Estymacja metodą najmniejszych kwadratów (LS) jest Jednym z najważniejszych narzędzi w analizowaniu danych geodezyjnych. Jednakże powszechne korzystanie z rej metody nie zawsze idzie w parze z pełnym uświadomieniem sobie jej podstaw. W standardowym formalizmie teorii estymacji LS w rzeczywistości istnieje kilka paradoksalnych i osobliwych zagadnień rzadko formułowanych wprost. Celem niniejszej pracy jest przedstawienie niektórych z tych zugadnień i przedyskutowanie ich konsekwencji w analizie danych gcodezyjnvch oraz problematyce estymacji parametrów. W pierwszej części pracy przedstawiony Jest alternatywny pogląd na podstawy statystyczne, które są tradycyjnie łączone z estymacją LS. W SZC7.ególności pokazano. że właściwość nieobciąźoności dla zwykłych estymatorów LS może być zastąpiona przez inne. równowazne JeJ uwarunkowanie, które powoduje, że zakres numeryczny nieznanych parametrów jest nieograniczonv. \V drugiej części pracy przedstawiono wady meiodv LS 7. czysto algebraicznego punktu widzenia. bez uwzględnienia pojęć z zakresu prot abilisryczncgo/sratysrycznego teorii estymacji. W szczególności ,, yjaśnione zostało. cło czego odnosi się 'najmnicjsz, · (least) w metodzie najmniejszych kwadratów. Z pewnością nie odnosi się cło błędów· wyznaczanych parametrów modelu. Ponadto stwierdzono, że w bielej inwersji modelu liniowego opartej na metodzie LS istnieje krytyczna zamiana pomiędzy normami euklidesowymi błędów wyznaczanych parametrów i wyrównanych residuów.

The paper presents an attempt to assess how random errors and systematic errors in gravity data affect the quality of the geoid model when it is computed using the FFf technique. Three groups of numerical tests were conducted with the use of gravity anomalies for Poland on 2' x 2' and 5' x 5' grid and with simulating random and systematic errors. In the first test, the effect of random errors on calculated geoid undulations was investigated, in the second one - the effect of systematic errors, and in the last one - the combined effect of both random and systematic errors. The effect of density of data set on the propagated error in geoid height was also examined. The results of numerical tests made possible to evaluate the effect of random errors as well as systematic errors on the accuracy of computed geoid undulation. They were also useful in evaluating the quality of the gravimetric quasigeoid model for Poland.

A number of new satellite-only Global Gravity Models (GGMs) become progressively available based on the CHAMP and GRACE satellite mission data. These models promise higher (compared to older GGMs) accuracy in the determination of the low and medium harmonics of the Earth's gravity field. In the present study, the latest GGMs generated from CHAMP and GRACE data (namely EIGEN2, EIGEN3p, GGM0IC, GGM0IS and GRACED IS) have been studied with respect ro their accuracy and performance when used in gravity field approximation. A spectral analysis of the new models has been carried out, employing their degree and error-degree variances. In this way, their performance against each other and with respect to EGM96 was assessed, and the parts of the gravity field spectrum that each model describes more accurately have been identified. The results of the analysis led to the development of a combined geopotential model, complete to degree and order 360, whose coefficients were those of CHAMP until degree 5, then GRACE until degree 116, and EGM96 for the rest of the spectrum. Finally, a validation of all models (the combined included) has been performed by comparing their estimates against GPS/levelling data in land areas and TOPEX/Poseidon sea surface heights in marine regions. All rests have taken place over Greece and the eastern part of the Mediterranean Sea. From the results obtained it was concluded that the combined GGM developed provides more accurate results (compared to EGM96), in terms of the differences with the control datasets, at the level of 1-2 cm geoid and 1-2 mGal for gravity (ICT). Furthermore, the absolute geoid accuracy that the combined GGM offers is 12.9 cm (ICT) for 11 = 120, 25 cm for 11 = 200 and 33 cm for n = 360, compared to 29 cm, 36 cm and 42 cm for EGM96, respectively.

