Topics in Particle Filtering and Smoothing

Particle filtering/smoothing is a relatively new promising class of algorithms to deal with the estimation problems in nonlinear and/or non- Gaussian systems. Currently, this is a very active area of research and there are many issues that are not either properly addressed or are still open. One of the key issues in particle filtering is a suitable choice of the importance function. The optimal importance function which includes the information from the most recent observation, is difficult to obtain in most practical situations. In this thesis, we present a new Gaussian approximation to this optimal importance function using the moment matching method and compare it with some other recently proposed importance functions. In particle filtering/smoothing, the posterior is represented as a weighted particle cloud. We develop a new algorithm for extracting the smoothed marginal maximum a posteriori (MAP) estimate from the available particle cloud of the marginal smoother, generated using either the forwardbackward smoother or the two filter smoother. The smoothed marginal MAP estimator is then applied to estimate the unknown initial state of a dynamic system. There are many approaches to deal with the unknown static system parameters within particle filtering/smoothing set up. One common approach is to model the parameters as a part of the state vector. This is followed by adding artificial process noises to this model and then estimate the parameters along with the other state variables. Although this approach may work well in (certain) practical situations, the added process noises may result in a unnecessary loss of accuracy of the estimated parameters. Here we propose some new particle filtering/smoothing based algorithms, where we avoid any effect of the artificial dynamics on the estimate of the parameters.