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B010314 - ESTIMATION AND IDENTIFICATION
Main information
Course Content
Learning Objectives
Prerequisites
Teaching Methods
Type of Assessment
Course program
Academic Year 2015-16
Course year
First year - Second Semester
Belonging Department
Information Engineering (DINFO)
Course Type
Single education field course
Scientific Area
ING-INF/04 - SYSTEMS AND CONTROL ENGINEERING
Credits
9
Teaching Hours
72
Teaching Term
01/03/2016 ⇒ 10/06/2016
Attendance required
No
Type of Evaluation
Final Grade
Course Content
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Course program
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Lectureship
Course Content
The course aims to provide statistical tools for the analysis and processing of data, with particular emphasis on the estimation of parameters, signals and models of dynamical systems.
The course consists of four parts:
1. STOCHASTIC SIGNALS AND SYSTEMS;
2. ESTIMATION THEORY;
3. RECURSIVE FILTERING AND ITS APPLICATIONS;
4. SYSTEM IDENTIFICATION.
The course consists of four parts:
1. STOCHASTIC SIGNALS AND SYSTEMS;
2. ESTIMATION THEORY;
3. RECURSIVE FILTERING AND ITS APPLICATIONS;
4. SYSTEM IDENTIFICATION.
Learning Objectives
To provide statistical tools for the analysis and processing of data, with particular emphasis on the estimation of parameters, signals and models of dynamical systems.
Prerequisites
Elements of probability theory.
Linear algebra.
Elements of control engineering.
Linear algebra.
Elements of control engineering.
Teaching Methods
Lectures.
Type of Assessment
Project and oral exam.
Course program
1. STOCHASTIC SIGNALS AND SYSTEMS
Stochastic processes. Moments of a stochastic process. Frequency analysis of stationary stochastic processes. Analysis of stochastic systems in steady-state. Spectral factorization. ARMA processes. Modeling of non stationary stochastic signals. First and second order statistics of signals: correlograms and periodograms. Transient time-domain analysis of linear stochastic systems.
2.ESTIMATION THEORY
Bayesian approach to estimation. Minimum Mean Square Error (MMSE) estimation. Optimal linear estimation. Estimation of stationary signals via Wiener filtering. MMSE prediction. Causal Wiener filtering.
3. RECURSIVE FILTERING
State estimation for a linear dynamical system. Kalman filter as the optimal (MMSE) observer. Stationary Kalman filter. Duality with the linear quadratic regulator. Prediction and smoothing. Kalman filter applications. Nonlinear filtering.
4. SYSTEM IDENTIFICATION
The identification procedure and its steps. Model classification. Non-parametric identification: correlation analysis and spectral analysis. Parametric identification: model classes; structural identifiability; "minimum prediction error" criterion of fit; experiment design and experimental identifiability; closed-loop identification; structure selection; validation.
Stochastic processes. Moments of a stochastic process. Frequency analysis of stationary stochastic processes. Analysis of stochastic systems in steady-state. Spectral factorization. ARMA processes. Modeling of non stationary stochastic signals. First and second order statistics of signals: correlograms and periodograms. Transient time-domain analysis of linear stochastic systems.
2.ESTIMATION THEORY
Bayesian approach to estimation. Minimum Mean Square Error (MMSE) estimation. Optimal linear estimation. Estimation of stationary signals via Wiener filtering. MMSE prediction. Causal Wiener filtering.
3. RECURSIVE FILTERING
State estimation for a linear dynamical system. Kalman filter as the optimal (MMSE) observer. Stationary Kalman filter. Duality with the linear quadratic regulator. Prediction and smoothing. Kalman filter applications. Nonlinear filtering.
4. SYSTEM IDENTIFICATION
The identification procedure and its steps. Model classification. Non-parametric identification: correlation analysis and spectral analysis. Parametric identification: model classes; structural identifiability; "minimum prediction error" criterion of fit; experiment design and experimental identifiability; closed-loop identification; structure selection; validation.