OVERVIEW

The course presents the main estimation and identification techniques to be used in the context of complex dynamic systems analysis, forecasting and control.

AIMS AND CONTENT

AIMS AND LEARNING OUTCOMES

The learning outcomes of the course refer to the capacity of:

• knowing the properties of an estimator;
• identifying the main features of an estimation problem as regards the characteristics of data and the features of a suitable estimator;
• designing the solution of an estimation problem, that is, defining the best estimator
• knowing the features of an identification problem;
• knowing the most important classes of identification models;
• designing the solution of an identification problem.

PREREQUISITES

The course prerequisites refer to basic elements of systems theory, statistics and optimization.

TEACHING METHODS

Aula lessons and laboratory exercises.

SYLLABUS/CONTENT

Estimation theory: parameter estimation (correctness, consistency and efficiency of the estimator), Cramer-Rao theorem, minimum variance estimation (UMVUE and BLUE estimators), maximum likelyhood estimation, linear estimation with measurement errors (least square estimation, Gauss Markov estimator). Bayesian estimation (minimum squared error estimation and linear minimum squared error estimation). Kalman filter.

Identification techniques: definition of the parameter identification problem, model families (ARX, ARMAX, OE,  ARXAR, BJ),  MPE identification: convergence theorems, identification for ARX models (least squares identification), for ARMAX models and for ARXAR models, batch and iterative algorithms.

RECOMMENDED READING/BIBLIOGRAPHY

L. Ljung, "System Identification: Theory for the user", Prentice Hall (2nd Edition), 1999.

S.M. Kay, "Fundamentals of Statistical Signal Processing: Estimation Theory", Prentice Hall, 1993.

TEACHERS AND EXAM BOARD

Exam Board

SIMONA SACONE (President)

MICHELA ROBBA

SILVIA SIRI (President Substitute)

LESSONS

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The evaluation consists in an oral exam.

ASSESSMENT METHODS

During the exam the student has to present the main arguments of the course, to solve numerical exercises and to explain the theoretical notions necessary for their solution

Exam schedule