Abstract
The velocity estimates and their uncertainties derived from position time series of Global Navigation Satellite System stations are affected by seasonal signals and their harmonics, and the statistical properties, i.e., the stochastic noise, contained in the series. If the deterministic model in the form of linear trend and periodic terms is not accurate enough to describe the time series, it will alter the stochastic model, and the resulting effect on the velocity uncertainties can be perceived as a result of a misfit of the deterministic model. The effects of insufficiently modeled seasonal signals will propagate into the stochastic model and falsify the results of the noise analysis, in addition to velocity estimates and their uncertainties. We provide the general dilution of precision (GDP) of velocity uncertainties as the ratio of uncertainties of velocities determined from to two different deterministic models while accounting for stochastic noise at the same time. In this newly defined GDP, the first deterministic model includes a linear trend, while the second one includes a linear trend and seasonal signals. These two are tested with the assumption of white noise only as well as the combinations of power-law and white noise in the data. The more seasonal terms are added to the series, the more biased the velocity uncertainties become. With increasing time span of observations, the assumption of seasonal signals becomes less important, and the power-law character of the residuals starts to play a crucial role in the determined velocity uncertainties. With reference frame and sea level applications in mind, we argue that 7 and 9 years of continuous observations is the threshold for white and flicker noise, respectively, while 17 years are required for random-walk to decrease GDP below 5% and to omit periodic oscillations in the GNSS-derived time series taking only the noise model into consideration.
Highlights
Today, Global Navigation Satellite System (GNSS) measurements, in particular those from the Global Positioning System (GPS), are fundamental to many geodetic and geophysical investigations (Kreemer et al 2014; Métivier et al 2014) and are frequently used during the construction of kinematic reference frames, such as, for example, the International Terrestrial Reference Frame 2014 (ITRF2014) (Altamimi et al 2016)
With reference frame and sea level applications in mind, we argue that 7 and 9 years of continuous observations is the threshold for white and flicker noise, respectively, while 17 years are required for random-walk to decrease general dilution of precision (GDP) below 5% and to omit periodic oscillations in the GNSS-derived time series taking only the noise model into consideration
We provide a general dilution of precision (GDP) of the velocity uncertainties being the ratio of uncertainties of velocities arising from two different assumptions of the deterministic model
Summary
Global Navigation Satellite System (GNSS) measurements, in particular those from the Global Positioning System (GPS), are fundamental to many geodetic and geophysical investigations (Kreemer et al 2014; Métivier et al 2014) and are frequently used during the construction of kinematic reference frames, such as, for example, the International Terrestrial Reference Frame 2014 (ITRF2014) (Altamimi et al 2016). The primary product from the analysis of these time series is often the linear rate of change, or velocity, and the associated uncertainty (Zhang et al 1997). The velocities are assumed to represent the linear movement of the earth’s crust due to tectonic plate motions (Larson et al 1997; Drewes 2009; Altamimi et al 2012) or the viscoelastic relaxation associated with glacial isostatic adjustment (Johansson et al 2002; Bradley et al 2009). Almost all sites within the global network of GPS
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