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

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.

Download Full-text

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

Remote Sensing ◽

10.3390/rs11040386 ◽

2019 ◽

Vol 11 (4) ◽

pp. 386 ◽

Cited By ~ 1

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.

Download Full-text

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

Remote Sensing ◽

10.3390/rs13142783 ◽

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.

Download Full-text

Analysis and Discussion on the Optimal Noise Model of Global GNSS Long-Term Coordinate Series Considering Hydrological Loading

Remote Sensing ◽

10.3390/rs13030431 ◽

2021 ◽

Vol 13 (3) ◽

pp. 431

Author(s):

Yuefan He ◽

Guigen Nie ◽

Shuguang Wu ◽

Haiyang Li

Keyword(s):

White Noise ◽

Flicker Noise ◽

Noise Analysis ◽

Vertical Direction ◽

Noise Model ◽

Series Data ◽

Noise Power ◽

The Impact ◽

Noise Models

The displacement of Global Navigation Satellite System (GNSS) station contains the information of surface elastic deformation caused by the variation of land water reserves. This paper selects the long-term coordinate series data of 671 International GNSS Service (IGS) reference stations distributed globally under the framework of World Geodetic System 1984 (WGS84) from 2000 to 2021. Different noise model combinations are used for noise analysis, and the optimal noise model for each station before and after hydrologic loading correction is calculated. The results show that the noise models of global IGS reference stations are diverse, and each component has different optimal noise model characteristics, mainly white noise + flicker noise (WN+FN), generalized Gauss–Markov noise (GGM) and white noise + power law noise (WN+PL). Through specific analysis between the optimal noise model and the time series velocity of the station, it is found that the maximum influence value of the vertical velocity can reach 1.8 mm when hydrological loading is considered. Different complex noise models also have a certain influence on the linear velocity and velocity uncertainty of the station. Among them, the influence of white noise + random walking noise is relatively obvious, and its maximum influence value in the elevation direction can reach over 2 mm/year. When studying the impact of hydrological loading correction on the periodicity of the coordinate series, it is concluded whether the hydrological loading is calculated or not, and the GNSS long-term coordinate series has obvious annual and semi-annual amplitude changes, which are most obvious in the vertical direction, up to 16.48 mm.

Download Full-text

STOCHASTIC MODEL OF THE BRAZILIAN GPS NETWORK COORDINATES TIME SERIES

Boletim de Ciências Geodésicas ◽

10.1590/s1982-21702018000400033 ◽

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.

Download Full-text

Spatial Variations of Stochastic Noise Properties in GPS Time Series

Remote Sensing ◽

10.3390/rs13224534 ◽

2021 ◽

Vol 13 (22) ◽

pp. 4534

Author(s):

Xiaoxing He ◽

Machiel Simon Bos ◽

Jean-Philippe Montillet ◽

Rui Fernandes ◽

Tim Melbourne ◽

...

Keyword(s):

Time Series ◽

Pacific Northwest ◽

Spectral Index ◽

Information Criteria ◽

Noise Model ◽

Power Spectral ◽

The Pacific ◽

Position Time Series ◽

The Stability ◽

Noise Models

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.

Download Full-text

Spatial variations of stochastic noise properties of GNSS time series

10.5194/egusphere-egu2020-21260 ◽

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&#8217;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&#8217;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>

Download Full-text