Analysis of the time series of coordinates is extremely important in geodynamic research. Indeed, the correct interpretation of coordinate changes may facilitate an understanding of the diverse geophysical processes taking place in the earth’s crust. At present, when rigorously processing global navigation satellite system (GNSS) observations, the influence of deformations in the surface of the earth’s crust is not considered. This article presents signal modelling for the influence on the analysis of noise occurring in the time series of GNSS station coordinates. The modelling of coordinate time series was undertaken using the classic least-squares estimation (LSE) method and the inverse continuous wavelet transform (CWT). In order to determine the type of noise character, the coefficient spectral index was used. Analyses have demonstrated that the nature of noise in measurement data does not depend on the signal estimation method. The differences between classic modelling (LSE) of the time series with annual and semiannual oscillation and signal reconstruction are very small ( $\Delta$ $\mathsf{\kappa }$ = 0.0 ÷−0.2).

The paper presents the results of testing the various methods of permanent stations’ velocity residua interpolation in a regular grid, which constitutes a continuous model of the velocity field in the territory of Poland. Three packages of software were used in the research from the point of view of interpolation: GMT (The Generic Mapping Tools), Surfer and ArcGIS. The following methods were tested in the softwares: the Nearest Neighbor, Triangulation (TIN), Spline Interpolation, Surface, Inverse Distance to a Power, Minimum Curvature and Kriging. The presented research used the absolute velocities’ values expressed in the ITRF2005 reference frame and the intraplate velocities related to the NUVEL model of over 300 permanent reference stations of the EPN and ASG-EUPOS networks covering the area of Europe. Interpolation for the area of Poland was done using data from the whole area of Europe to make the results at the borders of the interpolation area reliable. As a result of this research, an optimum method of such data interpolation was developed. All the mentioned methods were tested for being local or global, for the possibility to compute errors of the interpolated values, for explicitness and fidelity of the interpolation functions or the smoothing mode. In the authors’ opinion, the best data interpolation method is Kriging with the linear semivariogram model run in the Surfer programme because it allows for the computation of errors in the interpolated values and it is a global method (it distorts the results in the least way). Alternately, it is acceptable to use the Minimum Curvature method. Empirical analysis of the interpolation results obtained by means of the two methods showed that the results are identical. The tests were conducted using the intraplate velocities of the European sites. Statistics in the form of computing the minimum, maximum and mean values of the interpolated North and East components of the velocity residuum were prepared for all the tested methods, and each of the resulting continuous velocity fields was visualized by means of the GMT programme. The interpolated components of the velocities and their residua are presented in the form of tables and bar diagrams.