STUDIA Z AUTOMATYKI I INFORMATYKI TOM 38 – 2013 Piotr Kozierski * , Marcin Lis † , Joanna Zi˛ etkiewicz ‡ RESAMPLING IN PARTICLE FILTERING – COMPARISON 1. I NTRODUCTION The Particle Filter (PF) method is becoming increasingly popular. Is often used especially for complex objects where other methods fail. The origins of particle filter are associated with introduction of resampling [6]. Previously, some methods without resampling were known (SIS – Sequential Importance Sampling), but the drawback was degeneration (the algorithm can work for a few iterations only). One can find a lot of resampling versions in the references. The purpose of this article is to bring together as many resampling methods as possible and their comparison. In second Section, Particle Filter principle of operation has been described. In third Sec- tion, different resampling methods have been shown with pseudo-code for every method pro- vided. Fourth Section describes how simulations have been performed and contains results. Conclusions and summary of the whole article are in last Section. 2. PARTICLE FILTER PF principle of operation is based on Bayes filter posterior    p  x (k) |Y (k)  = likelihood    p  y (k) |x (k)  · prior    p  x (k) |Y (k-1)  p  y (k) |Y (k-1)     evidence , (1) where: x (k) – vector of object state in k-th time step, y (k) – vector of measurements in k-th time step, Y (k) – set of measurements from beginning to k-th time step. Evidence in (1) is a normalizing coefficient, so it can be written as posterior    p  x (k) |Y (k)  ∝ likelihood    p  y (k) |x (k)  · prior    p  x (k) |Y (k-1)  , (2) ∗ Poznan University of Technology, Faculty of Electrical Engineering, Institute of Control and Information Engi- neering, Piotrowo 3a street, 60-965 Pozna´ n, e-mail: piotr.kozierski@gmail.com † Poznan University of Technology, Faculty of Electrical Engineering, Institute of Electrical Engineering and Electronics, Piotrowo 3a street, 60-965 Pozna´ n, e-mail: mail.dla.studenta@gmail.com ‡ Poznan University of Technology, Faculty of Electrical Engineering, Institute of Control and Information Engi- neering, Piotrowo 3a street, 60-965 Pozna´ n, e-mail: joanna.zietkiewicz@put.poznan.pl c  Pozna´ nskie Towarzystwo Przyjaciól Nauk 2013, sait.cie.put.poznan.pl