B028469 - NAVIGATION AND ESTIMATION OF MOBILE ROBOTS

Italian or, on request, english.

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.

We report hereafter the expected acquired skills as well as competences according to the Dublin descriptors.

CA2: Applying knowledge and understanding related to the analysis and optimization of mechanical devices and systems, as well as to their innovation also through the development and improvement of design methods, constantly confronting with the rapid evolution of mechanical engineering.

CA5: Applying in-depth knowledge and understanding related to the choice and use of appropriate equipment, tools, procedures and methods, knowing their limits and potential; in particular the ability to conduct even complex experiments, manage and employ advanced instrumentation and software, with appropriate analytical capabilities.

CA6: Applying knowledge and understanding related to the identification, location and retrieval of data and information necessary for the assessment.

CA12: Applying adequate knowledge and understanding to understand English texts.

CC10: Knowledge and understanding of the automation and control industry. Knowledge and understanding of mechatronic systems.

Elements of probability theory.
Linear algebra.
Elements of control engineering.

Lectures and exercise in class.

The exam consists of an optional project and an interview, aiming to ascertain the acquired skills as well as the competences reported in the educational goals.

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.

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.