INVESTIGATION OF LONG-RANGE DEPENDENCIES IN DAILY GPS SOLUTIONS

The self-similarity of GPS time series is constantly being proved nowadays. The long-range dependence of the stochastic part of topocentric coordinates changes (North, East, Up) results in relatively high autocorrelation values. One of the reason of such self-similarity of the GPS time series are the noises that are commonly recognized to prevail in the form of the flicker noise model. To prove the self-similarity of the stochastic part of GPS time series, the authors used more than 130 ASG-EUPOS stations from the area of Poland with 5-years span of the daily topocentric coordinate changes. The deterministic part of time series was removed from the time series by means of the least-squares method, median absolute deviation criterion and the sequential t-test algorithm, respectively. Then the self-similarity of the residua was proved by the results of the Ljung-Box test, which values close to zero showed the dependence of the stochastic part of the GPS time series. The residua were analyzed by means of the Rescaled Range (R/S) method with the H parameter and the Detrended Fluctuation Analysis (DFA) with the scaling exponent a. Both H and a values ranged within assumed long-range dependence limits. These analyses were followed by noise investigation with the Maximum Likelihood Estimation (MLE). The combination of white plus power-law noise models were assumed a-priori, what gave us spectral indices K between -0.4 and -1.2 for all of the time series. It proved that the fractional white noise overweighs other types of noises in GPS time series. We found here, that the long-range dependence methods by missing the information of noise amplitudes lead to underestimation of H values and their misinterpretation. The larger the non-included amplitude is, the greater are the differences between the noise character estimated with R/S values in comparison to the reference values of K. Some of these differences exceed even the value of 0.6 what may result in wrongly estimated noise character in GPS data falsifying in this way the conclusions.