Recursive Bayesian inference in dynamic models: Advances and applications

When analyzing noisy observation sequences of dynamical systems, various estimation problems arise depending on the application. These include statistical inference over the probability distributions of future, current, or past system states, as well as the estimation of the most likely states or state sequences. This work abstracts such problems in the framework of Bayesian inference to probabilistic state observation models. Both discrete-state and continuous-state models are considered, under Gaussian and non-Gaussian assumptions.
The thesis makes practical contributions to position tracking and trajectory decoding in wireless sensor networks, for example through the integration of geometric constraints into model parameters or through hierarchical data association for robust multiple object tracking with unlabeled observations. The main contribution is the development of foundational inference techniques. In contrast to existing methods, these techniques enable recursive decoding of coherent states or plausible state sequences for the general model case, whereas existing techniques are limited to special cases of discrete-state models or Gaussian models.
In the course of deriving these recursive Bayesian decoders, the problem of recursive Bayesian smoothing for mixture models was solved analytically, which had been considered open for over three decades.