Statistical moments have been used in different applications as in shape analysis of object, pattern recognition, edge detection texture analysis etc. The idea is to use the moments as features of high level for surface matching. The essential goal of surface matching is to determine transformation parameters between two surfaces generated in TIN or DEM without identical points. Statistical moments are considered as features that are applied to solve that goal, One of the main problems with using statistical moments for surface matching and for other applications is a very expensive computation time. To overcome this difficulty many algorithms have already been proposed. New approach of efficient computation of inertial moments for surface matching is proposed in the paper. The approach is based on Green's theorem that allows for transforming double integral into a line integral. In the consequence computation time of inertial moments of a single TIN-model (triangle) is reduced by a factor 4 as compared with time consumed by the use of direct method of double integral. The direct computation using line integral, that does not involve any approximation, ensures preservation of the accuracy of computed moments.

The use of a network of reference stations instead of a single reference station allows to model some systematic errors in a region, and to increase the operational distance between the rover and reference stations. Permanent GPS reference stations exist in many countries, and GPS observations are available for the users in real-time mode and in post-processing. The paper presents DGPS post-processing positioning with the use of three reference stations. The traditional DGPS technique is based on one reference station. It has been shown that the accuracy of such positioning is about 1-2 meters, depending on the number of satellites being tracked and the resulting value of POOP (Position Dilution of Precision). The accuracy of DGPS positioning degrades when the distance between the rover and the base station increases. The paper shows that when three reference stations are used simultaneously, pseudorange corrections for a virtual reference station, located in the vicinity of an unknown station can be created, and distribution of pseudorange corrections over time can be analysed and modelled. Three reference stations give redundant observations and enable to reduce some measurement errors and biases. Practical calculations and analysis of accuracy have been presented for medium-long and long distances between the rover and reference stations.

A geo-radar method is used for detection of underground installations with the use of electromagnetic waves. Results of investigations of installations depend on physical properties of soil media, which properties result in suppression, reflection and refraction of electromagnetic waves. Three parameters, electric permittivity E, magnetic permittivity μ and the medium conductivity a play the major role in establishing electric features of a material medium. Suppression of the electromagnetic wave has the basic influence on detection of underground installations with the use of the geo-radar, and, in particular, on the depth range of the method. Relation between designing parameters of the geo-radar equipment and its depth range is determined by the basic equation of the geo-radar method. Solution of the basic equation of the geo-radar method for the needs of detection of underground installations requires performing experimental measurements. Measurements of the maximum depth of detection of underground installations with the use of the geo-radar have been performed in media of known physical properties, i.e. in the air, water and water solutions of NaCl of various concentrations. Two steel pipes of diameters of</!= 0.03 m and O. l Om were the objects for testing. Measurements were performed with the use of antennae of frequencies of !OOO MHz and 200 MHz. The results obtained in the form of echograms were analysed in order to determine the maximum distances for which the tested pipes were recorded. Experiments allowed to state that the maximum measurements of the depth range of the geo-radar equipment is rapidly decreased with the decrease of the background's specific resistance below 50 Qm. An increase of the soil resistance above 500 Q m results in slight increase of the depth range of measurements. Tests and analyses performed concerned homogenous media, i.e. metal installations, for which the electromagnetic wave is fully reflected.

The choice of global geopotential model used in remove-restore technique for determination of regional quasi geoid from gravity data may affect the solution, in particular when the accuracy is supposed to reach a centimetre level. Global geopotential model plays also an important role in validating height anomalies at GPS/levelling sites that are used for the estimation of the external accuracy of quasigeoid models. Six different global geopotential models are described in the paper. Three kinds of numerical tests with use of terrestrial gravity data and GPS/levelling height anomalies were conducted. The first one concerned comparison of height anomalies at GPS/levelling sites ia Poland with corresponding ones computed from various global geopotential models. In the second one the terrestrial gravity anomalies in Poland and neighbouring countries were compared with corresponding gravity anomalies computed from global geopotential models. Finally the quasigeoid models obtained from gravity data with use of different global geopotential models were verified against corresponding height anomalies at GPS/levelliag sites in Poland. Data quality was discussed and best fitting global geopotential model in Poland was specified.

This paper investigates the terrain-aliasing effects on geoid determination using different gravimetric reduction schemes. The high resolution of digital terrain model (DTM), if available, should be used for every gravimetric reduction scheme since it can precisely map the details of the terrain. The reduction methods used in this study are the Rudzki inversion method, Helmert's second method of condensation, the residual terrain model (RTM) method, and the Pratt-Hayford (PH) topographic-isostatic reduction technique. The effect of using different DTM grid resolutions of 6", 15", 30", 45", I' and 2' on gravity anomalies and absolute geoid undulations is studied for each of these reduction schemes. A rugged area in the Canadian Rockies bounded by latitude between 49°N and 54°N and longitude between 236°E and 246°E is selected to conduct numerical tests. Our results suggest that a DTM grid resolution of 6" or higher is required for precise geoid determination with an accuracy of a decimetre or higher for any gravimetric reduction method chosen to treat the topographical masses above the geoid in rugged areas. The most precise geoid models obtained in this test are the ones obtained using Rudzki, Helmert, and RTM methods with 6" DTM resolution.

