Chameleonic noise in GPS position series: what is the true color of the GPS error spectra?

2020 ◽  
Author(s):  
Alvaro Santamaría-Gómez ◽  
Jim Ray
Keyword(s):  
Time Series ◽  
Skin Color ◽  
Colored Noise ◽  
Flicker Noise ◽  
Linear Trend ◽  
Pink Noise ◽  
Noise Levels ◽  
Color Noise ◽  
Position Time Series ◽  
True Color

<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>

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.

scholarly journals General Geometric Model of GNSS Position Time Series for Crustal Deformation Studies – A Case Study of CORS Stations in Vietnam

2021 ◽  
Vol 1 (2) ◽  
Author(s):  
Dinh Trong TRAN ◽  
Quoc Long NGUYEN ◽  
Dinh Huy NGUYEN
Keyword(s):  
Time Series ◽  
Crustal Deformation ◽  
Linear Trend ◽  
Geometric Model ◽  
Real Data ◽  
Deformation Monitoring ◽  
Calculation Results ◽  
Position Time Series ◽  
Seismic Deformation ◽  
Gnss Position Time Series

In processing of position time series of crustal deformation monitoring stations by continuousGNSS station, it is very important to determine the motion model to accurately determine the displacementvelocity and other movements in the time series. This paper proposes (1) the general geometric model foranalyzing GNSS position time series, including common phenomena such as linear trend, seasonal term,jumps, and post-seismic deformation; and (2) the approach for directly estimating time decay ofpostseismic deformations from GNSS position time series, which normally is determined based on seismicmodels or the physical process seismicity, etc. This model and approach are tested by synthetic positiontime series, of which the calculation results show that the estimated parameters are equal to the givenparameters. In addition they were also used to process the real data which is GNSS position time series of4 CORS stations in Vietnam, then the estimated velocity of these stations: DANA (n, e, u = -9.5, 31.5, 1.5mm/year), HCMC (n, e, u = -9.5, 26.2, 1.9 mm/year), NADI (n, e, u = -10.6, 31.5, -13.4 mm/year), andNAVI (n, e, u = -13.9, 32.8, -1.1 mm/year) is similar to previous studies.

scholarly journals Effects of Spatiotemporal Filtering on the Periodic Signals and Noise in the GPS Position Time Series of the Crustal Movement Observation Network of China

2018 ◽  
Vol 10 (9) ◽  
pp. 1472 ◽  
Author(s):  
Peng Yuan ◽  
Weiping Jiang ◽  
Kaihua Wang ◽  
Nico Sneeuw
Keyword(s):  
Time Series ◽  
Velocity Field ◽  
Colored Noise ◽  
Environmental Loading ◽  
Movement Observation ◽  
Observation Network ◽  
Uncertainty Estimates ◽  
Position Time Series ◽  
Periodic Signals ◽  
Gps Velocity Field

Analysis of Global Positioning System (GPS) position time series and its common mode components (CMC) is very important for the investigation of GPS technique error, the evaluation of environmental loading effects, and the estimation of a realistic and unbiased GPS velocity field for geodynamic applications. In this paper, we homogeneously processed the daily observations of 231 Crustal Movement Observation Network of China (CMONOC) Continuous GPS stations to obtain their position time series. Then, we filtered out the CMC and evaluated its effects on the periodic signals and noise for the CMONOC time series. Results show that, with CMC filtering, peaks in the stacked power spectra can be reduced at draconitic harmonics up to the 14th, supporting the point that the draconitic signal is spatially correlated. With the colored noise suppressed by CMC filtering, the velocity uncertainty estimates for both of the two subnetworks, CMONOC-I (≈16.5 years) and CMONOC-II (≈4.6 years), are reduced significantly. However, the CMONOC-II stations obtain greater reduction ratios in velocity uncertainty estimates with average values of 33%, 38%, and 54% for the north, east, and up components. These results indicate that CMC filtering can suppress the colored noise amplitudes and improve the precision of velocity estimates. Therefore, a unified, realistic, and three-dimensional CMONOC GPS velocity field estimated with the consideration of colored noise is given. Furthermore, contributions of environmental loading to the vertical CMC are also investigated and discussed. We find that the vertical CMC are reduced at 224 of the 231 CMONOC stations and 170 of them are with a root mean square (RMS) reduction ratio of CMC larger than 10%, confirming that environmental loading is one of the sources of CMC for the CMONOC height time series.

scholarly journals Positioning Performance of BDS Observation of the Crustal Movement Observation Network of China and Its Potential Application on Crustal Deformation

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3353 ◽  
Author(s):  
Xiaoning Su ◽  
Guojie Meng ◽  
Haili Sun ◽  
Weiwei Wu
Keyword(s):  
Time Series ◽  
Crustal Deformation ◽  
Potential Application ◽  
Flicker Noise ◽  
Crustal Movement ◽  
Movement Observation ◽  
North East ◽  
Noise Characteristics ◽  
Observation Network ◽  
Position Time Series

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.

