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 Influence of non-tidal atmospheric and oceanic loading deformation on the stochastic properties of over 10,000 GNSS vertical land motion time series

2021 ◽  
Author(s):  
Kevin Gobron ◽  
Paul Rebischung ◽  
Olivier de Viron ◽  
Michel Van Camp ◽  
Alain Demoulin
Keyword(s):  
Time Series ◽  
White Noise ◽  
Power Law ◽  
Noise Amplitude ◽  
Vertical Land Motion ◽  
Motion Time ◽  
Stochastic Parameters ◽  
Position Time Series ◽  
Stochastic Properties ◽  
Gnss Position Time Series

<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>

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 Empirical White Noise Processes and the Subjective Probabilistic Approaches

2019 ◽  
Vol 48 (1) ◽  
pp. 19-30
Author(s):  
András Rövid ◽  
László Palkovics ◽  
Péter Várlaki
Keyword(s):  
White Noise ◽  
Random Number ◽  
White Noise Process ◽  
Random Number Generators ◽  
Noise Process ◽  
Complementary Approach ◽  
Fuzzy Random

The paper discusses the identification of the empirical white noise processes generated by deterministic numerical algorithms.The introduced fuzzy-random complementary approach can identify the inner hidden correlational patterns of the empirical white noise process if the process has a real hidden structure of this kind. We have shown how the characteristics of auto-correlated white noise processes change as the order of autocorrelation increases. Although in this paper we rely on random number generators to get approximate white noise processes, in our upcoming research we are planning to turn the focus on physical white noise processes in order to validate our hypothesis.

The exact bispectra for bilinear realizable processes with hermite degree 2

1991 ◽  
Vol 23 (04) ◽  
pp. 798-808 ◽  
Author(s):  
György Terdik ◽  
Laurie Meaux
Keyword(s):  
White Noise ◽  
Discrete Time ◽  
Hermite Polynomial ◽  
Transfer Functions ◽  
Gaussian White Noise ◽  
Second Order ◽  
Bilinear Model ◽  
White Noise Process ◽  
Noise Process ◽  
Gaussian White Noise Process

This paper deals with the stationary bilinear model with Hermite degree 2 in discrete time which is built up by the first- and second-order Hermite polynomial of a Gaussian white noise process. The exact spectrum and bispectrum is constructed in terms of the transfer functions of the model.

Statistics of an Appealing Class of Random Processes

2021 ◽  
pp. 260-276
Author(s):  
Shaival Hemant Nagarsheth ◽  
Shambhu Nath Sharma
Keyword(s):  
White Noise ◽  
Stochastic Systems ◽  
Correction Term ◽  
Random Processes ◽  
Random Perturbations ◽  
White Noise Process ◽  
Coloured Noise ◽  
Diffusion Operator ◽  
Noise Process ◽  
Special Cases

The white noise process, the Ornstein-Uhlenbeck process, and coloured noise process are salient noise processes to model the effect of random perturbations. In this chapter, the statistical properties, the master's equations for the Brownian noise process, coloured noise process, and the OU process are summarized. The results associated with the white noise process would be derived as the special cases of the Brownian and the OU noise processes. This chapter also formalizes stochastic differential rules for the Brownian motion and the OU process-driven vector stochastic differential systems in detail. Moreover, the master equations, especially for the coloured noise-driven stochastic differential system as well as the OU noise process-driven, are recast in the operator form involving the drift and modified diffusion operators involving an additional correction term to the standard diffusion operator. The results summarized in this chapter will be useful for modelling a random walk in stochastic systems.

The exact bispectra for bilinear realizable processes with hermite degree 2

1991 ◽  
Vol 23 (4) ◽  
pp. 798-808 ◽  
Author(s):  
György Terdik ◽  
Laurie Meaux
Keyword(s):  
White Noise ◽  
Discrete Time ◽  
Hermite Polynomial ◽  
Transfer Functions ◽  
Gaussian White Noise ◽  
Second Order ◽  
Bilinear Model ◽  
White Noise Process ◽  
Noise Process ◽  
Gaussian White Noise Process

This paper deals with the stationary bilinear model with Hermite degree 2 in discrete time which is built up by the first- and second-order Hermite polynomial of a Gaussian white noise process. The exact spectrum and bispectrum is constructed in terms of the transfer functions of the model.

Optimal Wiener Filter for a Body Mounted Inertial Attitude Sensor

2008 ◽  
Vol 61 (3) ◽  
pp. 455-472 ◽  
Author(s):  
Peter Rizun
Keyword(s):  
Spectral Density ◽  
White Noise ◽  
Power Spectral Density ◽  
Human Body ◽  
Linear Acceleration ◽  
Mean Square ◽  
White Noise Process ◽  
Noise Process ◽  
Power Spectral ◽  
The Mean

An optimal attitude estimator is presented for a human body-mounted inertial measurement unit employing orthogonal triads of gyroscopes, accelerometers and magnetometers. The estimator continuously fuses gyroscope and accelerometer measurements together in a manner that minimizes the mean square error in the estimate of the gravity vector, based on known spectral characteristics for the gyroscope noise and the linear acceleration of points on the human body. The gyroscope noise is modelled as a white noise process of power spectral density δn2/2 while the linear acceleration is modelled as the derivative of a band-limited white noise process of power spectral density δv2/2. The estimator is robust to centripetal acceleration and guaranteed to have zero mean error regardless of the motion of the sensor. The mean square angular error in attitude is shown to be independent of the module's angular velocity and equal to 21/2g−1/2δn3/2δv1/2.

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