


Politecnico di Torino  
Academic Year 2017/18  
01RKYQW, 01RKYOV Estimation, filtering, and system identification 

Master of sciencelevel of the Bologna process in Mechatronic Engineering  Torino Master of sciencelevel of the Bologna process in Computer Engineering  Torino 





Esclusioni: 02MPL 
Subject fundamentals
The course is taught in English.
The purpose of this course is to provide basic methodologies and software tools for building mathematical models of linear and nonlinear (static or dynamic) systems from experimental data. 
Expected learning outcomes
The student shall acquire the following knowledge and develop the following abilities:
 Knowledge of main methods and software tools for building mathematical models (based on physicallaws or in form of difference equations, inputstateoutput equations or transfer functions) of linear and nonlinear (static or dynamic) systems  Knowledge of main methods and software tools for evaluating estimate reliability and model quality  Knowledge of basic theoretical properties of main methods for building mathematical models of static or dynamic systems  Skill in building mathematical models of linear and nonlinear systems exploiting both physical information and experimental data  Skill in evaluating estimate reliability and model quality 
Prerequisites / Assumed knowledge
The following notions are essential: knowledge of the representations of linear dynamic systems (inputstateoutput equations, transfer functions) and of their fundamental properties (stability, controllability, observability); essentials of probability theory and statistics; basic concepts of linear algebra and Zeta transform. The knowledge of the MATLAB software environment is required.

Contents
Course topics and relative devoted time:
 Introduction to estimation and prediction problems. Main statistical estimation methods (least squares, weighted leastsquares, maximum likelihood estimators, Bayesian estimators) and their basic properties (correctness, consistency, efficiency), with evaluation of parametric estimation error (18 hours)  Setmembership estimation theory for different norm assumptions on noise, with evaluation of Estimate Uncertainty Sets and Intervals. Optimal and Central estimates, with evaluation of Feasible Parameter Sets and Parameter Uncertainty Intervals (7 hours)  Introduction to Kalman filtering problem: dynamic onestep and multistep predictors, dynamic optimal filter, steadystate onestep predictor and filter, nonlinear predictors and filters (11 hours)  Identification of linear dynamic systems from inputoutput measurements: FIR, ARX, ARMAX and OE models. Predictive approach and models in predictor form. Asymptotic analysis of predictionerror identification methods. Leastsquares method: probabilistic analysis, persistence of excitation, practical procedure. Recursive leastsquares methods. Model structure selection and validation (whiteness test and residual analysis; FPE, AIC and MDL criteria) (18 hours)  Identification of nonlinear dynamic systems from inputoutput measurements: statistical and setmembership methods. Neural networks: approximation properties, learning (6 hours) 
Delivery modes
Exercise sessions are focused on the development of both academic and applicative examples.
Some other sessions (18 hours) are carried out in computer laboratories and are focused on modelling realworld static or dynamic systems (position transducer, hair dryer, water heater) and on Kalman predictor and filter design and simulation for a given linear dynamic system, using MATLAB toolboxes (Control System, System Identification, Neural Network based System Identification). 
Texts, readings, handouts and other learning resources
The following textbooks have been mainly addressed in the organization of the course:
 S. Bittanti, "Teoria della Predizione e del Filtraggio", VII edition, Pitagora Editrice Bologna, 2004 (in Italian)  S. Bittanti, "Identificazione dei Modelli e Sistemi Adattativi", VI edition, Pitagora Editrice Bologna, 2004 (in Italian)  T. Kailath, A. H. Sayed, B. Hassibi, "Linear Estimation", Prentice Hall, Upper Saddle River, N.J. (U.S.A.), 2000  L. Ljung, "System Identification: Theory for the User", II edition, Prentice Hall PTR, Upper Saddle River, N.J. (U.S.A.), 1999  L. Ljung, "System Identification Toolbox User’s Guide", The MathWorks Inc., Natick, MA (U.S.A.), 19881997 On the course web page www.ladispe.polito.it/corsi/MIC/ , teaching material is available about specific issues addressed in the course, like: lecture slides, laboratory exercises with proposed solutions, official formulary. 
Assessment and grading criteria
The final assessment consists of a written test, about three hours long, to be performed in the computer laboratory using the MATLAB software tools, and it is aimed at evaluating the competencies of the student with reference to all the topics of the course program. The examination is typically made of a model building practice of an unknown system starting from given data and a second exercise on Kalman predictor and/or filter design and simulation for a given linear dynamic system.
The exam is closed books; the student is not allowed to use textbooks or notes, except the official formulary, directly provided by the teacher during the exam as .pdf file (and downloadable before the exam from the course web page). No other material is allowed, i.e., no personal notes, exercises, portions of MATLAB code or solutions of specific exercises, in complete or partial form, anyway coded. 
