Afterwards one is able to:
- Analyze jointly Gaussian processes and determine optimal linear estimators
- Build, analyse and implement (extended) Kalman filters for a given (non-)linear system
- Explain the mathematical principles behind particle filtering (PF)
- Reformulate estimation problems in terms of PF and implement it using computer software such as MATLAB.
This course deals with the complexity of describing random, time-varying functions. This knowledge is essential for stochastic modeling. The course further zooms in on the stochastic filtering problem, where the main goal is to estimate an unknown stochastic process from related observations. This has many applications. For instance, if GPS data tells us the position of a car at certain moments in time then with filtering we can predict where the car might be 30 seconds later, even if the GPS data itself is not fully reliable. The course covers in detail the famous Kalman filter (KF). It is used in navigation and control of aircrafts but also in economics and finance and biomedical engineering. A full treatment of the Kalman filter is provided and some variations of it, most notably the extended Kalman filter (EKF) which is applicable to nonlinear models where KF is not. The course also treats the theory of particle filter (PF), a Monte Carlo based simulation technique that has recently emerged as an alternative to EKF or any other variation of KF. It is highly effective in practice and can accommodate in the model almost any sort of nonlinearity and almost any sort of process noise. To be able to treat these filtering techniques, we shall first learn some concepts from measure theoretic probability, conditional probability distribution and projection theory.|
Obligatory prior knowledge: Basic knowledge of “Probability and Statistics” as covered in the modules Signalen en Onzekerheid (201300182) and Statistiek en Analyse (201400218).
Desired prior knowledge: Basics of “Systems Theory” as covered in the module Dynamische Systemen (201500103) and the basic knowledge of MATLAB.