OPTIMAL FILTERING AND DATA ANALYSIS from Kolmogorov-Wiener to Kalman

Taking decisions in presence of uncertainty is a fundamental challenge for engineering. The problem may take a variety of facets, and is encountered not only in industry but also in physics, biology, economics, astronomy and so on. In this course some of the main facets are considered, with special reference to optimal prediction and filtering. The course is organized in three parts:

- Part I Kolmogorov-Wiener Prediction And Predictive Identification

Kolmogorov-Wiener prediction theory enables the determination of a predictor for a given time series or a given system with a simple procedure. The predictive approach to system identification is based on such a technique.

- Part II Kalman Filtering

Kalman filtering (KF) is one of the milestone achievements of the XX Century. It enables estimating an unknown variable by processing the snapshots of observable signals. Hence Kalman filtering provides a "virtual sensor", that is a device for the "virtual" measurement of non-directly accessible signals. The method relies on a state-space linear stochastic model of the underlying process or system. The theory has been extended to nonlinear models, leading to various methods such as the Extended KF (EKF) and the Particle Filter (PF).

- Part III Optimization of Uncertain Systems

The environment in which we live is beset with uncertainty. As a consequence, uncertainty is a fundamental ingredient that we have to take care of when setting up any decision theory and, specifically, theories aiming at optimizing the decision result. This part of the course will focus on optimization where uncertainty is accounted for by means of a sample of constraints directly built from experimental data (scenario approach).

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This course aims at providing a strong methodological basis on filtering and data analysis via a self-contained set of lectures, with a minimum requirement of pre-requisites. A number of real applications will be discussed.

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Lecture notes will be indicated during classes.

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Instructors: S. Bittanti(*), P. Bolzern(*), M. Campi(**) , G. De Nicolao (***) , S. Formentin(*), S. Garatti(*), , M. Prandini(*), S. M. Savaresi (*)

(*) Politecnico di Milano
(**) Università degli Studi di Brescia
(***) Università degli Studi di Pavia

Students will be asked to solve homeworks on the topics presented in the lectures.