# Stochastic processes : Estimation and prediction

LINMA1731  2018-2019  Louvain-la-Neuve

Stochastic processes : Estimation and prediction
5.0 credits
30.0 h + 30.0 h
2q

Teacher(s)
Language
Anglais
Online resources
Prerequisites
• LEPL1106 (or equivalent training in signals and systems)
• LEPL1108 (or equivalent training in probabilities and statistics)

The prerequisite(s) for this Teaching Unit (Unité d’enseignement – UE) for the programmes/courses that offer this Teaching Unit are specified at the end of this sheet.

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
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”.

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.
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.

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.
Bibliography

Course notes, written by the two lecturers, are available.

Faculty or entity

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

Program title
Sigle
Credits
Prerequisites
Aims
Master [120] in Electrical Engineering
5
-

Minor in Engineering Sciences: Applied Mathematics
5
-

Bachelor in Engineering