Stochastic processes : Estimation and prediction

linma1731  2020-2021  Louvain-la-Neuve

Stochastic processes : Estimation and prediction
Due to the COVID-19 crisis, the information below is subject to change until September 13, in particular that concerning the teaching mode (presential, distance or in a comodal or hybrid format).
5 credits
30.0 h + 30.0 h
Q2
Teacher(s)
Language
English
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.
Aims

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.
 

The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the programme(s) can be accessed at the end of this sheet, in the section entitled “Programmes/courses offering this Teaching Unit”.
Content
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.
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
  • Exam
  • Other activities, such as quizzes and homework exercises, can be taken into account in the final grade.
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
Aims
Master [120] in Electrical Engineering

Minor in Engineering Sciences: Applied Mathematics (only available for reenrolment)

Specialization track in Applied Mathematics

Minor in Applied Mathematics