Stochastic processes : Estimation and prediction

linma1731  2017-2018  Louvain-la-Neuve

Stochastic processes : Estimation and prediction
5 credits
30.0 h + 30.0 h
Q2
Teacher(s)
Absil Pierre-Antoine; Vandendorpe Luc coordinator;
Language
English
Prerequisites
  • FSAB1106 (or equivalent training in signals and systems)
  • FSAB1105 (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.
Online resources
http:// http://moodleucl.uclouvain.be/course/view.php?id=4753
Bibliography
Les notes de cours des co-titulaires sont disponibles.
Faculty or entity
MAP


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

Title of the programme
Sigle
Credits
Prerequisites
Aims
Master [120] in Electrical Engineering
ELEC2M
5
Master [120] in Statistics: General
STAT2M
5
Minor in Engineering Sciences: Applied Mathematics
LMAP100I
5
Additionnal module in Mathematics
LMATH100P
5
Additionnal module in Mathematics
TMATH100P
5