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.
The aim of the paper is the comparison of the least squares prediction presented by Heiskanen and Moritz (1967) in the classical handbook “Physical Geodesy” with the geostatistical method of simple kriging as well as in case of Gaussian random fields their equivalence to conditional expectation. The paper contains also short notes on the extension of simple kriging to ordinary kriging by dropping the assumption of known mean value of a random field as well as some necessary information on random fields, covariance function and semivariogram function. The semivariogram is emphasized in the paper, for two reasons. Firstly, the semivariogram describes broader class of phenomena, and for the second order stationary processes it is equivalent to the covariance function. Secondly, the analysis of different kinds of phenomena in terms of covariance is more common. Thus, it is worth introducing another function describing spatial continuity and variability. For the ease of presentation all the considerations were limited to the Euclidean space (thus, for limited areas) although with some extra effort they can be extended to manifolds like sphere, ellipsoid, etc.
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.
In monitoring vertical displacements in elongated structures (e.g. bridges, dams) by means of precise geometric levelling a reference base usually consists of two subgroups located on both ends of a monitored structure. The bigger the separation of the subgroups, the greater is the magnitude of undetectable displacement of one subgroup with respect to the other. With a focus on a method of observation differences the question arises which of the two basic types of computation datum, i.e. the elastic and the fixed, both applicable in this method, is more suitable in such a specific base configuration. To support the analysis of this problem, general relationships between displacements computed in elastic datum and in fixed datum are provided. They are followed by auxiliary relationships derived on the basis of transformation formulae for different computational bases in elastic datum. Furthermore, indices of base separation are proposed which can be helpful in the design of monitoring networks. A test network with simulated mutual displacements of the base subgroups, is used to investigate behaviour of the network with the fixed and the elastic datum being applied. Also, practical guidelines are given concerning data processing procedures for such specific monitoring networks. For big separation of base subgroups a non-routine procedure is recommended, aimed at facilitating specialist interpretation of monitoring results.
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.
In the paper a frequency method of filtering airborne laser data is presented. A number of algorithms developed to remove objects above a terrain (buildings, vegetation etc.) in order to obtain the terrain surface were presented in literature. Those all methods published are based on geometrical criteria, i.e. on a specific threshold of elevation differences between two neighbouring points or groups of points. In other words, topographical surface is described in a spatial domain. The proposed algorithm operates on topographical surface described in a frequency domain. Two major tools, i.e. Fast Fourier Transform (FFT) and digital filters are used. The principal assumption is based on the idea that low frequencies are responsible for a terrain surface, while high frequencies are connected to objects above the terrain. The general guidelines of this method were for the first time presented at (Marmol and Jachimski, 2004). Due to the fact that the preliminary results showed some limitations, two-stage filtering algorithm has been introduced. The frequency filter was modified in such a manner that different filter parameters are used to detect buildings than those to recognize vegetation. In the first stage of data processing the filtering concerning elimination of points connected with urban areas was applied. The low-pass filter with parameters determined for urban area was used for the whole tested terrain in that stage. The purpose of the second stage was to eliminate vegetation by using the filter for forest areas. The presented method was tested by using data sets obtained in the ISPRS test on extracting DTM from point clouds. The results of using the two-stage algorithm were com- pared with both reference data and with filtering results of eight method reported to ISPRS test. A numerical comparison of the filter output with a reference data set shows that the filter generates DTM of a satisfactory quality. The accuracy of DTM produced by the frequency algorithm fits the average accuracy of eight methods reported in the ISPRS test.
Abstract In this article the author makes an attempt to characterize the factors which are to be taken into consideration while designing the ground radar component of Air Defense systems, in order to enable them to operate on the modern battlefield. He presents the latest theoretical views on the relationship between the usage of anti-radar weapons and the organizational and technical defense mechanisms which can be deployed against such weapons. In particular the author emphasizes the protection of radars against anti-radiation missiles (ARMs) which present the biggest threat for effective Air Defense systems. He also stresses the need to combine radars into one system which enables the streamlining of their work parameters and thus ensuring their complex usage. The gaining of those capabilities will guarantee that the parameters of the air surveillance radar zone can be defined effectively.