Box particle filtering for nonlinear state estimation using interval analysis

In recent years particle …lters have been applied to a variety of state estimation problems. A particle …lter is a sequential Monte Carlo Bayesian estimator of the posterior density of the state using weighted particles. The e¢ ciency and accuracy of the …lter depend mostly on the number of particles used in the estimation and on the propagation function used to re-allocate weights to these particles at each iteration. If the imprecision, i.e. bias and noise, in the available information is high, the number of particles needs to be very large in order to obtain good performances. This may give rise to complexity problems for a real-time implementation. This kind of imprecision can easily be represented by interval data if the maximum error is known. Handling interval data is a new approach successfully applied to di¤erent real applications. In this paper, we propose an extension of the particle …lter algorithm able to handle interval data and using interval analysis and constraint satisfaction techniques. In standard particle …ltering, particles are punctual states associated with weights whose likelihoods are de…ned by a statistical model of the observation error. In the box particle …lter, particles are boxes associated with weights whose likelihood is de…ned by a bounded model of the observation error. Experiments using actual data for global localization of a vehicle show the usefulness and the e¢ ciency of the proposed approach. Key words: State …ltering and estimation; sensor fusion; particle …lter; Kalman …lter; interval analysis.