Functional and stochastic models estimation for GNSS coordinates time series

GNSS has been largely used in Geodesy and correlated areas for positioning. The position and velocity of terrestrial stations have been estimated using GNSS data based on daily solutions. So, currently it is possible to analyse the GNSS coordinates time series aiming to improve the functional and stochastic models what can help to understand geodynamic phenomena. Several sources of errors are mathematically modelled or estimated in the GNSS data processing to obtain precise coordinates what in general is carried out by using scientific software. However, due to impossibility to model all errors some kind of noises can remain contaminating the coordinate time series, especially those related with seasonal effects. The noise affecting GNSS coordinate time series can be composed by white and coloured noises what can be characterized from Variance Component Estimation technique through Least Square Method. The methodology to characterize noise in GNSS coordinates time series will be presented in this paper so that the estimated variance can be used to reconstruct stochastic and functional models of the times series providing a more realistic and reliable modeling of time series. Experiments were carried out by using GNSS time series for few Brazilian stations considering almost ten years of daily solutions. The noises components were characterized as white, flicker and random walk noise and applied to estimate the times series functional model considering semiannual and annual effects. The results show that the adoption of an adequate stochastic model considering the noises variances of time series can produce more realistic and reliable functional model for GNSS coordinate time series. Such results may be applied in the context of the realization of the Brazilian Geodetic System.