Theory of Generalized Particle Filtering

In the past decade, particle filtering has generated astounding interest among engineers and scientists with its capacity to process data that are modeled by dynamic systems. These methods belong to the family of procedures for sequential signal processing where the objectives are to filter, predict, or smooth unknown and time-varying signals from available observations. The general area of work in this research effort is the building of a new class of particle filters, the development of their theory, and their application to a number of important tasks. The known particle filtering methods require a mathematical representation of the system dynamics and assumptions about the state transition probability distribution function, and the likelihood of the states. These probabilistic assumptions are often inaccurate and made out of convenience, and in many cases lead to formidable degradations in performance of the particle filters. We develop a more general class of particle filters which do not use probabilistic model assumptions. Instead, the new filters are based on discrete measures defined by particle streams and associated costs that are sequentially updated. With the developed theory, we are able to build particle filters that are simpler, more accurate, more robust, and more flexible than the conventional ones. The standard particle filters, however, are particular instances of the new filters. We investigate in great detail various important issues including the foundations of the new filters, their convergence, connections of the new theory with existing theories, and its extensions to batch type signal processing. The filters are tested on various challenging problems.