A new 3D approach to automated outliers rejection in GNSS time series

Permanent GNSS stations have become fundamental for geodynamic studies thanks to their capability of providing consistent coordinate time series. The time series analysis is becoming more and more sophisticated and there are several approaches, fully automated or not, helping the users to derive the main parameters of interest such as: trends, periodical signals, discontinuities, types of noises, blunders. Typically, however, the analysis of the time series is still performed considering separately each of the three coordinate components. Actually, this neglects the three-dimensional nature of the GNSS position solutions, which are computed simultaneously, and may have some impact on the analysis. We should also bear in mind that the values of the coordinates time series depend on the reference system orientation. For instance, the time series values expressed in geocentric coordinates (X, Y, Z) are usually different from the same ones represented in a topocentric (E, N, V) reference. Therefore, if the analysis is performed separately on the three coordinate components, results will be different depending on the adopted reference system.
The aim of this work is to address the issue concerning the automated rejection of outliers potentially present in the GNSS time series. This is a fundamental aspect considering the large amount of data that nowadays shall be continuously processed and analyzed, thus requiring procedures as automated as possible. A viable approach is to search for outliers by analyzing the error distribution of the coordinates after having removed trends and signals, assuming that these behave like casual errors and follow a normal density distribution. It is then possible to set a statistical threshold in order to reject iteratively all the solutions with higher residual values. This approach is usually implemented by considering mono-dimensional time series in which the three coordinate components are processed separately. Nevertheless, from a statistical point of view, each GNSS position solution should be considered to be a 3D variable, thus characterized by a probability density function defined in a 3D space. In particular, by considering a chi-square distribution with three degrees of freedom it is possible to consider an ellipsoidal density function that well fit the error distribution of a 3D casual variable such as the GNSS coordinates.
In this work, numerical results obtained from the analysis of real dataset will be presented. In particular, six years of daily position solutions obtained from 12 GNSS permanent stations have been considered. The time series have been analyzed starting from both geocentric and topocentric coordinates using alternatively two different approaches: a classical one, in which the three coordinate components have been processed separately, and the 3D approach that allowed to consider the three coordinates at once. Results show that the second approach is mostly independent from the starting reference system, whereas the classical approach is affected by the orientation of the Cartesian axes used to project the same positions.