A modified differencing method of the detection of irregular jumping changes in discrete measuring signals (e.g. time series of changes of coordinate points GPS) in the presence of disruptions of the signal with random measuring noise (white noise) and of accidental diverging observations (outliers) was shown at the work. The method consists in replacing the moving average in the classic algorithm of the differencing method through the median, what to a considerable degree the influence of diverging observation is being limited by. The method was tested on simulated measuring signals. How the test calculations demonstrated, the method is effective even for relatively narrow window on the side of following observations after tested measuring epoch. It allows on relatively fast alarming because of becoming known the irregular change about the amplitude even on the border of measuring noise (3 sigma). The method can find application in automatic control-measuring systems using the satellite system GPS for displacement monitoring of engineering objects, in particular for monitoring of hydro technical, industrial and mining objects’ deformations.

Abstract: Thematic maps of cities can be weakly readable in case of high concentration of point information. One of possibilities to cope with this problem is creating cartograms (anamorphic maps), which increase local scale of area with high concentration of point symbols and decrease where this information is rare. Variable-scale cartogram transformations are made on the basis of isotropic scale changing (using eg. logarithmic representation) or heterogeneous anisotropic transformation through local analysis of point data distribution. An attempt of using points data spatial density coefficient to creating cartogram of urban area maps is shown in this paper. A map of Wrocław was chosen as a testing data. Proposed procedure of creating such thematic maps was implemented and tested using vector data in GIS environment.

Nowadays large-scale maps are making in information systems but digital map data are not still free from traditional tasks of analogue map. The typical tasks of large-scale map are distances and areas determining, for example to realize of investment project. The paper presents analysis of accuracy in calculation of the area of a polygon from coordinates (X, Y) of its vertexes taking their mean errors (m_X , m_Y ) under consideration. Results of analysis of influence root mean square error of a position of the boundary points on accuracy analytical determination of the area of a parcel are also given in the paper. Besides, admissible divergence in twice determining areas is calculated with the proposed new formula.