPS) data, provide valuable information for the evaluation of global atmospheric reanalysis products such as ERA-Interim. Identifying the correct noise characteristics in the ZTD time series is an important step to assess the "true" magnitude of ZTD trend uncertainties. The ZTD residual time series for 1995–2015 are generated from our homogeneously re-processed and homogenized GPS time series from over 700 globally distributed stations classified into five major climate zones. The annual peak of ZTD data ranges between 10 and 150 mm with the smallest values for the polar and Alpine zone. The amplitudes of daily curve fall between 0 and 12 mm with the greatest variations for the dry zone. The autoregressive process of fourth order plus white noise model were found to be optimal for ZTD series. The tropical zone has the largest amplitude of autoregressive noise (9.59 mm) and the greatest amplitudes of white noise (13.00 mm). All climate zones have similar median coefficients of AR(1) (0.80 ± 0.05) with a minimum for polar and Alpine, which has the highest coefficients of AR(2) (0.27 ± 0.01) and AR(3) (0.11 ± 0.01) and clearly different from the other zones considered. We show that 53 of 120 examined trends became insignificant, when the optimum noise model was employed, compared to 11 insignificant trends for pure white noise. The uncertainty of the ZTD trends may be underestimated by a factor of 3 to 12 compared to the white noise only assumption.

scholarly journals Spatiotemporal Slip Distributions Associated with the 2018-2019 Bungo Channel Long-Term Slow Slip Event Inverted from GNSS Data

2021 ◽  
Author(s):  
Yukinari Seshimo ◽  
Shoichi Yoshioka
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Total Duration ◽  
Series Data ◽  
Slow Slip ◽  
Slow Slip Events ◽  
Bungo Channel ◽  
Slip Event ◽  
Gnss Time Series

Abstract Long-term slow slip events (L-SSEs) have occurred beneath the Bungo Channel with durations of several months to a couple of years repeatedly with a recurrence interval of approximately six years. We estimated the spatiotemporal slip distributions of the 2018–2019 Bungo Channel L-SSE inverted from processed GNSS time series data. This event was divided into two subevents, with the first on the southwest side of the Bungo Channel from 2018.3 to 2018.7 and the second beneath the Bungo Channel from 2018.8 to 2019.4. Tectonic tremors became active on the downdip side of the L-SSE occurrence region when large slow slips took place beneath the Bungo Channel. Compared with the previous Bungo Channel L-SSEs, this spatiotemporal slip pattern and amount were similar to those of the 2003 L-SSE. However, the slip expanded in the northeast-southwest direction in the latter half of the second subevent. We also found that the total duration of the two subevents was 1.0 year, which was the shortest among the four recent L-SSEs beneath the Bungo Channel identified using GNSS time series data. The maximum amount of slip, the maximum slip velocity, the total released seismic moment, and the moment magnitude of the 2018–2019 L-SSE were estimated to be 27 cm, 53 cm/year, 4.1×1019 Nm, and 7.0, respectively, all of which were the largest among the four L-SSEs.

scholarly journals STOCHASTIC MODEL OF THE BRAZILIAN GPS NETWORK COORDINATES TIME SERIES

2018 ◽  
Vol 24 (4) ◽  
pp. 545-563
Author(s):  
Christian Gonzalo Pilapanta Amagua ◽  
Claudia Pereira Krueger ◽  
Alfonso Rodrigo Tierra Criollo
Keyword(s):  
Time Series ◽  
Random Walk ◽  
White Noise ◽  
Power Law ◽  
Fractional Power ◽  
Noise Model ◽  
Coastal Zones ◽  
White Noise Process ◽  
Noise Process ◽  
Stochastic Properties

Abstract It is well known that daily estimates of GPS coordinates are highly temporally correlated and that the knowledge and understanding of this correlation allows to establish more realistic uncertainties of the parameters estimated from the data. Despite this, there are currently no studies related to the analysis and calculation of the noise sources in geodetic time series in Brazil. In this context, this paper focuses on the investigation of the stochastic properties of a total of 486 coordinates time series from 159 GPS stations belonging to the Brazilian Network for Continuous Monitoring of GNSS (RBMC) using the maximum likelihood estimation approach. To reliably describe the GPS time series, we evaluate 4 possible stochastic models as models of each time series: 3 models with integer spectral indices (white noise, flicker plus white noise and random-walk plus white noise model) and 1 with fractional spectral index (fractional power-law plus white noise). By comparing the calculated noise content values for each model, it is possible to demonstrate a stepwise increase of the noise content, being the combination of a fractional power-law process and white noise process, the model with smaller values and the combination of random walk process with white noise process, the model with greater values. The analysis of the spatial distribution of the noise values of the processes allow demonstrate that the GPS sites with the highest accumulated noise values, coincide with sites located in coastal zones and river basins and that their stochastic properties can be aliased by the occurrence of different physical signals typical of this type of zones, as the case of the hydrological loading effect.

scholarly journals Spatiotemporal Filtering and Noise Analysis for Regional GNSS Network in Antarctica Using Independent Component Analysis

2019 ◽  
Vol 11 (4) ◽  
pp. 386 ◽  
Author(s):  
Wenhao Li ◽  
Fei Li ◽  
Shengkai Zhang ◽  
Jintao Lei ◽  
Qingchuan Zhang ◽  
...  
Keyword(s):  
Time Series ◽  
Independent Component Analysis ◽  
White Noise ◽  
Flicker Noise ◽  
Component Analysis ◽  
Independent Component ◽  
Noise Model ◽  
Residual Time ◽  
Noise Characteristics ◽  
Noise Models

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.

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