MP estimation is a method which concerns estimating of the location parameters when the probabilistic models of observations differ from the normal distributions in the kurtosis or asymmetry. The system of Pearson’s distributions is the probabilistic basis for the method. So far, such a method was applied and analyzed mostly for leptokurtic or mesokurtic distributions (Pearson’s distributions of types IV or VII), which predominate practical cases. The analyses of geodetic or astronomical observations show that we may also deal with sets which have moderate asymmetry or small negative excess kurtosis. Asymmetry might result from the influence of many small systematic errors, which were not eliminated during preprocessing of data. The excess kurtosis can be related with bigger or smaller (in relations to the Hagen hypothesis) frequency of occurrence of the elementary errors which are close to zero. Considering that fact, this paper focuses on the estimation with application of the Pearson platykurtic distributions of types I or II. The paper presents the solution of the corresponding optimization problem and its basic properties. Although platykurtic distributions are rare in practice, it was an interesting issue to find out what results can be provided by MP estimation in the case of such observation distributions. The numerical tests which are presented in the paper are rather limited; however, they allow us to draw some general conclusions.
One of the fundamental problems of modern geodesy is precise de fi nition of the gravitational fi eld and its changes in time. This is essential in positioning and navigation, geophysics, geodynamics, oceanography and other sciences related to the climate and Earth’s environment. One of the major sources of gravity data is satellite altimetry that provides gravity data with almost 75% surface of the Earth. Satellite altimetry also provides data to study local, regional and global geophysical processes, the geoid model in the areas of oceans and seas. This technique can be successfully used to study the ocean mean dynamic topography. The results of the investigations and possible products of altimetry will provide a good material for the GGOS (Global Geodetic Observing System) and institutions of IAS (International Altimetry Service). This paper presents the achievements in satellite altimetry in all the above disciplines obtained in the last years. First very shorly basic concept of satellite altimetry is given. In order to obtain the highest accuracy on range measurements over the ocean improved of altimetry waveforms performed on the ground is described. Next, signi fi cant improvements of sea and ocean gravity anomalies models developed presently is shown. Study of sea level and its extremes examined, around European and Australian coasts using tide gauges data and satellite altimetry measurements were described. Then investigations of the phenomenon of the ocean tides, calibration of altimeters, studies of rivers and ice-sheets in the last years are given.
Land consolidation procedures are an attempt to comprehensively change the existing spatial structure of land in rural areas. This treatment also brings many other social and economic benefits, contributing to the development of consolidated areas. Land consolidation in mountain areas differs in many respects from those implemented in areas with more favorable conditions for the functioning of agriculture. The unfavorable values of land fragmentation indices, terrain conditions and lower than the average soil quality affect both the dominant forms of agricultural activity and the limited opportunities to improve the distribution of plots in space, parameters of shape, and the area as a result of land consolidation. For this reason, the effectiveness of land consolidation in mountain areas can be achieved by improving the quality of transportation network and the accessibility of the plots, arranging ownership issues and improving the quality of cadastral documentation. This article presents the evaluation of the measures of effectiveness of land consolidation realized in mountain areas on the example of Łetownia Village in the Małopolska Province, located in the southern part of Poland. Selected village is an area with unfavorable conditions for the functioning of agriculture and high values of land fragmentation indices.
The processing of cartographic data demands human involvement. Up-to-date algorithms try to automate a part of this process. The goal is to obtain a digital model, or additional information about shape and topology of input geometric objects. A topological skeleton is one of the most important tools in the branch of science called shape analysis. It represents topological and geometrical characteristics of input data. Its plot depends on using algorithms such as medial axis, skeletonization, erosion, thinning, area collapse and many others. Area collapse, also known as dimension change, replaces input data with lower-dimensional geometric objects like, for example, a polygon with a polygonal chain, a line segment with a point. The goal of this paper is to introduce a new algorithm for the automatic calculation of polygonal chains representing a 2D polygon. The output is entirely contained within the area of the input polygon, and it has a linear plot without branches. The computational process is automatic and repeatable. The requirements of input data are discussed. The author analyzes results based on the method of computing ends of output polygonal chains. Additional methods to improve results are explored. The algorithm was tested on real-world cartographic data received from BDOT/GESUT databases, and on point clouds from laser scanning. An implementation for computing hatching of embankment is described.