The recently released global crustal model CRUST 2.0 has been validated both globally and regionally focusing on its information content regarding the crust-mantle boundary. The numerical assessment of the metric information given by the database in terms of thickness and position of individual crustal layers with respect to sea level takes place by investigating correlations with the surface topography and by comparing those values with known theoretical approaches that describe the compensation mechanism between crust and mantle. The investigations described focused especially on the last crustal layer of CRUST 2.0, which represents the boundary surface between crust and mantle, widely known as Mohorovicic discontinuity. A direct comparison of the Moho structure as given from the crustal model CRUST 2.0 with the respective compensation depths derived theoretically from the application of the Airy/Heiskanen hypothesis is carried out both globally and regionally. The comparisons, especially those referring to selected regions of the globe expressing characteristic tectonic features, such as mountain belts or oceanic ridges, enable both the numerical assessment of the database while giving at the same time a preliminary insight on the local and regional behaviour of known isostatic mechanisms.

In GIS systems, the neighbourhood of areas within an analysed region is a term applied usually to raster-screened data. The aim of the study was to adapt this term to vector and descriptive data as well as to systemize models of so defined neighbourhood. The starting point was the assumption that the basic area neighbourhood model may be based on spatial data illustrated with a graph and described with a neighbourhood matrix. It provides the basis for building subsequent models, that are linked with the introduction of new neighbourhood measures, i.e. measures resulting from the characteristics of areas entered in tables of their attributes. Based on the proposed models, spatial analysis related to area neighbourhood can be performed and aggregate models, considered essential in multidimensional analysis of neighbourhood can be developed.

The paper presents a general concept of geodetic observations adjustment based on application of the Edgeworth' series and the principle of an alternative choice. The Edgeworth' series approximates the empirical distribution of measurement errors and gives an opportunity to modify the empirical characteristics of errors distribution. The method of estimation used is based on the principle of the alternative choice. Its natural robustness for outliers was the basis for newly created method called PAC-E. The paper presents the algorithm and some numerical tests that were carried out to compare the results of the proposed method with the results of the classical LS adjustment. Special attention was paid on the effect of non-zero excess and robustness of the proposed method.

The radar method, executed with the use of ground penetrating radars - the georadars, belongs to non-intrusive methods of positioning subsurface structures and objects. The direct result of the survey is the so-called radargram - a radar image, that is a vertical cross-section of the penetrated medium. It brings an information on the existence and mutual position of ground layers and subsurface structures and objects. The radargram, as the direct result of measurement, demands further processing for its interpretation and use. The consecutive steps leading from a non-metric radargram to the metric 3D model, based on corresponding surveying and georadar data are presented. The paper concentrates on the problem of broadening the scope of interpretation and applications of georadar surveys thanks to proper integration of advanced filtering programs, graphical software and programs from the CAD and SIT environment. The aim of the integration is a metric 3D model of subsurface objects and structures located with the georadar method. The ways and stages of generation of the spatial subsurface models, presented in the paper, complement surveying sources of data for thematic maps.

The paper discusses the problems of the calibration process of very close range semi-metric digital cameras. Using such cameras for precise measurement of small objects, the photographs have to be taken at a very large scale, ranging from 1 :20 to 1:50. To ensure the submillimetre accuracy of the photogrammetric measurement, the specific calibration tests and procedures for determination of the interior orientation parameters, including the coefficients for image systematic errors, must be applied. The results of two calibration approaches, based on 3D and 2D calibration tests, have been presented in the paper. The experiment is a part of the research project concerning the numerical modelling of small 3D fragments of the broken archaeological items for reconstruction of the context of the archaeological monument.

The paper addresses the problem of solving overdetermined systems of linear equations by means of methods of robust estimations, which eliminate the effect of outliers on the estimation results. The process of estimating a vector of parameters was accomplished by means of circular in structure neural networks. Formulating the problem in the aspect of a method for estimating parameters requires formulating an energy function (objective function) whose form was modified by means of a determined weighting function. In the final part of the paper the effectiveness of the methods described was evaluated in terms of controlling and diagnosing a geodetic observation system. The article is merely an introduction to a broadly understood problem of geodetic uses of robust estimators.

