The paper presents the operation of two neuro-fuzzy systems of an adaptive type, intended for solving problems of the approximation of multi-variable functions in the domain of real numbers. Neuro-fuzzy systems being a combination of the methodology of artificial neural networks and fuzzy sets operate on the basis of a set of fuzzy rules “if-then”, generated by means of the self-organization of data grouping and the estimation of relations between fuzzy experiment results. The article includes a description of neuro-fuzzy systems by Takaga-Sugeno-Kang (TSK) and Wang-Mendel (WM), and in order to complement the problem in question, a hierarchical structural self-organizing method of teaching a fuzzy network. A multi-layer structure of the systems is a structure analogous to the structure of “classic” neural networks. In its final part the article presents selected areas of application of neuro-fuzzy systems in the field of geodesy and surveying engineering. Numerical examples showing how the systems work concerned: the approximation of functions of several variables to be used as algorithms in the Geographic Information Systems (the approximation of a terrain model), the transformation of coordinates, and the prediction of a time series. The accuracy characteristics of the results obtained have been taken into consideration.

Movement is one of the most spectacular phenomena involving glaciers. Deter- mining glacier surface velocity is now a routine aspect of glaciological studies. These are geodetic methods, especially satellite positioning, that most frequently is applied in such work. Using the Hans Glacier (SW Spitsbergen) as an example, the presented paper is an attempt at defining the time resolution limit of changes in the velocity determined using GPS positioning technology. A test network was established in the area of the examined glacier in order to define the size and variability of the main satellite positioning biases as well as to define their impact on determining position and the calculated velocity. A discussion relating to achieved accuracy (differentiated from measurement precision) for baselines of a length of several kilometres in the high latitudes has also been presented.

The sequential method of integrating navigational parameters obtained from non-simultaneous navigational measurements is presented. The proposed algorithm of position coordinates estimation is general and includes two modes of data processing – from simultaneous and non-simultaneous measurements. It can be used in hybrid receivers of radionavigation systems integrating non-homogeneous position lines or in integrated navigation systems, particularly in receivers combining the measurements of various satellite navigation systems.

A method of the improvement of the total station observations 3D adjustment by using precise geoid model is presented. The novel concept of using the plumb line direction obtained from the precise geoid model in combined GPS/total station data adjustment is applied. It is concluded that results of the adjustment can be improved if data on plumb line direction is used. Theoretical background shown in the paper was proved with an experiment based on the total station and GPS measurements referred to GRS80 geocentric reference system and with the use of GUGIK2001 geoid model for Poland.