The paper presents a summary of research activities concerning theoretical geodesy performed in Poland in the period of 2011–2014. It contains the results of research on new methods of the parameter estimation, a study on robustness properties of the M-estimation, control network and deformation analysis, and geodetic time series analysis. The main achievements in the geodetic parameter estimation involve a new model of the M-estimation with probabilistic models of geodetic observations, a new Shift-M split estimation, which allows to estimate a vector of parameter differences and the Shift- M split (+) that is a generalisation of Shift- M split estimation if the design matrix A of a functional model has not a full column rank. The new algorithms of the coordinates conversion between the Cartesian and geodetic coordinates, both on the rotational and triaxial ellipsoid can be mentioned as a highlights of the research of the last four years. New parameter estimation models developed have been adopted and successfully applied to the control network and deformation analysis. New algorithms based on the wavelet, Fourier and Hilbert transforms were applied to find time-frequency characteristics of geodetic and geophysical time series as well as time-frequency relations between them. Statistical properties of these time series are also presented using different statistical tests as well as 2 nd , 3 rd and 4 th moments about the mean. The new forecasts methods are presented which enable prediction of the considered time series in different frequency bands.

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.

Sea level monitoring at tide gauges plays an important role in geodesy, geodynamics research and oceanography. It provides data for referencing vertical datum, for modelling geoid in coastal regions, for determination of vertical land movements and for studying ocean dynamics. Investigation of Baltic Sea level variations ·is considered an important component of geodynamics research in Central and Northern Europe. The analysis of tide gauge records from Baltic sites was conducted in the framework of the project on a cm geoid in Poland. Those records showed strong common features that were further used for deriving the model of Baltic Sea level variations. High level of correlations of the model with individual site data proved its adequacy. Regional characteristics of the model were investigated using regression and correlation analysis. It was shown that the model represents very well both global and regional features of Baltic Sea level variations. The use of the model as reference to investigate local features of tide gauge records that reflect site-specific variations of sea level was also discussed. Spectral analysis of the model of Baltic Sea level variations indicates the existence of distinguished term of Chandler period besides two major terms of annual and semi-annual periods. The existence of polar motion component in Baltic Sea level variations was investigated using correlation analysis. Also the land vertical movement derived from Baltic tide gauge data was determined and compared with literature data.