Bayesian Inference for Nonlinear Dynamical Systems : Applications and Software Implementation

Abstract: The topic of this thesis is estimation of nonlinear dynamical systems, focusing on the use of methods such as particle filtering and smoothing. There are three areas of contributions: software implementation, applications of nonlinear estimation and some theoretical extensions to existing algorithms. The common theme for all the work presented is the pyParticleEst software framework, which has been developed by the author. It is a generic software framework to assist in the application of particle methods to new problems, and to make it easy to implement and test new methods on existing problems. The theoretical contributions are extensions to existing methods, specifically the Auxiliary Particle Filter and the Metropolis Hastings Improved Particle Smoother, to handle mixed linear/nonlinear models using Rao Blackwellized methods. This work was motivated by the desire to have a coherent set of methods and model-classes in the software framework so that all algorithms can be applied to all applicable types of models. There are three applications of these methods discussed in the thesis. The first is the modeling of periodic autonomous signals by describing them as the output of a second order system. The second is nonlinear grey-box system identification of a quadruple-tank laboratory process. The third is simultaneous localization and mapping for indoor navigation using ultrasonic range-finders.