The paper describes the estimation of covariance parameters in least squares collocation (LSC) by the cross-validation (CV) technique called leave-one-out (LOO). Two parameters of Gauss-Markov third order model (GM3) are estimated together with a priori noise standard deviation, which contributes significantly to the covariance matrix composed of the signal and noise. Numerical tests are performed using large set of Bouguer gravity anomalies located in the central part of the U.S. Around 103 000 gravity stations are available in the selected area. This dataset, together with regular grids generated from EGM2008 geopotential model, give an opportunity to work with various spatial resolutions of the data and heterogeneous variances of the signal and noise. This plays a crucial role in the numerical investigations, because the spatial resolution of the gravity data determines the number of gravity details that we may observe and model. This establishes a relation between the spatial resolution of the data and the resolution of the gravity field model. This relation is inspected in the article and compared to the regularization problem occurring frequently in data modeling.

The summary of research activities concerning general theory and methodology performed in Poland in the period of 2015–2018 is presented as a national report for the 27th IUGG (International Union of Geodesy and Geophysics) General Assembly. It contains the results of research on new or improved methods and variants of robust parameter estimation and their application, especially to control network analysis. Reliability analysis of the observation system and an integrated adjustment approach are also given. The identifiability (ID) index as a new measure for minimal detectable bias (MDB) in the observation system of a network, has been introduced. A new method of covariance function parameter estimation in the least squares collocation has been developed. The robustified version of the Shift-Msplit estimation, termed as Shift-M*split estimation, which enables estimation of parameter differences (robustly), without the need of prior estimation of the parameters, has been introduced. Results on the analysis of geodetic time series, particularly Earth orientation parameter time series, geocenter time series, permanent station coordinates and sea level variation time series are also provided in this review paper. The entire bibliography of related works is provided in the references.

The GOCE (Gravity Field and Steady-State Ocean Circulation Explorer) has significantly upgraded the knowledge on the Earth gravity field. In this contribution the accuracy of height anomalies determined from Global Geopotential Models (GGMs) based on approximately 27 months GOCE satellite gravity gradiometry (SGG) data have been assessed over Poland using three sets of precise GNSS/levelling data. The fits of height anomalies obtained from 4th release GOCE-based GGMs to GNSS/levelling data were discussed and compared with the respective ones of 3rd release GOCE-based GGMs and the EGM08. Furthermore, two highly accurate gravimetric quasigeoid models were developed over the area of Poland using high resolution Faye gravity anomalies. In the first, the GOCE-based GGM was used as a reference geopotential model, and in the second – the EGM08. They were evaluated with GNSS/levelling data and their accuracy performance was assessed. The use of GOCE-based GGMs for recovering the long-wavelength gravity signal in gravimetric quasigeoid modelling was discussed.