Fakulta elektrotechniky a informatiky / Faculty of Electrical Engineering and Informatics
Stálý URI pro tuto komunituhttps://hdl.handle.net/10195/3847
Práce obhájené před rokem 2008 jsou uloženy pouze v kolekci Vysokoškolské kvalifikační práce
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Článekpeer-reviewedpostprint Omezený přístup Verification and estimation of uncertainties of Tobias Mayer's 18th century astronomical observations(Elsevier Science BV, 2023) Marek, Jaroslav; Tuček, JiříPerceiving the uncertainty of the measurement has been changing over the past centuries, reflecting the advancement in the experimental techniques, the urge for reliable and reproducible measurement methodology, and development of mathematical data processing and evaluating algorithms. From the historical perspective, the concepts of considering the measurement uncertainty were firstly introduced with geographic and cartographic measurements. In this context, the works of Tobias Mayer on lunar landscape measurements are widely highlighted which, at that time, presented innovative approaches in data processing with the method of averages and pioneeringly addressed the issue of measurement error. In this study, we analyze in details the Mayer's set of 27 non-linear equations with 3 unknown parameters and discuss the effect of Mayer's linearization and subsequent mathematical procedures on the accuracy of the parameter values in contrast with the results from rigorous treatment of non-linear regression model involving the least-square method. In particular, we compare the values of the unknown parameters and their uncertainties in several variants in the linearized and nonlinearized model, providing monitoring of a small deviation of the Mayer's linearization. The results, presented here, show that despite the conceptual and computational simplification of the Mayer's method, such an approach to data processing can be exploited, with an acceptable level of accuracy, in several practical situations even today.Článekpeer-reviewedpostprint Omezený přístup Survey of Point Cloud Registration Methods and New Statistical Approach(MDPI, 2023) Marek, Jaroslav; Chmelař, PavelThe use of a 3D range scanning device for autonomous object description or unknown environment mapping leads to the necessity of improving computer methods based on identical point pairs from different point clouds (so-called registration problem). The registration problem and three-dimensional transformation of coordinates still require further research. The paper attempts to guide the reader through the vast field of existing registration methods so that he can choose the appropriate approach for his particular problem. Furthermore, the article contains a regression method that enables the estimation of the covariance matrix of the transformation parameters and the calculation of the uncertainty of the estimated points. This makes it possible to extend existing registration methods with uncertainty estimates and to improve knowledge about the performed registration. The paper's primary purpose is to present a survey of known methods and basic estimation theory concepts for the point cloud registration problem. The focus will be on the guiding principles of the estimation theory: ICP algorithm; Normal Distribution Transform; Feature-based registration; Iterative dual correspondences; Probabilistic iterative correspondence method; Point-based registration; Quadratic patches; Likelihood-field matching; Conditional random fields; Branch-and-bound registration; PointReg. The secondary purpose of this article is to show an innovative statistical model for this transformation problem. The new theory needs known covariance matrices of identical point coordinates. An unknown rotation matrix and shift vector have been estimated using a nonlinear regression model with nonlinear constraints. The paper ends with a relevant numerical example.Článekpeer-revieweduncorrected proof Omezený přístup Investigating growth models with linearization domain analysis and residual analysis(Oxford University Press, 2022) Marek, Jaroslav; Pozdílková, Alena; Kupka, LiborGrowth modelling is of interest to scientists in various disciplines. In our article, we will collect 17 models designed for growth modelling, appraise these models and contribute to the discussion of their applicability. The merit of the paper lies in studying the convergence properties of nonlinear regression in selected models. Our studies will be performed mainly concerning the quality of the obtained estimates, which are closely related to the intrinsic curvature of the model according to Bates and Watts. This curvature determines the size of the linearization domains. Only if the initial solution is in this domain, then the convergence of the estimate in nonlinear regression is guaranteed. The primary goal is to design a methodology for selecting a growth model. We will demonstrate fruitfulness of our methodology on the weight measurements of 10 calves under 25 months of age from cowsheds in the village Zaluzi in the Czech Republic. Estimated parameters of growth curves, sizes of linearization domain, calculated residues and coefficients of determination indices will be the subject of discussion.Článekpeer-reviewedpublished version Otevřený přístup Boscovich Fuzzy Regression Line(MDPI, 2021) Skrabanek, Pavel; Marek, Jaroslav; Pozdílková, AlenaWe introduce a new fuzzy linear regression method. The method is capable of approximating fuzzy relationships between an independent and a dependent variable. The independent and dependent variables are expected to be a real value and triangular fuzzy numbers, respectively. We demonstrate on twenty datasets that the method is reliable, and it is less sensitive to outliers, compare with possibilistic-based fuzzy regression methods. Unlike other commonly used fuzzy regression methods, the presented method is simple for implementation and it has linear time-complexity. The method guarantees non-negativity of model parameter spreads.Článekpeer-reviewedpublished version Otevřený přístup Monitoring Of Apartment Prices In The Czech Republic Through Parsing A Web Advertising Server(2020) Pozdílková, Alena; Marek, Jaroslav; Nedvědová, MarieTime series of apartment prices in the Czech Republic are available only in the partial statistics of the Statistical Office. Apartment prices are presented mainly in the articles and comments from the real estate agents. Data unavailability leads to a small number of statistically oriented publications on the real estate market. The main aim of our paper is thus to introduce a software solution for parsing real estate websites. Of course, we are only able to retrieve data on demanded prices from advertisements, actual prices are not achieved. By automatic polling, we are able to get data on the floor area of advertised apartments and the asked purchase price. A Python script was written to retrieve data from sreality.cz. The MongoDB database is used to store ads. New ads are saved directly to the database. Then, daily average apartment price of 1 square meter for each municipality are calculated. The filtered data can then be displayed or exported to a file via the web interface. In the statistical analyses, we present graphs showing the development of apartment prices and the number of advertisements in various municipalities of the Czech Republic in the period of 09/2018 – 12/2019. Next, we address the issue of clustering of municipalities with regard to the similarity of relative price changes.