Space weather describes varying conditions between the Sun and Earth that can degrade Global Navigation Satellite Systems (GNSS) operations. Thus, these effects should be precisely and timely corrected for accurate and reliable GNSS applications. That can be modeled with the Vertical Total Electron Content (VTEC) in the Earth’s ionosphere. This study investigates different learning algorithms to approximate nonlinear space weather processes and forecast VTEC for 1 h and 24 h in the future for low-, mid- and high-latitude ionospheric grid points along the same longitude. VTEC models are developed using learning algorithms of Decision Tree and ensemble learning of Random Forest, Adaptive Boosting (AdaBoost), and eXtreme Gradient Boosting (XGBoost). Furthermore, ensemble models are combined into a single meta-model Voting Regressor. Models were trained, optimized, and validated with the time series cross-validation technique. Moreover, the relative importance of input variables to the VTEC forecast is estimated. The results show that the developed models perform well in both quiet and storm conditions, where multi-tree ensemble learning outperforms the single Decision Tree. In particular, the meta-estimator Voting Regressor provides mostly the lowest RMSE and the highest correlation coefficients as it averages predictions from different well-performing models. Furthermore, expanding the input dataset with time derivatives, moving averages, and daily differences, as well as modifying data, such as differencing, enhances the learning of space weather features, especially over a longer forecast horizon.

Abstract:The revitalized Russian GLONASS system provides new potential for real-time retrieval of zenith tropospheric delays (ZTD) and precipitable water vapor (PWV) in order to support time-critical meteorological applications such as nowcasting or severe weather event monitoring. In this study, we develop a method of real-time ZTD/PWV retrieval based on GLONASS and/or GPS observations. The performance of ZTD and PWV derived from GLONASS data using real-time precise point positioning (PPP) technique is carefully investigated and evaluated. The potential of combining GLONASS and GPS data for ZTD/PWV retrieving is assessed as well. The GLONASS and GPS observations of about half a year for 80 globally distributed stations from the IGS (International GNSS Service) network are processed. The results show that the real-time GLONASS ZTD series agree quite well with the GPS ZTD series in general: the RMS of ZTD differences are about 8 mm (about 1.2 mm in PWV). Furthermore, for an inter-technique validation, the real-time ZTD estimated from GLONASS-only, GPS-only, and the GPS/GLONASS combined solutions are compared with those derived from Very Long Baseline Interferometry (VLBI) at co-located GNSS/VLBI stations. The comparison shows that GLONASS can contribute to real-time meteorological applications, with almost the same accuracy as GPS. More accurate and reliable water vapor values, about 1.5-2.3 mm in PWV, can be achieved when GLONASS observations are combined with the GPS ones in the real-time PPP data processing. The comparison with radiosonde data further confirms the performance of GLONASS-derived real-time PWV and the benefit of adding GLONASS to stand-alone GPS processing.

We present and discuss JTRF2014, the Terrestrial Reference Frame (TRF) the Jet Propulsion Laboratory constructed by combining space‐geodetic inputs from very long baseline interferometry (VLBI), satellite laser ranging (SLR), Global Navigation Satellite Systems (GNSS), and Doppler orbitography and radiopositioning integrated by satellite submitted for the realization of ITRF2014. Determined through a Kalman filter and Rauch‐Tung‐Striebel smoother assimilating position observations, Earth orientation parameters, and local ties, JTRF2014 is a subsecular, time series‐based TRF whose origin is at the quasi‐instantaneous center of mass (CM) as sensed by SLR and whose scale is determined by the quasi‐instantaneous VLBI and SLR scales. The dynamical evolution of the positions accounts for a secular motion term, annual, and semiannual periodic modes. Site‐dependent variances based on the analysis of loading displacements induced by mass redistributions of terrestrial fluids have been used to control the extent of random walk adopted in the combination. With differences in the amplitude of the annual signal within the range 0.5–0.8 mm, JTRF2014‐derived center of network‐to‐center of mass (CM‐CN) is in remarkable agreement with the geocenter motion obtained via spectral inversion of GNSS, Gravity Recovery and Climate Experiment (GRACE) observations and modeled ocean bottom pressure from Estimating the Circulation and Climate of the Ocean (ECCO). Comparisons of JTRF2014 to ITRF2014 suggest high‐level consistency with time derivatives of the Helmert transformation parameters connecting the two frames below 0.18 mm/yr and weighted root‐mean‐square differences of the polar motion (polar motion rate) in the order of 30 μas (17 μas/d).

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In this paper, we demonstrate the advantage of applying a Kalman filter for the parameter estimation in very-long-baseline interferometry (VLBI) data analysis. We present the implementation of a Kalman filter in the VLBI software VieVS@GFZ. The performance is then investigated by looking at the accuracy obtained for various parameters, like baseline lengths, Earth Orientation Parameters, radio source coordinates, and tropospheric delays. The results are compared to those obtained when the classical least squares method (LSM) is applied for the parameter estimation, where clocks and zenith wet delays are estimated with 30-min intervals and gradients with 120-min intervals. We show that the accuracy generally is better for the Kalman filter solution, for example, the baseline length repeatabilities are on average about 10 % better compared to the LSM solution. We also discuss the possibilities to use the Kalman filter to estimate sub-diurnal station position variations and show that the variations caused by solid Earth tides can be retrieved with an accuracy of about 2 cm.