Monitoring non-linear and switching dynamical systems
This thesis discusses monitoring tasks in a.o. industrial processes as inference problems in non-linear and switching dynamical systems. These inference problems are notoriously hard. In the thesis several novel approximation schemes are introduced. Contributions to the inference problem in switching systems include the analysis of expectation propagation for the switching linear dynamical system, a description of the link between expectation propagation and a Bethe free energy with weak consistency constraints, and a generalization of this framework. For a certain class of non-linear systems a proof is given that approximations based on local linearizations will always fail. An efficient new algorithm is presented that strongly resembles particle filtering, but which includes an equivalent smoother.