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.
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.
Elements of probability theory.
Elements of control engineering.
Lectures and exercise in class.
Type of Assessment
The exam consists of a project and an interview.
The project, assigned to groups of 1-4 students, aims to verify the capabilities of using CAD data processing tools for solving practical problems involving parameter, signal, state and dynamical system model estimation.
The interview aims to assess, by means of exercises and theoretical questions, the acquired knowledge on estimation and system identification.
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.
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.