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Geodetic GNSS networks are the backbone for tropospheric tomography studies. In addition, dense low-cost GNSS networks, InSAR interferograms or GNSS radio occultation profiles are valuable assets, which can provide important complementary information for stabilizing the tomography system and further increase the spatio-temporal resolution of the reconstructed water vapor field. Therefore, the IAG tomography working group was establishing a benchmark dataset covering the meteorological conditions before, during and after the Central European floods in July 2021. The created dataset consists of a suite of complementing observing techniques and thus, was designed to contribute to developing and testing of new tomography-based concepts for sensing small-scale structures in the troposphere. In this presentation, we thereby focus on the achievements made in the last four years in supporting the analysis and prediction of extreme weather events with 3D water vapour products available in (near) real-time; improving the spatio-temporal resolution of derived tomography products by sensor fusion of ground-based GNSS, InSAR and radio occultation measurements; and establishing new standards in dynamic model parameterization., The 28th IUGG General Assembly (IUGG2023) (Berlin 2023)

Microwave signals of space geodetic techniques are sensitive to the atmospheric constituents along the propagation ray, especially the effects of high spatio-temporal variations of atmospheric water vapor are difficult to model. Unmodeled tropospheric delays deteriorate the accuracy of remote sensing and geodetic techniques. For high-precision applications, these delays are typically estimated during the processing of the measurements. For example, in Global Navigation Satellite Systems (GNSS) the so-called zenith total delay (ZTD) is estimated together with the other unknown parameters. This thesis uses advanced mathematical tools to improve the knowledge about the meteorological products derived from space geodetic techniques and to model tropospheric observations of satellite signals. More precisely, we make use of and/or model observations of ground-based GNSS, GNSS radio occulations (RO) and Interferometric Synthetic Aperture Radar (InSAR). For this purpose, two main signal processing methods are used, namely least-squares collocation adjustment and machine learning (ML) algorithms. Initially, we analyze tropospheric delays obtained from GNSS and InSAR. In addition, numerical weather prediction (NWP) data are used as independent method to validate the microwave techniques. The motivation of this work is to address the question whether GNSS-retrieved delays can help improve the InSAR phase unwrapping issues, especially for complex mountainous areas at X-band radar wavelengths. From this work, we could demonstrate the importance of GNSS network size and resolution. In addition, an extended sensitivity analysis of the parameter tuning in collocation showed the importance of a careful selection of horizontal and vertical correlation lengths. The analyzed delays display differences in their statistical behavior, due to the different nature of the retrieved delays, namely: 1) GNSS delays that are interpolated/collocated to InSAR location, 2) InSAR delays that are spatially filtered based on residuals of actual measurements and 3) NWP delays that are ray-traced through the NWP grid. The agreement in terms of standard deviation is in the range of 3.8-4.4 mm, which is about 13-15% of the SAR wavelength. Densification of the network and fine-tuning of the signal model in collocation are the main recommendations to further improve these results. Afterwards, we presented a combination of GNSS and InSAR delays based on a collocation framework. For this purpose, the collocation software COMEDIE of ETH-IGP, was further upgraded to process simultaneously GNSS total zenith delays and InSAR slant delays. The combination makes use of InSAR relative delays which are a direct output of the InSAR processing without additional assumptions. A quantitative, closed-loop validation of the combination using simulated observations from NWP models and a qualitative evaluation of the combination based on real observations were studied. In terms of relative delays, the combination results in values closer to the InSAR-estimated products, and in terms of absolute retrieved ZTDs a few mm improvement is noticed. In a further study, we evaluated the collocation capabilities to model refractivity fields. We compared collocation to GNSS tomography, a typical technique deployed to retrieve 3D information of the atmospheric structure based on GNSS observations. Initially, we evaluated, theoretically and experimentally, the collocation models. Then, we compared fields of refractivity retrieved by means of collocation and tomography. At low altitudes, they agree at the level of few ppm (N-units), while at high altitudes the fields are quite similar. Tomography is less prone to biases in case it is aided by the a-priori field applied, while collocation can better model the relative variations of voxels located at the same height. Furthermore, we evaluated the applicability of both methods to detect a weather front incoming over Switzerland. Both methods could sense the weather front and they could capture it better for networks with stations that are well-distributed in large altitude range. We also used machine learning to model ZTDs based on ground meteorological parameters. Using Neural Networks, we predicted the ZTD with an accuracy of ~1.6 cm, and a maximal error smaller than 2 cm. We reported that the water vapor amount (and its variability) is smaller in winter months and at higher stations. Also, the geographical distribution of the errors was depending on the variability of the water vapor. The ML results were clearly better than the ZTDs predicted using empirical models, such as the Saastamoinen model. ML could, however, not predict very well the ZTDs at new (untrained) locations. To overcome this limitation, we proposed a combination of ML and collocation, where we could exploit the different spatio-temporal modeling capabilities of the methods. ML can model accurately time series at trained locations and collocation can successfully interpolate ZTDs. A simple loosely coupled architecture, where the methods are used sequentially, resulted in very accurate ZTD fields. Performing an iterative validation, where always one station was removed from the training process in ML and the predicted delays of the other stations were collocated/interpolated at its location, resulted in an accuracy of 1-2 cm, with a similar distribution as if all stations were used to train ML models. Hence, high spatio-temporal fields of tropospheric delays (and refractivity) could be predicted for the network. In addition, we applied ML to GNSS radio occultations (RO) to create gridded products of the RO-based refractivity. ML was applied for interpolation purposes, and it outperformed Bayesian interpolation (BI), a state-of-the-art method used to map RO data. We also produced maps of RO through a combination of BI and ML, namely BI&ML, where residuals of BI were used to train the ML models. This combined solution resulted in the best results. Furthermore, we performed a spectral analysis, where maps were projected into spherical harmonics. We could show an improvement in the horizontal resolution, as it was possible to increase the spherical harmonics development from degree 8 for BI-only to degree 14 for BI&ML. The temporal resolution was also improved, where ML (and BI&ML) can produce maps at hourly resolution, while BI needs at least 3 days of observations. Finally, we performed preliminary tests, where RO observations were mapped into gridded products with the scope to detect an atmospheric river. We could show in simulation mode that, while a constellation of 12 or 24 satellites can sense the river structure at a general level, a constellation of 48 satellites can capture its intensity and timespan very accurately.

