The course will be held by prof. Eric Grivel (University of Bordeaux)
Date:
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SCHEDULE
EXAM: multiple-answer questionnaire at the end of the last lesson
ABSTRACT
This course provides an introduction to estimation problems based on Kalman filtering. This approach is used in a wide range of applications, including parameter estimation, speech enhancement, object tracking in radar applications, GPS navigation, and channel estimation in mobilecommunication systems. It is applied not only in statistical signal processing but also in the field of control. The course first focuses on the state-space representation of dynamical systems.
The Kalman filter is then introduced in the linear Gaussian case and subsequently extended to nonlinear Gaussian settings, for which several variants of the Kalman filter have been proposed. In particular, the Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF) are briefly presented and compared, with an emphasis on their underlying assumptions, approximation strategies, and respective advantages and limitations.
In the final part, the course examines estimation problems in which the system dynamics evolve over time. Multiple-model approaches are introduced to account for such non-stationary behaviors, with a particular focus on the Interacting Multiple Model (IMM). Note that the IMM can also be applied in situations where certain parameters of the state-space model are unknown. Moreover, since some parameters of the IMM—namely the transition probabilities between the different
assumptions made on the system model—must be set a priori but are not necessarily known, methods to estimate them over time will also be presented. The selection of the different models will likewise be discussed. Throughout the course, the concepts and algorithms are illustrated using object tracking scenarios.
BIO
Eric Grivel received his PhD in signal processing in 2000 in Bordeaux (France). He joined Bordeaux Institute of Technology (Bordeaux INP) in 2001 as an assistant professor and then as a professor in 2011. For more than 20 years, he has been with the Signal & Image research group at IMS lab (which is a joint research unit for the French National Center for Scientific Research CNRS, University of Bordeaux and Bordeaux INP). His research activities deal with statistical signal processing with applications in speech and audio processing, mobile communication systems, radar processing, GPS navigation and biomedical. From 2010 to 2017, he was the head of the Telecommunications department at ENSEIRB-MATMECA, one of the graduate schools of engineering at Bordeaux INP. From 2014 to 2022, he was in charge of the Scientific Interest Group with Thales, University of Bordeaux, University of Poitiers, University of Limoges, Bordeaux INP, INRIA and CNRS. From 2021 to 2025, he was the Vice Dean of the international relations of Bordeaux INP.