1 Department of Informatics and Mathematical Modeling, Technical University of Denmark2 Cognitive Systems, Department of Informatics and Mathematical Modeling, Technical University of Denmark3 Copenhagen Center for Health Technology, Center, Technical University of Denmark
The two main focus areas of this thesis are State-Space Models and multi modal signal processing. The general State-Space Model is investigated and an addition to the class of sequential sampling methods is proposed. This new algorithm is denoted as the Parzen Particle Filter. Furthermore, the Markov Chain Monte Carlo (MCMC) approach to filtering is examined and a scheme for MCMC to be used in on-line applications is proposed. In estimating parameters, it is shown that the EM-algorithm exhibits slow convergence especially in the low noise limit. It is demonstrated how a general gradient optimizer can be applied to speed up convergence. The linear version of the State-Space Model, the Kalman Filter, is applied to multi modal signal processing. It is demonstrated how a State-Space Model can be used to map from speech to lip movements. Besides the State-Space Model and the multi modal application an information theoretic vector quantizer is also proposed. Based on interactions between particles, it is shown how a quantizing scheme based on an analytic cost function can be derived.
Markov Chain Monte Carlo; EM-algorithm; State-Space Models; Particle Filter