Filtering in hybrid dynamic Bayesian networks

We demonstrate experimentally that inference in a complex hybrid dynamic Bayesian network (DBN) is possible using the 2-time slice DBN (2T-DBN) from (D. Koller et al., Sequential Monte Carlo Methods in Practice: p.445-464, Springer-Verlag, NY, 2000) to model fault detection in a watertank system. In this, 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 (R. v.d. Merwe et al., Tech. Rep. CUED/F-INFENG/TR-380, Dept. of Eng., Cambridge Uni., 2000).