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 Impacts on Noise Analyses of GNSS Position Time Series Caused by Seasonal Signal, Weight Matrix, Offset, and Helmert Transformation Parameters

2018 ◽  
Vol 10 (10) ◽  
pp. 1584 ◽  
Author(s):  
Guo Chen ◽  
Qile Zhao ◽  
Na Wei ◽  
Jingnan Liu
Keyword(s):  
Time Series ◽  
Colored Noise ◽  
Deterministic Model ◽  
Simulated Data ◽  
Weight Matrix ◽  
Helmert Transformation ◽  
Seasonal Signals ◽  
Position Time Series ◽  
Power Law Noise ◽  
Transformation Parameters

The noise characteristics of the Global Navigation Satellite System (GNSS) position time series can be biased by many factors, which in turn affect the estimates of parameters in the deterministic model using a least squares method. The authors assess the effects of seasonal signals, weight matrix, intermittent offsets, and Helmert transformation parameters on the noise analyses. Different solutions are obtained using the simulated and real position time series of 647 global stations and power law noise derived from the residuals of stacking solutions are compared. Since the true noise in the position time series is not available except for the simulated data, the authors paid most attention to the noise difference caused by the variable factors. First, parameterization of seasonal signals in the time series can reduce the colored noise and cause the spectral indexes to be closer to zero (much “whiter”). Meanwhile, the additional offset parameters can also change the colored noise to be much “whiter” and more offsets parameters in the deterministic model leading to spectral indexes closer to zero. Second, the weight matrices derived from the covariance information can induce more colored noise than the unit weight matrix for both real and simulated data, and larger biases of annual amplitude of simulated data are attributed to the covariance information. Third, the Helmert transformation parameters (three translation, three rotation, and one scale) considered in the model show the largest impacts on the power law noise (medians of 0.4 mm−k/4 and 0.06 for the amplitude and spectral index, respectively). Finally, the transformation parameters and full-weight matrix used together in the stacking model can induce different patterns for the horizontal and vertical components, respectively, which are related to different dominant factors.

scholarly journals GPS measurements on pre-, co- and post-seismic surface deformation at first multi-parametric geophysical observatory, Ghuttu in Garhwal Himalaya, India

2020 ◽  
Vol 10 (1) ◽  
pp. 136-144
Author(s):  
P.K. Gautam ◽  
S. Rajesh ◽  
N. Kumar ◽  
C.P. Dabral
Keyword(s):  
Time Series ◽  
Surface Deformation ◽  
Translational Motion ◽  
Anomalous Behavior ◽  
Deformation Pattern ◽  
Local Earthquakes ◽  
Position Time Series ◽  
Continuous Gps ◽  
Gps Time Series ◽  
Gps Station

Abstract We investigate the surface deformation pattern of GPS station at MPGO Ghuttu (GHUT) to find out the cause of anomalous behavior in the continuous GPS time series. Seven years (2007-2013) of GPS data has been analyzed using GAMIT/GLOBK software and generated the daily position time series. The horizontal translational motion at GHUT is 43.7 ± 1 mm/yr at an angle of 41°± 3° towards NE, while for the IGS station at LHAZ, the motion is 49.4 ±1 mm/yr at 18 ± 2.5° towards NEE. The estimated velocity at GHUT station with respect to IISC is 12 ± 1 mm/yr towards SW. Besides, we have also examined anomalous changes in the time series of GHUT before, after and during the occurrences of local earthquakes by considering the empirical strain radius; such that, a possible relationship between the strain radius and the occurrences of earthquakes have been explored. We considered seven local earthquakes on the basis of Dobrovolsky strain radius condition having magnitude from 4.5 to 5.7, which occurred from 2007 to 2011. Results show irrespective of the station strain radius, pre-seismic surface deformational anomalies are observed roughly 70 to 80 days before the occurrence of a Moderate or higher magnitude events. This has been observed for the cases of those events originated from the Uttarakashi and the Chamoli seismic zones in the Garhwal and Kumaun Himalaya. Occurrences of short (< 100 days) and long (two years) inter-seismic events in the Garhwal region plausibly regulating and diffusing the regional strain accumulation.

