The relationship between internal response-based reliability and conditionality is investigated for Gauss-Markov (GM) models with uncorrelated observations. The models with design matrices of full rank and of incomplete rank are taken into consideration. The formulas based on the Singular Value Decomposition (SVD) of the design matrix are derived which clearly indicate that the investigated concepts are independent of each other. The methods are presented of constructing for a given design matrix the matrices equivalent with respect to internal response-based reliability as well as the matrices equivalent with respect to conditionality. To analyze conditionality of GM models, in general being inconsistent systems, a substitute for condition number commonly used in numerical linear algebra is developed, called a pseudo-condition^number. Also on the basis of the SVD a formula for external reliability is proposed, being the 2-norm of a vector of parameter distortions induced by minimal detectable error in a particular observation. For systems with equal nonzero singular values of the design matrix, the formula can be expressed in terms of the index of internal response-based reliability and the pseudo-condition^number. With these measures appearing in explicit form, the formula shows, although only for the above specific systems, the character of the impact of internal response-based reliability and conditionality of the model upon its external reliability. Proofs for complementary properties concerning the pseudo-condition^number and the 2-norm of parameter distortions in systems with minimal constraints are given in the Appendices. Numerical examples are provided to illustrate the theory.

This paper proposes a modification of the classical process for evaluating the statistical significance of displacements in the case of heterogeneous (e.g. linear-angular) control networks established to deformation measurements and analysis. The basis for the proposed solution is the idea of local variance factors. The theoretical discussion was complemented with an example of its application on a simulated horizontal control network. The obtained results showed that the evaluation of the statistical significance of displacements in the case of heterogeneous control networks should be carried out using estimators of local variance factors.

The paper describes the estimation of covariance parameters in least squares collocation (LSC) by the cross-validation (CV) technique called leave-one-out (LOO). Two parameters of Gauss-Markov third order model (GM3) are estimated together with a priori noise standard deviation, which contributes significantly to the covariance matrix composed of the signal and noise. Numerical tests are performed using large set of Bouguer gravity anomalies located in the central part of the U.S. Around 103 000 gravity stations are available in the selected area. This dataset, together with regular grids generated from EGM2008 geopotential model, give an opportunity to work with various spatial resolutions of the data and heterogeneous variances of the signal and noise. This plays a crucial role in the numerical investigations, because the spatial resolution of the gravity data determines the number of gravity details that we may observe and model. This establishes a relation between the spatial resolution of the data and the resolution of the gravity field model. This relation is inspected in the article and compared to the regularization problem occurring frequently in data modeling.

The aim of this study is to present an exemplary cartographic visualization of fi re hydrants data consisting of a set of thematic maps containing various information related to the location of hydrants, buildings and driveways in geographic space, and relationships existing between them. Identification of these relationships requires spatial analysis, and illustrating them requires the use of appropriate cartographic presentation methods. The study was conducted on a part of the city of Poznan using data on hydrants’ location and type collected and provided by the Fire Department. Geometric data, obtained using geoprocessing algorithms, were assigned appropriate symbols, which lets differentiate them qualitatively and quantitatively. An emphasis is placed on the use of adequate visual variables and on the cartographic communication efficiency. The result of the study is a cartographic visualization in the form of series of thematic maps arranged in a logical sequence, and providing information about the secured area. The thematic layers presenting the same area were arranged in different arrangements with maintenance of the reference layers, ensuring the ease of correlation. Such a cartographic visualization provides knowledge about the spatial distribution and diversity of objects and the relationships between them. It may be an important source of knowledge both at the identification stage and at the operational stage when conducting a fire fighting action.

Monitoring of permanent stations that make up the reference frame is an integral part of the geodesists work. Selection of reference stations is based on analysis of parameters characterizing them (hardware, coordinates’ stability, mounting, location). In this paper, we took into account phase residual as an indicator of unmodelled signal. Phase residuals were computed based on ASG-EUPOS and EPN observation processing. The results show the connection between the method of mounting the antenna and the residuals. We have reviewed multipath effect at ASG-EUPOS stations, and chosen those which are characterized by the highest value of phase residual. The results show that LC phase residual is a good factor to characterize site’s solutions’ reliability. For majority of sites RMS values were less than 10 mm. Modulations associated with multipath effect were observed for few ASG-EUPOS sites only. Phase residuals are distributed specifically for sites, which antennas are mounted on pillars (more common for EPN sites). For majority of analysed sites phase residual distribution was similar for different days and did not depend directly on atmosphere condition.

The article describes the process of creating 3D models of architectural objects on the basis of video images, which had been acquired by a Sony NEX-VG10E fixed focal length video camera. It was assumed, that based on video and Terrestrial Laser Scanning data it is possible to develop 3D models of architectural objects. The acquisition of video data was preceded by the calibration of video camera. The process of creating 3D models from video data involves the following steps: video frames selection for the orientation process, orientation of video frames using points with known coordinates from Terrestrial Laser Scanning (TLS), generating a TIN model using automatic matching methods. The above objects have been measured with an impulse laser scanner, Leica ScanStation 2. Created 3D models of architectural objects were compared with 3D models of the same objects for which the self-calibration bundle adjustment process was performed. In this order a PhotoModeler Software was used. In order to assess the accuracy of the developed 3D models of architectural objects, points with known coordinates from Terrestrial Laser Scanning were used. To assess the accuracy a shortest distance method was used. Analysis of the accuracy showed that 3D models generated from video images differ by about 0.06 ÷ 0.13 m compared to TLS data.

Classification techniques have been widely used in different remote sensing applications and correct classification of mixed pixels is a tedious task. Traditional approaches adopt various statistical parameters, however does not facilitate effective visualisation. Data mining tools are proving very helpful in the classification process. We propose a visual mining based frame work for accuracy assessment of classification techniques using open source tools such as WEKA and PREFUSE. These tools in integration can provide an efficient approach for getting information about improvements in the classification accuracy and helps in refining training data set. We have illustrated framework for investigating the effects of various resampling methods on classification accuracy and found that bilinear (BL) is best suited for preserving radiometric characteristics. We have also investigated the optimal number of folds required for effective analysis of LISS-IV images.

The paper presents the results of real time measurements of test geodetic control network points using the RTK GPS and RTX Extended technologies. The Trimble RTX technology uses the xFill function, which enables real measurements without the need for constant connection with the ASG EUPOS system reference stations network. Comparative analyses of the results of measurements using the methods were performed and they were compared with the test control network data assumed to be error-free. Although the Trimble RTX technology is an innovative measurement method which is rarely used now, the possibilities it provides in surveying works, including building geodetic control networks, are satisfactory and it will certainly contribute to improving the organisation of surveying works.