Particle Filtering Combined with Interval Methods for Tracking Applications [chapter]

Amadou Gning, Lyudmila Mihaylova, Fahed Abdallah, Branko Ristic
2014 Integrated Tracking, Classification, and Sensor Management  
This chapter presents a new approach combining the Bayesian framework with interval methods. When the system dynamics and measurement models have interval types of uncertainties, instead of point state estimates, guaranteed (interval) estimation is a promising approach. First, fundamental concepts from the interval analysis are introduced. Next, a Box Particle Filter (Box-PF) is presented and its theoretical derivation is given based on a mixture of uniform probability density functions. The
more » ... y functions. The efficiency of the Box-PF is significant compared with the generic sampling importance resampling particle filter (SIR PF). With few particles the Box-PF can achieve the same estimation accuracy that the SIR PF achieves with thousands of particles. The performance of the proposed Box-PF is studied and results over examples both with simulated and real data are presented. Introduction State estimation for complex stochastic systems, in the presence of non-Gaussian noisy measurements, is of paramount importance for many applications and has been actively investigated during the last decades. One of the most popular state estimation approaches is the Bayesian inference approach [1, 2] . Within the Bayesian framework the posterior probability density function (pdf) of the state of interest is calculated, conditioned on the available measurements. Among the Bayesian approaches different algorithms have been used such as the Extended Kalman Filter (EKF) [3], un-
doi:10.1002/9781118450550.ch02 fatcat:xcedj5njrfdjppd3frosg6nhwi