Stochastic processes : Estimation and prediction [ LINMA1731 ]

• FSAB1106 (or equivalent training in signals and systems)
• FSAB1105 (or equivalent training in probabilities and statistics)

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.

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.

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.

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.

- Prerequisites :

• FSAB1106 (or equivalent training in signals and systems)
• FSAB1105 (or equivalent training in probabilities and statistics)

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