Gauss process regression for real-time ionospheric delay estimation from GNSS observations

The number of devices equipped with global satellite positioning has exceeded seven billion recently. There are a wide variety of receivers regarding their accuracy and reliability. Low cost, multi-frequency units have been released on the market latterly; however, the number of single-frequency receivers is still significant. Since their measurements are influenced by ionospheric delay, accurate ionosphere models are of utmost importance to reduce the effect. This paper summarizes how Gauss process regression (GPR) can be applied to derive near real-time regional ionosphere models using raw Global Navigation Satellite System (GNSS) observations of permanent stations. While Gauss process is widely used in machine learning, GPR is a nonparametric, Bayesian approach to regression. GPR has several benefits for ionosphere monitoring since it is quite robust and efficient to derive a grid model from data available in irregular set of ionospheric pierce points. The corresponding instrumental delays are estimated by a parallel Kalman filter. The presented algorithm can be applied near real-time, however the results are offline calculated and are compared to two high quality TEC map products. Based on the analysis, the accuracy of the GPR modell is in 2 TECu range. The developed methods could be efficiently applied in the field of autonomous vehicle navigation with meeting both accuracy and integrity requirements.

Interval maximum likelihood inversion for well logging data and statistical properties of estimated parameters

During the conventional petrophysical interpretation fixed (predefined) zone parameters are applied for every interpretation zone (depth intervals). Their inclusion in the inversion process requires the extension of a likelihood function for the whole zone. This allows to define the extremum problem for fitting the parameter set to the full interval petrophysical model of the layers crossed by the well, both for the parameters associated with the depth points (e.g. porosity, saturations, rock matrix composition etc.) and for the zone parameters (e.g. formation water resistivity, cementation factor etc.). In this picture the parameters form a complex coupled and correlated system. Even the local parameters associated with different depths are coupled through the zone parameter change. In this paper, the statistical properties of the coupled parameter system are studied which fitted by the Interval Maximum Likelihood (ILM) method. The estimated values of the parameters are coupled through the likelihood function and this determines the correlation between them.

Differences and similarities between precipitation patterns of different climates

In recent years water-related issues are increasing globally, some researchers even argue that the global hydrological cycle is accelerating, while the number of meteorological extremities is growing. With the help of large number of available measured data, these changes can be examined with advanced mathematical methods. In the outlined research we were able to collect long precipitation datasets from two different climatical regions, one sample area being Ecuador, the other one being Kenya. Using the methodology of spectral analysis based on the discrete Fourier-transformation, several deterministic components were calculated locally in the otherwise stochastic time series, while by the comparison of the results, also with previous calculations from Hungary, several global precipitation cycles were defined in the time interval between 1980 and 2019. The results of these calculations, the described local, regional, and global precipitation cycles can be a helpful tool for groundwater management, as precipitation is the major resource of groundwater recharge, as well as with the help of these deterministic cycles, precipitation forecasts can be delivered for the areas.