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Prof. Luigi Chisci, Università degli Studi di Firenze - Italy - "Linear and nonlinear Kalman filtering: theory and applications", 12,14,19,21 January 2021

16 hours (4 credits)


From remote by using Microsoft Teams. The link will be sent in due time to all students who registered to the seminar.

To register to the course, click here


Short Abstract:
This course aims to provide both theoretical and practical tools to tackle estimation problems encountered in several areas of engineering and science. In particular, it is shown how to formulate such estimation problems as instances of a general dynamical system state estimation problem and how to derive the mathematical solution of the latter problem. Then it is shown that, for a linear Gaussian system, such a solution yields the well-known Kalman filter. Further, approximate techniques (e.g. extended and unscented Kalman filters, particle filter, etc.) are presented for the case of nonlinear and/or non-Gaussian systems, for which an exact closed-form solution cannot be found. To conclude the theoretical part, theoretical limitations (i.e. the Cramer-Rao lower bound) on the quality of estimation are discussed. In the second part of the course, we illustrate some applications of linear/nonlinear Kalman filtering (e.g., tracking, robotic navigation, environmental data assimilation).

Course Contents in brief:

  1. A general dynamic estimation problem in state-space form
  2. Recursive Bayesian filtering
  3. Kalman filter as recursive Bayesian filter in the linear Gaussian case
  4. Beyond the Kalman filter: nonlinear filters for nonlinear and/or non-Gaussian estimation problems (extended Kalman filter, unscented Kalman filter, particle filter, Gaussian sum filter).
  5. Theoretical limits on the quality of estimation
  6. Applications to surveillance, robotic navigation and environmental data assimilation.


  1. January 12, 2021 – 9:30-12:45
  2. January 14 2021 –  9:30-12:45
  3. January 19, 2021 – 9:30-12:45
  4. January 21, 2021 – 9:30-12:45