Framework of belief condensation filtering and deterministic discrete filters

Inferring a sequence of variables from observations is a prevalent task in a multitude of applications. However, in some nonlinear or non-Gaussian scenarios, traditional techniques such as Kalman filters (KFs) and particle filters (PFs) fail to provide satisfactory performance. Moreover, there is a lack of a unifying framework for the analysis and development of different filtering techniques. In this paper, we present a general framework for filtering that allows to formulate an optimality criterium leading to the concept of belief condensation filtering (BCF). Moreover, we develop discrete BCFs that are optimal under such framework. Finally, simulation results are presented for the important filtering task that arises in ultrawide bandwidth (UWB) ranging. We show that BCF can obtain accuracies approaching the theoretical benchmark but with a smaller complexity than PFs.