Lecturer: Federico Di Palma  

Course name: Identificazione dei modelli e analisi dei dati LS (mn)
Course code: 064210
Degree course: Ingegneria Informatica
Disciplinary field of science: ING-INF/04
The course relates to:
University credits: CFU 6
Course website: http://sisdin.unipv.it/labsisdin/teaching/teaching.php

Specific course objectives

The course aims to give the base notion of the identification problem, the main identification techniques and the basic model representation. By the end of the course the students are expected to be able to choose the right of model and the best identification technique according to the available data and noise information.

Course programme

The course is aimed at providing the main tools for the model identification from real (noisy) data. Lectures will be mainly focused to describe different estimation techniques for both static and dynamic models, although some proofs will still be detailed. Real examples and exercises will be presented to clarify the theoretical lectures. Some lectures will be devoted to the analysis of real data using MatLab. By the end of the course the students are expected to be able to choose the right of model and the best identification technique according to the available data.

Brief review of statics fundamentals

• Probability: definition, conditional probability, law of total probability, Bayes theorem.
• Random variables: probability distributions, first and second moment, vector of random variables, joint distribution.
• Principal distribution: Gaussian, Bernoulli, Poisson, Exponential.

Introduction

• Identification problem: main idea, principal components
• Main defintions: Process, Model, Identification Techniques, Experiment, Model Validation.

Stochastic Process

• Formal definitions:,stochastic process, stationarity, stationarity up to order m, weak-sense stationarity, wide-sense stationarity.
• Power spectral density: definition and properties.
• Stationary process example: white random process (white noise), gaussian random process.

Identification Techniques.

• Main properties: unbiased, optimality, consistency, efficiency.
• Base techniques: Gauss estimation (LS), Markov Estimation (M), Best linear unbiased estimation (BLUE), Maximum likelihood (ML).
• Prior-base techniques: Maximum a posteriori (MAP), Bayes Estimation(B). Prior Examples.
• Examples: analysis of noisy measurement using Matlab.

Models

• Model Properties: Static and dynamic, Linear, Linear regression models.
• Dynamic models: AutoRegressive (AR), AutoRegressive with exogenous inputs (ARX), autoregressive moving average (ARMA), autoregressive moving average with exogenous inputs (ARMAX).
• Application of Identification Techniques to some of the proposed model.
• Example: time series analysis of economic data using Matlab.

Model Validation

• Model comparison: Cross correlation, F-Test.
• Performance indexes: Final Prediction Error (FPE), Akaike's Information Criterion (AIC).
• Examples: time series analysis of economic data using Matlab.

Course entry requirements

Math fundamental gained during the bachelor programme: matrix algebra, multiple integral, maximization of function of more than one variable, Fourier transform.

Course structure and teaching

Lectures (hours/year in lecture theatre): 28
Practical class (hours/year in lecture theatre): 14
Practicals / Workshops (hours/year in lecture theatre): 15
Project work (hours/year in lecture theatre): 15

Suggested reading materials

T. Söderström, P. Stoica. System Identification. Prentice Hall, Upper Saddle River, N.J., 1989 .

A. Papoulis. Probability, Random Variables, and Stochastic Processes. MCGraw-Hill.

Testing and exams

The candidate knowledge is tested by an oral examination. In particular, the student is expected to know the main theoretical aspects and to correctly face a real problem.