# Stochastic processes : Estimation and prediction

linma1731  2022-2023  Louvain-la-Neuve

Stochastic processes : Estimation and prediction
5.00 credits
30.0 h + 30.0 h
Q2
Teacher(s)
Absil Pierre-Antoine; Vandendorpe Luc; Wiame Charles (compensates Vandendorpe Luc);
Language
Prerequisites
• LEPL1106 (or equivalent training in signals and systems)
• LEPL1108 (or equivalent training in probabilities and statistics)
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.
Learning outcomes
 At the end of this learning unit, the student is able to : 1 1.1; 1.2; 1.3 3.1; 3.2; 3.3 4.2 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 performances ; Synthetize predictors, filters and smoothers, in both Wiener or Kalman frameworks.
Content
• Part 1 - Estimation: probability theory (reminder), Fisher and Bayesian estimation, bias, covariance, mean square error, Cramér--Rao bound, asymptotic properties, classical estimators (maximum likelihood, best linear unbiased, maximum a posteriori, conditional mean...), hidden Markov model, nonlinear filtering, particle filtering, Kalman filter.
• Part 2 - Stochastic Processes and LTI Filters: complex random variables, stochastic processes, stationarity, ergodism, autocovariance, power spectral density, transformation by LTI systems, white noise, spectral factorization, finite-dimensional models (AR, MA, ARMA...), Wiener filter.
Teaching methods
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.
Evaluation methods
• Project during the course semester (40% of the final mark)
• Exam (60% of the final mark)
• Other activities, such as quizzes and homework exercises, can be taken into account in the project grade
• In case of a second session the mark obtained for the project remains unchanged with respect to that of the first session; the project cannot be redone for the second session.
Precisions are given in the course outline (plan de cours) available on Moodle.
Online resources
Bibliography
Les notes de cours des co-titulaires sont disponibles.
Faculty or entity

#### Programmes / formations proposant cette unité d'enseignement (UE)

Title of the programme
Sigle
Credits
Prerequisites
Learning outcomes
Minor in Applied Mathematics

Specialization track in Applied Mathematics