In the process of development and modernisation or updating lands or buildings register database the knowledge of the accuracy of analytical determination of areas is required. The knowledge of accurately determined areas is also indispensable for other activities, as e.g. in the case of geodetic maintenance of investments or in the process of control of direct subsidies for agriculture, which are performed within the Integrated Administration and Control System (IACS). In the case of double determination of area of an object, basing on co-ordinates of its vertices, determined from two independent measurements of the same accuracy, the results of calculations differ from one another. The value of that difference, generated in the natural way - following the law of error propagation - should be discussed with respect to its permissibility. This paper presents the analysis of technical and legal regulations, which are obligatory in Poland and which concern permissible errors of analytical determination of areas. Then, a method of determination of values of permissible differences of double determination of areas of cadastral (and other) objects basing on co-ordinates of vertices, under the assumption that those areas are determined with obligatory accuracy (i.e. which total error of position of a point does not exceed O. I O m) and with consideration of shapes of a geometrical object and its area is presented. A formula, which defines the maximum value of the permissible difference of double calculation of an area, which is the function of the parcel area, its shape and the accuracy of determination of position of vertices, has been proposed. Results obtained with the use of the proposed formula were then compared with those obtained with the use of the formula, which recently is obligatory in Poland, as well as other formulae acquired from professional literature. It has been proved that in order to record areas of cadastral objects according to existing regulations, the accuracy of determination of position of border points, should be considerably improved.

Today, the new era with Very High Resolution Satellite (VHRS) imageries as IKON OS, QuickBird, EROS, Orb View etc., provides orthophoto in large scale of 1 :5 OOO, to update existing maps, to compile general-purpose or thematic maps. Orthophotomap in the scale of I :5 OOO with Ground Sampling Distance of 0.5 m is one of three important sources for establishing GIS together with a Digital Elevation Model of ±LO m accuracy in height and a topographic map in the scale of 1: IO OOO. Therefore, the accuracy of products of VHRS imageries affects reliability of GIS. Nevertheless, the accuracy of products of processing VHRS imageries is at first dependent on chosen geometrical sensor models. The understanding of geometrical sensor models of VHRS imageries is very important for improving processing of VHRS imageries. The polynomial models are to provide a simple, generic set of equations to represent the indirect relationship between the ground and its image. The polynomial models or replacement sensor models must not only model the ground-to-image relationship accurately. Physical (or parametrical) model describes dir~ctly strict geometrical relations between the terrain and its image, using satellite's orbital parameters and basing on the co-linearity condition. In such model, the above-mentioned multi-source distorting factors are taken into consideration. In this paper a review of practical accuracy of geometrical models of VHRS imageries taken from different research institutions in the world in last years has been presented.

Modelling quasigeoid with centimetre accuracy requires taking into account irregularities of topography in the vicinity of a gravity station. i.e. the terrain correction w surveyed gravity. Accuracy of determination of the terrain correction affects quality of quasi geoid model determined. It depends on the resolution and accuracy of terrain data that usually is provided in the form of a digital terrain model DTM. Investigations were conducted with the use of the Digital Terrain Elevation Data - DTED2 model developed for Poland according to the NATO-STANAG 3809 standard, as well as global models SRTM3 and SRTM30 (The Shuttle Radar Topography Mission). Also height data from the gravity database was considered. The prism method of determination of terrain corrections was applied in majority of numerical tests. Practical method for determining the optimum radius of the integration cap considering roughness of topography as well as required accuracy of terrain corrections was developed. The effect of vertical and horizontal uncertainty of a DTM as well as its resolution on the quality of the terrain corrections was investigated. The terrain corrections obtained using a prism method were also compared with the respective ones calculated using the FIT approach. The usefulness of the available topography data for precise terrain correction computation in Poland was discussed. The results of the investigations were used to determining the strategy of computation of the terrain corrections to point gravity data in the gravity database for Poland. The "2005" terrain correction set calculated for I 078 046 gravity stations contributes to the increase of precision of gravimetric quasigeoid models developed for Poland.