Since its launch in 2002, NASA’s dual-satellite GRACE mission has provided invaluable data on Earth’s gravity field, enabling the study of mass redistribution through changes in equivalent water height (EWH). However, gaps in GRACE data hinder accurate climate modelling. This thesis investigates gap-filling using neural networks, with a focus on error and uncertainty quantification. Neural networks are trained on ESA’s Swarm EWH data and NASA’s GLDAS soil moisture data to predict GRACE EWH. The impact of sampling additional training data using quantified input errors is also explored. An experiment involving 20,400 models across major river basins demonstrates that neural networks achieve lower errors in EWH gravity field solutions compared to Swarm. The inclusion of additional training data significantly reduces errors and uncertainties, underscoring the potential of incorporating noise-level variation to enhance future models and improve climate change predictions.

Recent years have seen an increased need for a lunar navigation service to support the large volume of missions planned for the coming decade. Supplying lunar navigation from the Earth suffers from limitations deriving from the long distance to the Moon. Thus, it must rely on a constellation of lunar navigation satellites. This thesis addresses the Orbit Determination (OD) of the satellites of a Lunar Navigation System (LNS) using range and Doppler observations from terrestrial stations. It provides a recommendation for the values of the design parameters of the OD system of a LNS to achieve the required OD accuracy and evaluates the impact of non-design factors such as the constellation's geometry and the observational noise. The parameters of the orbit propagation and the length of the estimation arc are identified as drivers of the OD accuracy. The relation between OD errors and navigation performance is also assessed.