@MASTERSTHESIS\{IMM2003-02435,
    author       = "M. N. Andersen and R. {\O}. Andersen",
    title        = "Filtering in hybrid dynamic Bayesian networks",
    year         = "2003",
    keywords     = "Hybrid Bayesian Networks, Dynamic Bayesian Networks, Particle Filtering, Extended Kalman Filter, Unscented Kalman Filter, Markov Chain Monte Carlo",
    school       = "Informatics and Mathematical Modelling, Technical University of Denmark, {DTU}",
    address      = "Richard Petersens Plads, Building 321, {DK-}2800 Kgs. Lyngby",
    type         = "",
    note         = "Supervisor: Lars Kai Hansen",
    url          = "http://www2.compute.dtu.dk/pubdb/pubs/2435-full.html",
    abstract     = "In this thesis we describe the use of the Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), generic Particle Filter ({PF,} a.k.a. condensation, survival of the fittest, bootstrap filter, {SIR,} sequential Monte Carlo, etc.), Particle Filter with {MCMC} steps (PFMC), Particle Filter with {EKF} proposal (PFEKF) and {MCMC} steps (PFEKFMC), Particle Filter with {UKF} proposal (PFUKF) and {MCMC} steps (PFUKFMC) in theory as well as in a practical framework.

We present pseudo-code (from Merwe00) for all algorithms and implement the filters in a Dynamic Bayesian Network (DBN) framework using Matlab. Furthermore, we demonstrate and compare the implementations on a simple one-dimensional state estimation problem, a more complex simulation of a watertank system and finally on a real-life problem in which we use a cyberglove to infer the angle, angular velocity and angular acceleration of a single fingerjoint during movement and use these variables as hidden nodes in a {2T-DBN} with {EMG} measurements from the lower arm as observations. Furthermore, we show how the filters differ theoretically as well as practically and when and how their strengths and weaknesses become visual. Finally, we conclude which filters are superior under different conditions and in different practical scenarios.

Theory and implementation is based on the theory and pseudo-code presented in Merwe00.

Dansk abstract:

I dette eksamensprojekt pr{\ae}senteres the Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), generic Particle Filter ({PF,} a.k.a. condensation, survival of the fittest, bootstrap filter, {SIR,} sequential Monte Carlo, etc.), Particle Filter med {MCMC} steps (PFMC), Partice Filter med {EKF} proposal (PFEKF) og {MCMC} steps (PFEKFMC), Particle Filter med {UKF} proposal (PFUKF) og {MCMC} steps (PFUKFMC).

En teoretisk gennemgang af filtrene afsluttes med opskrivning af pseudo-koden (fra Merwe00) for en implementering af det enkelte filter.

Desuden implementeres de forskellige filtre i et Dynamisk Bayesiansk netv{\ae}rks (DBN) framework vha. Matlab og vi demonstrerer og sammenligner teknikkerne vha. et simpelt en-dimensionalt state estimations problem og en st{\o}rre og mere kompleks simulation af et vandtankssystem. Endelig anvendes udvalgte filtre p{\aa} et problem fra den virkelige verden, hvor vi anvender en cyberglove til at inferere vinkel, vinkelhastighed og vinkelacceleration for et enkelt fingerled i bev{\ae}gelse og anvender disse variable som skjulte knuder i et {2T-DBN} med {EMG} m{\aa}linger fra underarmen som observationer."
}