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The goal of the course is to provide the background for advanced modelling and data analysis, together with Kalman Filter techniques for parameters and virtual sensors estimation. The course has both a theoretical and a practical flavour, and is focused on the following topics: Stationary stochastic processes generated as output of dynamic systems. ARMA and ARMAX models. Prediction. Non-parametric models based on the spectral characteristics of a process. Estimation methods based on minimum prediction error. Model complexity analysis and parameters identification. Virtual sensors: Kalman Filter; Extended Kalman Filter for gray-box parameters identification.
Description of the contents of the course:
- Introduction to the concept of model identification
o Data-based modelling
o Black-Box and Gray-Box models
- The mathematical framework: stochastic processes
o Basic features (mean value; covariance function; spectrum)
o Practical estimation from measured data
- Classes of Black-box linear models
o AR/MA/ARMA
o ARMAX
o Analysis of stochastic processes with ARMA/ARMAX structure
- The concept of optimal prediction
o Canonical form
o Optimality
o Optimal prediction for ARMA/ARMAX processes
- Identification from data of ARX/ARMAX models
o LS identification
o ML identification
o Optimality
o Design of Experiment
o Optimal choice of model classes
- Kalman filtering
o The concept of SW-sensing
o Linear Kalman filtering
o Extended Kalman filter
o Kalman filter for Gray-box identification
- Data-preprocessing:
o Trend removal
o Period-components removal
o Missing-data
- Practical examples
- System Identification using Matlab
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