Abstract
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.
Highlights
It is well known that the noise in continuous GPS observations, as with many geophysical phenomena, can be described as a power-law process (Mandelbrot and Van Ness, 1968; Agnew, 1992)
This paper focuses on the analysis of the stochastic properties of the time series of weekly position estimates for 159 sites of the Brazilian Network for Continuous Monitoring of GPS using the modified maximum likelihood estimator (MLE) algorithm established by Bos et al, (2013)
One of the most used tests is the Bayesian Information Criteria (BIC), which is defined as BIC = −2MLE + p ln ( N )
Summary
It is well known that the noise in continuous GPS observations, as with many geophysical phenomena, can be described as a power-law process (Mandelbrot and Van Ness, 1968; Agnew, 1992). There are many different methods for assessing the noise content and their elements in time series (Johnson and Agnew, 1995; Langbein and Johnson, 1997; Wdowinski et al, 1997; Zhang et al, 1997; Mao et al, 1999), the most robust is the Maximum Likelihood Estimator (MLE) (Bos et al, 2008, 2013; Williams, 2008) It estimates the noise components and the other parameters of the stochastic model, finding the set of values of the model that maximize their likelihood function (Langbein and Johnson, 1997). They are a classic white noise (WN), a flicker plus white noise (FL+WN), a random-walk plus white noise RW+WN) and a fractional power-law noise model
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