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Stochastic processes : Estimation and prediction [ LINMA1731 ]


5.0 crédits ECTS  30.0 h + 30.0 h   2q 

Teacher(s) Absil Pierre-Antoine ; Vandendorpe Luc (coordinator) ;
Language French
Place
of the course
Louvain-la-Neuve
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 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 methods

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.

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. -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.

Other information

- 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.

Cycle et année
d'étude
> Bachelor in Mathematics
> Master [120] in Statistics: General
> Bachelor in Psychology and Education: General
> Bachelor in Information and Communication
> Bachelor in Philosophy
> Bachelor in Engineering : Architecture
> Bachelor in Computer Science
> Bachelor in Economics and Management
> Bachelor in Motor skills : General
> Bachelor in Human and Social Sciences
> Bachelor in Sociology and Anthropology
> Bachelor in Political Sciences: General
> Bachelor in Biomedicine
> Bachelor in Engineering
> Bachelor in Pharmacy
> Bachelor in Religious Studies
> Master [120] in Computer Science and Engineering
> Master [120] in Electrical Engineering
Faculty or entity
in charge
> MAP


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