Mathematical Processing of Geodetic Measurements

Major: Earth Sciences
Code of subject: 6.103.00.O.020
Credits: 6.00
Department: Cartography and Geospatial Modelling
Lecturer: Professor Petro Zazuliak
Semester: 3 семестр
Mode of study: денна
Learning outcomes: • Ability to demonstrate knowledge of the basics of measurement error theory. • Apply knowledge of parametric and correlative methods for balancing different types of geodetic networks. • Ability to demonstrate basic knowledge of the least squares method. • Apply knowledge and understanding to calculate root mean square errors and weights of functions of measured values. • Ability to perform mathematical processing of measurement results and their estimation of accuracy. • Ability to demonstrate knowledge of the basics of probability theory. • Apply knowledge and understanding to solve mathematical statistics problems. • Ability to find event probabilities. • Apply knowledge and understanding of statistical estimates of distribution parameters to construct their confidence intervals. • Ability to explore statistical hypotheses.
Required prior and related subjects: • Computer science and geo-programming. • Higher Mathematics Part 1, 2. • Surveying Part 1.
Summary of the subject: 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. 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.
Assessment methods and criteria: • Written reports on laboratory work, verbal examination (40%). • Final control (exam): written, verbal form (60%).
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.