scholarly journals Benchmarking homogenization algorithms for monthly data

2012 ◽  
Vol 8 (1) ◽  
pp. 89-115 ◽  
Author(s):  
V. K. C. Venema ◽  
O. Mestre ◽  
E. Aguilar ◽  
I. Auer ◽  
J. A. Guijarro ◽  
...  
Keyword(s):  
Time Series ◽  
Performance Metrics ◽  
Linear Trend ◽  
Simulated Data ◽  
Integrated Approach ◽  
Global Network ◽  
Temperature And Precipitation ◽  
Skill Scores ◽  
Simulated Network ◽  
The Individual

Abstract. The COST (European Cooperation in Science and Technology) Action ES0601: advances in homogenization methods of climate series: an integrated approach (HOME) has executed a blind intercomparison and validation study for monthly homogenization algorithms. Time series of monthly temperature and precipitation were evaluated because of their importance for climate studies and because they represent two important types of statistics (additive and multiplicative). The algorithms were validated against a realistic benchmark dataset. The benchmark contains real inhomogeneous data as well as simulated data with inserted inhomogeneities. Random independent break-type inhomogeneities with normally distributed breakpoint sizes were added to the simulated datasets. To approximate real world conditions, breaks were introduced that occur simultaneously in multiple station series within a simulated network of station data. The simulated time series also contained outliers, missing data periods and local station trends. Further, a stochastic nonlinear global (network-wide) trend was added. Participants provided 25 separate homogenized contributions as part of the blind study. After the deadline at which details of the imposed inhomogeneities were revealed, 22 additional solutions were submitted. These homogenized datasets were assessed by a number of performance metrics including (i) the centered root mean square error relative to the true homogeneous value at various averaging scales, (ii) the error in linear trend estimates and (iii) traditional contingency skill scores. The metrics were computed both using the individual station series as well as the network average regional series. The performance of the contributions depends significantly on the error metric considered. Contingency scores by themselves are not very informative. Although relative homogenization algorithms typically improve the homogeneity of temperature data, only the best ones improve precipitation data. Training the users on homogenization software was found to be very important. Moreover, state-of-the-art relative homogenization algorithms developed to work with an inhomogeneous reference are shown to perform best. The study showed that automatic algorithms can perform as well as manual ones.

scholarly journals Precision of continuous GPS velocities from statistical analysis of synthetic time series

2018 ◽  
Author(s):  
Christine Masson ◽  
Stephane Mazzotti ◽  
Philippe Vernant
Keyword(s):  
Time Series ◽  
Extreme Values ◽  
Regression Tree ◽  
Simple Method ◽  
Position Time Series ◽  
Gps Velocities ◽  
Synthetic Time Series ◽  
Continuous Gps ◽  
Automatic Treatment ◽  
Gps Noise

Abstract. We use statistical analyses of synthetic position time series to estimate the potential precision of GPS velocities. The synthetic series represent the standard range of noise, seasonal, and position offset characteristics, leaving aside extreme values. This analysis is combined with a new simple method for automatic offset detection that allows an automatic treatment of the massive dataset. Colored noise and the presence of offsets are the primary contributor to velocity variability. However, regression tree analyses show that the main factors controlling the velocity precision are first the duration of the series, followed by the presence of offsets and the noise (dispersion and spectral index). Our analysis allows us to propose guidelines, which can be applied to actual GPS data, that constrain the velocity accuracies (expressed as 95 % confidence limits) based on simple parameters: (1) Series durations over 8.0 years result in high velocity accuracies in the horizontal (0.2 mm yr−1) and vertical (0.5 mm yr−1); (2) Series durations of less than 4.5 years cannot be used for high-precision studies since the horizontal accuracy is insufficient (over 1.0 mm yr−1); (3) Series of intermediate durations (4.5–8.0 years) are associated with an intermediate horizontal accuracy (0.6 mm yr-1) and a poor vertical one (1.3 mm yr−1), unless they comprise no offset. Our results suggest that very long series durations (over 15–20 years) do not ensure a better accuracy compare to series of 8–10 years, due to the noise amplitude following a power-law dependency on the frequency. Thus, better characterizations of long-period GPS noise and pluri-annual environmental loads are critical to further improve GPS velocity precisions.

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