@MISC\{IMM2004-03171,
    author       = "M. N. Andersen and R. {\O}. Andersen and K. Wheeler",
    title        = "Filtering in hybrid dynamic Bayesian networks (center)",
    year         = "2004",
    month        = "may",
    keywords     = "Hybrid dynamic Bayeian networks, particle filtering, extended Kalman filter, unscented Kalman filter, Rao-Blackwellisation",
    publisher    = "",
    address      = "",
    url          = "http://www2.compute.dtu.dk/pubdb/pubs/3171-full.html",
    abstract     = "We demonstrate experimentally that inference in a complex hybrid Dynamic Bayesian Network (DBN) is possible using the {2-}Time Slice {DBN} (2T-DBN) from (Koller \& Lerner, 2000) to model fault detection in a watertank system. In (Koller \& Lerner, 2000) a generic Particle Filter (PF) is used for inference. We extend the experiment and perform approximate inference using The Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF). Furthermore, we combine these techniques in a 'non-strict' Rao-Blackwellisation framework and apply it to the watertank system. We show that {UKF} and {UKF} in a {PF} framework outperform the generic {PF,} {EKF} and {EKF} in a {PF} framework with respect to accuracy and robustness in terms of estimation {RMSE} (root-mean-square error). Especially we demonstrate the superiority of {UKF} in a {PF} framework when our beliefs of how data was generated are wrong. We also show that the choice of network structure is very important for the performance of the generic {PF} and the {EKF} algorithms, but not for the {UKF} algorithms. Furthermore, we investigate the influence of data noise in the watertank simulation. Theory and implementation is based on the theory presented in (v.d. Merwe et al., 2000)."
}