STATISTICAL DATA ANALYSIS
Lectures in Italian
The aim of the course is to provide the theoretical and practical aspects for the best estimation of observed and derived quantities for any experimental application. Particular attention is paid to applications in the fields of survey and navigation.
Knowledge and understanding: The student must demonstrate to known and understand the issues related related to data processing and statistical analysis of measurements, with particular attention to those relative to navigation and survey.
Ability to Apply Knowledge and Understanding: The student must demonstrate how to use the acquired concepts and the tools necessary to determine the most probable values of the observations and their accuracies.
Judgment autonomy: The student must be able to know how to evaluate situations different from the standard presented by the teacher during the course and to adopt the best resolution methods.
Communicative Skills: The student must have the ability to submit an elaborate about data observation and treatment by using the correct scientific language.
Learning Skills: The student must be able to update continuously through the consultation of texts and publications in order to acquire the ability to deepen the topics of the observation processing.
It is necessary to acquire and assimilate the knowledge provided by the courses of Mathematical Analysis 1 and Basic Informatics courses
- General considerations on the observation:
- Direct and indirect measurement
- Measurements subject to condition,
-Types of errors
-1D statistical variable: Definition of statistical variable,
- Graphic and synthetic representations of the statistical variable,
1D Random variable: definition of random event,
- Random variable function of random variable,
-Combination of independent random variables,
- Significant probability distributions.
MultidimensionaI Distributions, Marginal and Conditional Distributions, Independence.
Continuous random variables,
Linear functions of random variables.
Direct Measurements: Direct observation as a random variable, direct measurement as a Gaussian random variable;
maximum likelihood principle, estimation of the mean and variance, variance propagation, Weighted average.
Indirect measurements: Indirect observation function of n measurements measured directly or indirectly;
- Indirect measurement of r quantities by means of a system of redundant equations,
-Application of the Least squares method;
- Normal system determination;
- Variance-Covariance matrix estimation;
-Adjustment of geodetic and topographic networks: The problem of the reference system,
-free networks, constrained networks, pseudo-constraints, methods of eliminating the standard deficiency of the normal system,
-Sequential Least squares methods.
- Robust methods for detecting gross errors
- Baarda test
Didactic materials (video-lessons and pdf presentations) on the e-learning platform.
TAYLOR J.R.: “Introduzione all’analisi degli errori”, Ed. Zanichelli.
BENCINI P.: “Nozioni sulle applicazioni della Teoria degli errori alla Geodesia operativa”. Collezione dei testi didattici. Istituto Geografico Militare. Firenze 1988.
CINA A.: “Trattamento delle osservazioni topografiche”, Celid, Torino, 2003.
Ghilani,Charles D.: "Adjustment computations, Spatial data Analisys. 2010,Fifth Edition, JOHN WILEY & SONS, INC.
The objective of the exam is to check the level of achievement of the above-mentioned training objectives.
The exam is oral, with an initial threshold question that enables the continuation of the test, centered on resolving a problem of propagation of variance.