LINMA1731: Stochastic processes: Estimation and prediction

This is the public website for the Université catholique de Louvain course LINMA1731 Stochastic processes: Estimation and prediction. This page is unofficial and for informational purposes only. Enrolled students should consult the course website hosted on Moodle.

Course description

This course will cover fundamental aspects of estimation theory. Topics include:

  • Minimum variance unbiased estimation & Cramer-Rao bound

  • Fisher estimation

  • Bayesian estimation

  • Kalman filters

  • Bayes filters

  • Particle filters

Learning outcomes

At the end of the course, the student will be able to:

  • Design Fisher and Bayes estimators and characterize their performance

  • Synthetize Kalman filters

  • Synthetize predictors, filters and smoothers, in both Wiener or Kalman frameworks.

Exercise sessions

The exercise sessions will cover exercise sets supervised by a TA to help practice the theoretical concepts seen in class.

Tentative schedule

Week Description
1 Course introduction & probability review
2 MVU Estimation and Cramer-Rao Bound
3 Fisher estimators
4 Bayesian estimators
5 Kalman filter & Bayes Filter
6 Particle filter
7 Project & Particle filter implementation
8 Stochastic processes (offered by Luc Vandendorpe)
9 Stochastic processes PT2 (offered by Luc Vandendorpe)
10 Spectral factorization and finite-dimensional models (offered by Luc Vandendorpe)
11 Filtering, prediction and smoothing (Wiener) (offered by Luc Vandendorpe)

Textbooks

  • S. M. Kay, “Statistical signal processing: estimation theory.” Prentice Hall, 1993.