The paper presents the results of the studies on the determination of the degree of dependence between the adjusted observations, on the basis of the levels of their coexistence in a network. An approximate model is proposed making it possible to estimate that dependence without the necessity to perform the adjustment procedure. This model can be applied in the procedures of gross error detection in observations. Additionally, a supplementary algorithm to determine the coexistence levels for the observations on the grounds of the matrix of coefficients in the observation equations is presented.

In the paper, the variation of the intensity of the geomagnetic field force is analysed in time and space. For the research, the data from measurements of the intensity of the geomagnetic field force at four airports (Kaunas, Klaip˙eda, Palanga andVilnius) and 6 geomagnetic field repeat stations aswell as the data from Belsk Magnetometric Observatory (Poland) were used. For the data analysis, the theory of covariance functions was applied. The estimates of the cross-covariance functions of the measured intensity of the geomagnetic field force or the estimates of auto-covariance functions of single data were calculated according to the random functions created from the force intensity measurement data arrays. The estimates of covariance functions were calculated upon varying the quantization interval on the time scale and applying the software created using Matlab package of procedures. The impact of radars of airports on the intensity of geomagnetic field variation and on changes of their covariance functions was established.

The paper presents the results of research on the DiSTFA method (Displacements and Strains using Transformation and Free Adjustment) for the determination of displacement and strains of a surface determined in unstable reference systems. Additionally, covariance matrices were introduced to assess the accuracy of estimation results. The theoretical discussion includes an example of its application in a simulated, three-dimensional geodetic network. The obtained results encourage further, more detailed analysis of real geodetic networks.

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 the paper is the comparison of the least squares prediction presented by Heiskanen and Moritz (1967) in the classical handbook “Physical Geodesy” with the geostatistical method of simple kriging as well as in case of Gaussian random fields their equivalence to conditional expectation. The paper contains also short notes on the extension of simple kriging to ordinary kriging by dropping the assumption of known mean value of a random field as well as some necessary information on random fields, covariance function and semivariogram function. The semivariogram is emphasized in the paper, for two reasons. Firstly, the semivariogram describes broader class of phenomena, and for the second order stationary processes it is equivalent to the covariance function. Secondly, the analysis of different kinds of phenomena in terms of covariance is more common. Thus, it is worth introducing another function describing spatial continuity and variability. For the ease of presentation all the considerations were limited to the Euclidean space (thus, for limited areas) although with some extra effort they can be extended to manifolds like sphere, ellipsoid, etc.

Single-frame methods of determining the attitude of a nanosatellite are compared in this study. The methods selected for comparison are: Single Value Decomposition (SVD), q method, Quaternion ESTimator (QUEST), Fast Optimal Attitude Matrix (FOAM) − all solving optimally the Wahba’s problem, and the algebraic method using only two vector measurements. For proper comparison, two sensors are chosen for the vector observations on-board: magnetometer and Sun sensors. Covariance results obtained as a result of using those methods have a critical importance for a non-traditional attitude estimation approach; therefore, the variance calculations are also presented. The examined methods are compared with respect to their root mean square (RMS) error and variance results. Also, some recommendations are given.

The primary goal of the study is to diagnose satisfaction and loyalty drivers in Polish retail banking sector. The problem is approached with Customer Satisfaction Index (CSI) models, which were developed for national satisfaction studies in the United States and European countries. These are multiequation path models with latent variables. The data come from a survey on Poles’ usage and attitude towards retail banks, conducted quarterly on a representative sample. The model used in the study is a compromise between author’s synthesis of national CSI models and the data constraints.

There are two approaches to the estimation of the CSI models: Partial Least Squares – used in national satisfaction studies and Covariance Based Methods (SEM, Lisrel). A discussion is held on which of those two methods is better and in what circumstances. In this study both methods are used. Comparison of their performance is the secondary goal of the study.