Recursive estimation methodologies, such as Kalman and Bayesian filters, typically require models of some kind to perform the estimation. This filtering process seeks to improve knowledge surrounding some quantities of interest, or states, over time by incorporation of imperfect observations. The models required pertain to the state dynamics, sensors from which measurements are obtained, and probabilistic models of the underlying stochastic processes. In addition to any number of necessary models, real-world application of a filter is normally accompanied by at least one, if not several, techniques to promote better performance. These methods vary in purpose from expanding the kinds of quantities that can be estimated, to reducing sensitivity in the presence of unexpected events and preventing degradation of numerical precision.
A more recently developed class of recursive filters, referred to as particle flow filters, introduce an update dynamics model to describe the evolution of the state probability density function (pdf) over the course of a measurement update. This is accomplished by moving particles, corresponding to samples of the a priori pdf, through the state space according to the update dynamics, or flow, model to approximate the a posteriori pdf given by Bayes’ rule. In doing so, the particle flow framework opens up new opportunities for improving filter performance by design of the flow model.
In this work, a new formulation of the Gaussian particle flow filter is presented using an information-theoretic approach. The developed information-based form advances the Gaussian particle flow framework in two ways: it imparts physical meaning in the flow dynamics and provides the ability to incorporate both well-established and novel methods for promoting better performance. The Gaussian information-based model is then leveraged to allow for the inclusion of Gaussian mixture models, resulting in a robust and adaptive filter framework that is demonstrated in three challenging estimation problems --Abstract, page iii
