Aims

At the end of this course, the students will be able to :
- Have a good understanding of and familiarity with random variables and stochastic processes ;
- Characterize and use stable processes and their spectral properties;
- Use the major estimators, and characterize their performences ;
- Synthetize predictors, filters and smoothers, in both Wiener or Kalman frameworks.

Main themes

The object of this course is to lead to a good understanding of stochastic processes, their most commonly used models and their properties, as well as the derivation of some of the most commonly used estimators for such processes : Wiener and Kalman filters, predictors and smoothers.

Content and teaching methods

The course is subdivided into four parts/chapters:
-Probabilities, random variables, moments, change of variables.
-Stochastic processes, independence, stability, ergodicity, spectral representation, classical models of stochastic processes.
-Estimation (for random variables) : biais, variance, bounds, convergence, asymptotic properties, classical estimators.
-Estimation (for random processes) : filtering, prediction, smoothing, Wiener and Kalman estimators.
-Learning will be based on courses interlaced with practical exercise sessions (exercises done in class or in the computer room using MATLAB). In addition, the training includes a project to be realized by groups of 2 or 3 students.

Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

-Prerequisite : INMA 2701 Mathématiques appliquées : signaux et systèmes

-Support : course notes, written by the two lecturers, are made available.

-Evaluation method : The evaluation will be based on a written exam made up of a few exercises (with use of the course textbook), and on an interview about the student's project.

Programmes in which this activity is taught

Other credits in programs