scholarly journals Detecting time-varying seasonal signal in GPS position time series with different noise levels

GPS Solutions ◽  
2017 ◽  
Vol 22 (1) ◽  
Author(s):  
Anna Klos ◽  
Machiel S. Bos ◽  
Janusz Bogusz
Keyword(s):  
Time Series ◽  
Time Varying ◽  
Noise Levels ◽  
Position Time Series ◽  
Seasonal Signal

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 Implication between Geophysical Events and the Variation of Seasonal Signal Determined in GNSS Position Time Series

2021 ◽  
Vol 13 (17) ◽  
pp. 3478
Author(s):  
Sorin Nistor ◽  
Norbert-Szabolcs Suba ◽  
Ahmed El-Mowafy ◽  
Michal Apollo ◽  
Zinovy Malkin ◽  
...  
Keyword(s):  
Time Series ◽  
Satellite System ◽  
Phase Lag ◽  
Time Frequency ◽  
Richter Scale ◽  
Different Types ◽  
Before And After ◽  
Position Time Series ◽  
Global Navigation Satellite ◽  
Seasonal Signal

The seasonal signal determined by the Global Navigation Satellite System (GNSS), which is captured in the coordinate time series, exhibits annual and semi-annual periods. This signal is frequently modelled by two periodic signals with constant amplitude and phase-lag. The purpose of this study is to explore the implication of different types of geophysical events on the seasonal signal in three stages—in the time span that contains the geophysical events, before and after the geophysical event, but also the stationarity phenomena, which is analysed on approximately 200 reference stations from the EPN network since 1995. The novelty of the article is demonstrated by correlating three different types of geophysical events, such as earthquakes with a magnitude greater than 6° on the Richter scale, landslides, and volcanic activity, and analysing the variation in amplitude of the seasonal signal. The geophysical events situated within a radius of 30 km from the epicentre showed a higher seasonal value than when the timespan did not contain a geophysical event. The presence of flicker and random walk noise was computed using overlapping Hadamard variance (OHVAR) and the non-stationary behaviour of the time series of the CORS coordinates in the time frequency analysis was done using continuous wavelet transform (CWT).

scholarly journals Wavelet ridge diagnosis of time-varying elliptical signals with application to an oceanic eddy

2006 ◽  
Vol 13 (5) ◽  
pp. 467-483 ◽  
Author(s):  
J. M. Lilly ◽  
J.-C. Gascard
Keyword(s):  
Time Series ◽  
Physical Properties ◽  
Perturbation Analysis ◽  
Instantaneous Frequency ◽  
Orbital Motion ◽  
Time Varying ◽  
Circular Case ◽  
Position Time Series ◽  
Oceanic Eddy ◽  
Wavelet Ridge

Abstract. A method for diagnosing the physical properties of a time-varying ellipse is presented. This essentially involves extending the notion of instantaneous frequency to the bivariate case. New complications, and possibilities, arise from the fact that there are several meaningful forms in which a time-varying ellipse may be represented. A perturbation analysis valid for the near-circular case clarifies these issues. Diagnosis of the ellipse properties may then be performed using wavelet ridge analysis, and slowly-varying changes in the ellipse structure may be decoupled from the fast orbital motion through the use of elliptic integrals, without the need for additional explicit filtering. The theory is presented in parallel with an application to a position time series of a drifting subsurface float trapped in an oceanic eddy.

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 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.

Selective Linear Segmentation for Detecting Relevant Parameter Changes*

2020 ◽  
Author(s):  
Arnaud Dufays ◽  
Elysee Aristide Houndetoungan ◽  
Alain Coën
Keyword(s):  
Time Series ◽  
Hedge Fund ◽  
Expectation Maximization Algorithm ◽  
Model Parameters ◽  
Relevant Parameter ◽  
Time Varying ◽  
Long Time ◽  
Model Selection Uncertainty ◽  
Penalized Likelihood Approach ◽  
Changes Over Time

Abstract Change-point (CP) processes are one flexible approach to model long time series. We propose a method to uncover which model parameters truly vary when a CP is detected. Given a set of breakpoints, we use a penalized likelihood approach to select the best set of parameters that changes over time and we prove that the penalty function leads to a consistent selection of the true model. Estimation is carried out via the deterministic annealing expectation-maximization algorithm. Our method accounts for model selection uncertainty and associates a probability to all the possible time-varying parameter specifications. Monte Carlo simulations highlight that the method works well for many time series models including heteroskedastic processes. For a sample of fourteen hedge fund (HF) strategies, using an asset-based style pricing model, we shed light on the promising ability of our method to detect the time-varying dynamics of risk exposures as well as to forecast HF returns.

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.

scholarly journals An Extended Time Series Algorithm for Modal Identification from Nonstationary Ambient Response Data Only

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Chang-Sheng Lin ◽  
Dar-Yun Chiang ◽  
Tse-Chuan Tseng
Keyword(s):  
Time Series ◽  
Arma Model ◽  
Identification Problem ◽  
Nonstationary Time Series ◽  
Modal Identification ◽  
Ambient Vibration ◽  
Time Varying ◽  
Varying Parameters ◽  
Response Data ◽  
Time Varying Parameters

Modal Identification is considered from response data of structural systems under nonstationary ambient vibration. The conventional autoregressive moving average (ARMA) algorithm is applicable to perform modal identification, however, only for stationary-process vibration. The ergodicity postulate which has been conventionally employed for stationary processes is no longer valid in the case of nonstationary analysis. The objective of this paper is therefore to develop modal-identification techniques based on the nonstationary time series for linear systems subjected to nonstationary ambient excitation. Nonstationary ARMA model with time-varying parameters is considered because of its capability of resolving general nonstationary problems. The parameters of moving averaging (MA) model in the nonstationary time-series algorithm are treated as functions of time and may be represented by a linear combination of base functions and therefore can be used to solve the identification problem of time-varying parameters. Numerical simulations confirm the validity of the proposed modal-identification method from nonstationary ambient response data.

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