Particle Filtering Combined with Interval Methods for Tracking Applications

Abstract

This chapter introduces a new approach for sequential nonlinear estimation based on a combination of particle filtering and interval analysis. It presents the Box Particle Filter (Box‐PF) in its original ad hoc formulation and also a theoretical Bayesian interpretation of the Box‐PF. The chapter introduces the basic concepts of the interval analysis and interval methods, and provides an overview of the Bayesian inference methodology. It provides a theoretical derivation of the Box‐PF as a sum of uniform pdfs, and demonstrates the advantages of the Box‐PF over a dynamic localization example. The Box‐PF steps can be described as follows: box particle initialization, time update, measurement update, and resampling. The Box‐PF algorithm seems to be more adapted to real‐time applications in comparison with the PF. The Box‐PF can be classified between the PF method and the Gaussian mixture method in terms of number of samples or components needed.