In our previous studies, we demonstrated that Global Navigation Satellite System (GNSS) signals can be processed, not only in Low Earth Orbit (LEO), but also in higher earth orbits, up to the Moon. In order to maximize the GNSSbased navigation performance, we implemented an adaptive orbital filter, which fuses the GNSS observations with a model of the spacecraft dynamics, achieving a navigation accuracy of approximately 100 meters, at Moon altitude. In this paper, we take a step forward and we investigate the design of an advanced multisensor solution that, in addition to combining GNSS with an orbital forces model, also adds the integration of an Inertial Navigation System (INS) and of a Star Tracker, in order to provide a versatile, real-time, on-board, autonomous orbit and attitude determination in different space mission scenarios, from LEO to GEO and beyond. First, we describe the designed architecture of the integrated system, then its implementation, and finally we report its achieved navigation performance for different altitudes up to the Moon, showing that the synergistic integration of the different sensors, can overcome their individual drawbacks and provide a better navigation performance than either could achieve individually.

In this research study we describe our last effort in further improving the achievable Global Navigation Satellite System (GNSS) based navigation performance in an Earth-Moon Transfer Orbit (MTO). The GNSS-based orbital filter we implemented previously with a dynamic approach, is modified by adopting a reduced-dynamics approach, which, with a certain accuracy, compensates for the dynamic model errors using a process noise model that weights observational and dynamical errors. Empirical accelerations are estimated as part of the state vector in a Kalman filter, adopting a deterministic forces model. Unlike the implementations reported in the existing literature, typically for orbit determination in Low Earth Orbit (LEO), here, in order to correctly weight observational and dynamical errors in the full trajectory from the Earth to the Moon, characterized by very variable signals and geometry conditions, an adaptive tuning of the filter is adopted. The observational and dynamical errors are predicted as function of different parameters, i.e., the estimated carrier-to-noise-ratio of the signals at the receiver position, the tracking loops setting, the kinematic state of the receiver and the combination of orbital forces modelled at different altitudes. The implemented orbital filter together with the developed receiver are designed in order to provide real-time autonomous on-board navigation on the way from the Earth to the Moon. Following a description of the simulation models and assumptions and of the existing orbit determination approaches, the paper focusses on the implementation of the proposed adaptive reduced-dynamic orbital filter and finally presents its performance in a MTO.

Through Global Navigation Satellite Systems (GNSS) Radio occultation (RO), the bending of radio signals due to their refractions while passing through earth’s atmosphere can be measured using Low Earth Orbit satellites. The refractivities determined with such measurements are crucial in the creation of Numerical Weather Models (NWM), which are used to display the atmosphere’s temperature, pressure, and humidity. Due to the sparse and non-uniform distribution of RO observations, this data cannot resolve synoptic variabilities, and improvements in horizontal resolution are necessary. This thesis compares the abilities of various Machine Learning algorithms - namely, Random Forest Regression (RFR), Extreme Gradient Boosting (XGBoost), Multilayer Perceptron (MLP), and Convolutional Neural Network (CNN) - to predict and map RO refractivity. Data from COSMIC-2 and ECMWF forecasts interpolated at 2 km height are used to train and test the models. Using only the COSMIC data, the RFR achieved the most accurate prediction with a posterior standard deviation of 8.72 N-units. Incorporating the ECMWF forecasts the CNN model was able to predict the refractivity with a standard deviation of 5.64 N-units. Additionally, the thesis assessed the impact of various factors such as different forecast times, temporal splitting of the training data, and the use of the refractivity residuals for training the models.