On the Performance of the Box Particle Filter for Extended Object Tracking Using Laser Data Nikolay Petrov 1 , Martin Ulmke 2 , Lyudmila Mihaylova 1 , Amadou Gning ♮ , Marek Schikora 2 , Monika Wieneke 2 and Wolfgang Koch 2 1 School of Computing and Communications, Lancaster University, United Kingdom 2 Department of Sensor Data and Information Fusion, Fraunhofer FKIE, Wachtberg 53343 Germany ♮ Department of Computer Science, University College London, United Kingdom E-mails: n.petrov@lancs.ac.uk, martin.ulmke@fkie.fraunhofer.de, mila.mihaylova@lancs.ac.uk, a.gning@cs.ucl.ac.uk Abstract—This paper considers the challenging task of real- time extended object tracking using cluttered measurements from laser range scanners. The performance of the recently proposed Box Particle Filter (Box PF) algorithm is evaluated utilising real measurements from laser range scanners obtained within a prototype security system replicating an airport corridor. The problem is expressed as the joint estimation of both state and parameters of an extended target. Circularly and elliptically shaped targets are considered. Promising results are presented. I. I NTRODUCTION The problem of tracking an extended object has been extensively studied in the recent years. Such objects of interest could be individual targets or a formation (considered as one target) such as a convoy of vehicles, a formation of aircrafts, a fleet of ships, a crowd of people, etc. The particularity here is that such objects are giving rise to many measurements and need sophisticated methods to cope with them. The proximity of the object and the resolution of the sensors may often be sufficient for the observer to infer some valuable information from the measurements about the shape and the size of the target’s extent. Usually the problem is formulated as a joint estimation of kinematic states and parameters, where the parameters relate to the extent of the object of interest [1], [2], [3], [4], [5], [6], [7] and the main methodology is the Bayesian framework. Various filters have been developed for extended target tracking: particle track-before-detect filters [8], cluster based approaches [9], [10], Poisson spatial models combined with particle filters (PFs) [11], [12], [13], [14] and mixture Kalman filters combined with data augmentation [1]. Recently various Probabilistic Hypothesis Density (PHD) filters for extended object tracking have been proposed, i.e. [15]. As an alternative, various interval algorithms have been developed, mainly for linear systems and linear mea- surements [16], [17], [18]. This paper proposes a Box Particle Filter (Box PF) framework for extended object tracking. The Box Particle filter is developed in [19] and applied for lo- calisation problems. The theoretical justification of the Box PF approach is derived in [20], [21]. The Box PF has also been applied to filtering problems within the random finite set statistics approach in [22] and in particular as a more efficient implementation of a Bernouli PF. In the present paper the Box PF addresses the problem of extended target tracking. The main contribution of this work is in presenting a general form for calculating the likelihood function based on solving a Constraint Satisfaction Problem (CSP) and the performance evaluation of the algorithm using real data from laser range scanners. The rest of this paper is organised as follows. Section II gives the main idea behind the Box PF. Section III presents the formulation of the problem within the Bayesian framework. Section IV introduces the necessary theoretical background from interval analysis. The Box Particle Filtering algorithm for extended target tracking is presented in Section V. The evaluation scenarios are described in Section VI, the results are given in Section VII and the conclusions in Section VIII. II. MAIN I DEA OF THE BOX PARTICLE FILTERING The main idea of the Box PF is to replace the point particles with region-particles, also called boxes. This approach is suitable for dealing with various types of uncertainties in the measurements: i.e. interval, stochastic and data association uncertainties [22]. These three types of uncertainties can be dealt with the same prediction and correction steps as in the case with the generic PF. However, there are some significant differences. The prediction step is performed in a similar way as in the classical PF, however, it is with respect to box particles. When a box particle is propagated via a non-linear function, the image of it is not necessarily a box particle. Hence, a function, called inclusion function, introduced in the previous section, is applied to convert the predicted region into a box particle. The measurement update step requires the calculation of the generalised likelihood function. Since the measurement noise is supposed to be bounded, a likelihood box is defined as a set containing the measurement and the noise boundaries. This generalised measurement likelihood function is calculated in a different way compared to the classical PF [23]. The measurement update step is based on finding the minimum boxes inside the box particles, consistent with the likelihood box. This is done with a procedure called contraction which