Mathematical Processing and Geodata Analysis

Major: Earth Sciences
Code of subject: 6.103.00.O.014
Credits: 6.00
Department: Cartography and Geospatial Modelling
Lecturer: Ph.D., Associate Professor Andrii Sohor
Semester: 2 семестр
Mode of study: денна
Мета вивчення дисципліни: The purpose of studying the academic discipline is to teach students the methods of mathematical processing of geodetic, astronomical, photogrammetric measurements. On the basis of certain methods of probability theory and mathematical statistics, the study of the features of the measurement process and the characteristics of the measurement results, establishing the laws of occurrence and distribution of measured quantities. As well as the study of certain aspects of the measurement process to obtain the most reliable results and their accuracy assessment.
Завдання: The study of an educational discipline involves the formation of competencies in students of education: General competences: ZK02. Ability to apply knowledge in practical situations. ZK07. Ability to work autonomously. Professional competences: SK01. The ability to apply fundamental knowledge to analyze phenomena of natural and man-made origin when performing professional tasks in the field of geodesy and land management. SK02. Ability to apply theories, principles, methods of physical and mathematical, natural, socio-economic, and engineering sciences when performing tasks of geodesy and land management. SK04. The ability to choose and use effective methods, technologies and equipment for carrying out professional activities in the field of geodesy and land management. SK06. The ability to perform remote, ground, field and camera research, engineering calculations for the processing of research results, form research results, prepare reports when solving geodesy and land management tasks.
Learning outcomes: PH1. (RN5. Apply conceptual knowledge of natural and socio-economic sciences when performing tasks of geodesy and land management.) PH2. (RN9. Collect, evaluate, interpret and use geospatial data, metadata about objects of natural and man-made origin, apply statistical methods of their analysis to solve specialized problems in the field of geodesy and land management.) PH3. (RN11. Organize and perform remote, ground, field and camera work in the field of geodesy and land management, prepare the results of work, prepare relevant reports.) PH4. (RN13. Plan and carry out geodetic, topographic and cadastral surveys, process the obtained results in geoinformation systems.)
Required prior and related subjects: • Higher Mathematics, part 1 • Higher Mathematics, part 2 • Informatics and programming of geotasks • Higher Mathematics, Part 3 • Geodesy, part 1 • Geodesy, part 2
Summary of the subject: Systems of random variables. Laws of distribution and moments of distribution of random variables. Dependent and independent quantities. Correlation moment, correlation coefficient. The law of large numbers. Basic theorems of the law of large numbers. Central limit theorem. Statistical (variational) series and their characteristics. Graphic methods of image of statistical material. Statistical estimates of distribution parameters. Exact distributions of sample characteristics. Estimates of small-sample distribution parameters. Confidence intervals. The essence of the measurement process. Classification of measurements and their errors. Distribution and properties of random errors. Processing of measurement series. The essence of the problem is the balancing of several measured quantities. Fundamentals of parametric balancing method. Estimation of accuracy of balancing results by parametric method. Weight of function of measured quantities. Basics of correlative balancing method. Evaluation of the accuracy of the results of equilibrium balancing. Conditional equations of corrections in geodetic networks using the correlative method of balancing.
Опис: The discipline "Mathematical processing and analysis of geodata" studies: systems of random variables; laws of distribution and moments of distribution of random variables; dependent and independent values; correlation moment, correlation coefficient; the law of large numbers; basic theorems of the law of large numbers; central limit theorem; statistical (variational) series and their characteristics; graphical methods of representing statistical material; statistical estimates of distribution parameters; exact distributions of sample characteristics; estimates of distribution parameters for small samples; confidence intervals. And also: the essence of the measuring process; classification of measurements and their errors; distribution and properties of random errors; processing of series of measurements; the essence of the task of balancing several measured values; the basics of the parametric balancing method; assessment of the accuracy of balancing results by the parametric method; the weight function of the measured values; the basics of the correlation method of balancing; assessment of the accuracy of balancing results using the correlation method; conditional equations of corrections in geodesic networks when using the correlation balancing method.
Assessment methods and criteria: • Written reports on laboratory work, verbal examination (40%). • Final control (exam): written, verbal form (60%).
Критерії оцінювання результатів навчання: 1. Performance of laboratory work (max. 35 points): Laboratory works No. 1, No. 2, No. 3, No. 4, No. 5, No. 6, No. 7 are evaluated with a maximum of 5 points. 2. Performance of calculation and graphic work (max 5 points). 3. Examination control (max. 60 points).
Порядок та критерії виставляння балів та оцінок: 100–88 points – (“excellent”) is awarded for a high level of knowledge (some inaccuracies are allowed) of the educational material of the component contained in the main and additional recommended literary sources, the ability to analyze the phenomena being studied in their interrelationship and development, clearly, succinctly, logically, consistently answer the questions, the ability to apply theoretical provisions when solving practical problems; 87–71 points – (“good”) is awarded for a generally correct understanding of the educational material of the component, including calculations, reasoned answers to the questions posed, which, however, contain certain (insignificant) shortcomings, for the ability to apply theoretical provisions when solving practical tasks; 70 – 50 points – (“satisfactory”) awarded for weak knowledge of the component’s educational material, inaccurate or poorly reasoned answers, with a violation of the sequence of presentation, for weak application of theoretical provisions when solving practical problems; 49-26 points - ("not certified" with the possibility of retaking the semester control) is awarded for ignorance of a significant part of the educational material of the component, significant errors in answering questions, inability to apply theoretical provisions when solving practical problems; 25-00 points - ("unsatisfactory" with mandatory re-study) is awarded for ignorance of a significant part of the educational material of the component, significant errors in answering questions, inability to navigate when solving practical problems, ignorance of the main fundamental provisions.
Recommended books: 1. Войтенко С.П., Шульц Р.В., Кузьмич О.Й., Кравченко Ю.В. Математичне оброблення геодезичних вимірів: підручник / за ред. С. П. Войтенка. – К.: Знання, 2015. – 654 с. 2. Зазуляк П.М., Гавриш В.І. Євсєєва Е.М., Йосипчук М.Д. Основи математичного опрацювання геодезичних вимірювань. Навчальний посібник. – Львів: Видавництво "Растр-7", 2007. – 408 с. 3. Рябчій В.А. Теорія похибок вимірювань. Навч. посібник / В. А. Рябчій, В. В. Рябчій ; Національний гірничий ун-т. – Д. : НГУ, 2006. – 165 с.
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Академічна доброчесність: The policy regarding the academic integrity of the participants of the educational process is formed on the basis of compliance with the principles of academic integrity, taking into account the norms "Regulations on academic integrity at the Lviv Polytechnic National University" (approved by the academic council of the university on June 20, 2017, protocol No. 35).