Linear and Nonlinear Filtering

Objectifs

Master the theoretical foundations of the Kalman filter and its extensions.

Understand the linear and non-linear filtering algorithms derived from it.

Use what you’ve learned to illustrate its uses in different engineering applications.

Plan

1: Bayesian estimation: importance and consideration of a priori information, minimum variance estimator and conditional distribution, conditioning in Gaussian random vectors.

2: Linear Gaussian systems: Kalman filter and smoother.

3: Non-linear systems: sub-optimal filters obtained by linearization (extended Kalman filter) or by Gaussian approximation.

4: General state models: Bayesian filter and Monte Carlo approximation (particle filter).

5: Illustration of the problem and implementation of algorithms.

Prérequis

Markov chains