We present a summary of research carried out in 2019–2022 in Poland in the area of general theory and methodology in geodesy. The study contains a description of original contributions by authors affiliated with Polish scientific institutions. It forms part of the national report presented at the 28th General Assembly of the International Union of Geodesy and Geophysics (IUGG) taking place on 11-20 July 2023 in Berlin, Germany. The Polish authors developed their research in the following thematic areas: robust estimation and its applications, prediction problems, cartographic projections, datum transformation problems and geometric geodesy algorithms, optimization and design of geodetic networks, geodetic time series analysis, relativistic effects in GNSS (Global Navigation Satellite System) and precise orbit determination of GNSS satellites. Much has been done on the subject of estimating the reliability of existing algorithms, but also improving them or studying relativistic effects. These studies are a continuation of work carried out over the years, but also they point to new developments in both surveying and geodesy.We hope that the general theory and methodology will continue to be so enthusiastically developed by Polish authors because although it is not an official pillar of geodesy, it is widely applicable to all three pillars of geodesy.

For over two decades, an essential information about global monthly gravity variations is provided by the GRACE mission and its successor, the GRACE Follow-On (GRACE-FO) mission. The temporal variations in gravity field from GRACE/GRACEFO are determined based on the measurement of distance changes between two identical satellites using microwave ranging instruments. This process is carried out by various processing centers, which adopt different processing strategies and background models. This causes discrepancies in the resulting gravity fields.We address this problem by determining a monthly homogenous GRACE-FO gravity field solutions from June 2018 to November 2022 as provided by different processing centers included in the Science Data System (SDS) project, i.e. the Center for Space Research (CSR), the German Research Center for Geosciences (GFZ) and the Jet Propulsion Laboratory (JPL). We test three different weighting schemes. We show that for the last 4 years, at least 65% of continental areas are characterized by water decrease. We show that proposed merged solutions contain more signal information than individual ones based on the square root of the degree variance values.We note that the largest signal differences between individual and combined solutions occur for sectoral coefficients up to degree 40, and for zonal coefficients, the signal differences are twice as small.We also present that the differences in the spherical harmonic coefficients cause differences in global and local equivalent water height (EWH) changes. For example, the proposed merged solutions reduce root mean square scatter ofEWHby 5–15% comparing to individual solutions.