Since 2000 when first imageries of Space Imaging of one metre resolution satellite products appeared on the World market, many institutions started using them for cartographic production such as orthophotomaps on a large scale. A choice of the mathematic sensor models of imageries for their orthorectification in producing orthophotomaps is one of the main investigation directions. In order to restitute the functional relation between imageries and their ground space, the use of sensor models is required. They can be grouped into two classes, the generalized sensor models (geometric or replacement sensor models) and physical or parametric models. The paper presents a brief overview of the geometric models such as RPC (Rational Polynomial Coefficients). Their properties, and in particular their advantages and disadvantages are discussed. Also the parametric models, developed by the authors are presented in this paper. They are based on time-dependent collinearity equation of the mathematic relation between ground space and its imageries through parameters describing the sensor position in satellite orbit and position of the orbit in the geocentric system.

Marine geoid modelling in the Atlantic coastal region of Argentina is problematic. Firstly, because of the insufficient amount of available shipborne gravity data, which renders a purely gravimetric solution not feasible. Secondly, because of the very strong ocean currents, that affect the quality of satellite altimetry data, so that a purely altimetrie model is too noisy, even after low-pass filtering the Sea Surface Heights (SSHs) to remove (part of) the influence of the oceanographic signals. Thus, the recommended solution is to employ a combination method and the use of all the available gravity and altimetry data together. This is a suitable solution since (i) combination methods such as least squares collocation and Input Output System Theory (!OST) inherently low-pass filter and weigh the data, and (ii) will make use of the altimetrie heights to fill the gaps of the shipborne gravity data. Following this idea, purely altimetrie, gravimetric and combined (using the !OST method) marine geoid models have been estimated for Argentina, employing all available shipborne gravity data, satellite altimetry SSHs and the latest Earth Gravity Models (EGMs) developed from CHAMP and GRACE missions. The new EGMs are especially useful to assess the quality of the new geoid models, especially against EGM96, which was used in an older ERSl-only solution for the same area. From the comparison of the estimated geoid models with respect to stacked TOPEX/Poseidon SSHs, the authors found that the altimetrie model provides the best agreement while the combined one improves the accuracy (I a) of the gravimetric solution.

A geo-radar image of a recorded underground conduit has a hyperbolic shape in an electrically homogeneous background. Echograms of conduits, which are located close to one another, overlap leading to possible interpretation errors. The paper presents a method of experimental determination of resolving power capabilities of a given type of geo-radar equipment for the needs of detection of underground installations. It has been proved, basing on performed experiments that the horizontal resolving power of detection of underground installations depends on the type of applied geo-radar equipment and on the frequency of electromagnetic waves. Together with the increase of the dielectric constant of the medium, where underground installations are located, the horizontal resolving power also increases.

An increased use of global navigation techniques for positioning, and in particular for height determination, led to a growing need for precise models of height reference surface, i.e. geoid or quasigeoid. Geoid or quasigeoid heights at a cm accuracy level, provided on growing number ofGPS/levelling sites, can not only be used for quality control of gravimetric geoid but they also can be integrated with gravity data for geoid/quasigeoid modelling. Such a model is of particular use for surveying practice. A method of quasigeoid modelling based on GPS/levelling data with support of geopotential model and gravity data was developed. The components of height anomaly are modelled with the deterministic part that consists of height anomaly based on EGM96 geopotential model and Molodensky's integral, as well as the polynomial representing trend, and from the stochastic part represented by the isotropic covariance function. Model parameters, i.e. polynomial coefficients and covariance function parameters are determined in a single process of robust estimation, resistant to the outlying measurements. The method was verified using almost a thousand height anomalies from the sites of the EUREF-POL, POLREF, EUVN'97 and WSSG (Military Satellite Geodetic Network) networks in Poland as well as geopotential model refined with gravity data in l' x l' grid. The estimated average mean square error of quasigeoid height is at the level of O.Ol m. The outlying measurements were efficiently detected.

Calculation of the effect of topography on the observed gravity becomes particularly important when modelling high-precision geoid. It requires a digital terrain model of appropriate resolution and accuracy. Various global, regional and local digital terrain models of different accuracy and resolution are recently available. Evaluation of the DTM used is required for verification and validation of its quality as well as for estimating accuracy of geoid model derived with considering the effect of topographic masses. Two DTMs: the SRTM3 of 3" x 3" resolution and the national DTM for Poland of l" x l" or l" x 2" resolution - called DTED2 - were evaluated with use of high-resolution local DTMs developed using digital photogrammetry of 25 m x 25 m as well as the regional model in Tatra mountains of 10 m x 10 m. Then the heights of almost 1000 GPS/levelling stations of Polish geodetic control were compared with the heights from the DTED2 model. The heights of over a million of gravity stations from gravity database, that were the basis of previous geoid modelling in Poland, were also compared with the heights from the DTED2 model. The effect of uncertainty of a DTM on estimation of mean gravity anomalies was discussed. In particular, the effect of replacing heights from gravity database with the heights from the DTED2 model in the process of calculating mean gravity anomalies, on the accuracy of geoid modelling was investigated. The use of the DTED2 model is at present recommended for determination of precise geoid model in Poland.

The paper presents estimation of positional accuracy of digital maps using statistical analysis. Investigations have been performed for four large-scale digital maps made using different methods of producing digital map data: new total station survey (object A), re-calculation of previous direct measurements (orthogonal and polar surveys) (object B), manual vectorisation of a raster orthophotomap image (object C) and graphical-and-digital processing of analogue maps (object D). Analysis has been performed for large statistical samples of sets of vectors of shift t: L of control points and their components, i.e. true errors t: x, t: r of increments of co-ordinates. In the case of a map produced by means of new survey with an electronic tacheometer, the true errors were represented by differences between co-ordinates of control points obtained from two separate set outs. In the case of other methods of data collection for digital map production true errors were represented by differences of co-ordinates acquired from an investigated map and co-ordinates calculated from new direct surveys.