Particle filter for state estimation of jump Markov nonlinear system with application to multi-targets tracking

Abstract

In this article, we first introduce the problem of state estimation of jump Markov nonlinear systems (JMNSs). Since the density evolution method for predictor equations satisfies Fokker–Planck–Kolmogorov equation (FPKE) in Bayes estimation, the FPKE in conjunction with Bayes’ conditional density update formula can provide optimal estimation for a general continuous-discrete nonlinear filtering problem. It is well known that the analytical solution of the FPKE and Bayes’ formula is extremely difficult to obtain except a few special cases. Hence, we try to design a particle filter to achieve Bayes estimation of the JMNSs. In order to test the viability of our algorithm, we apply it to multiple targets tracking in video surveillance. Before starting simulation, we introduce the ‘birth’ and ‘death’ description of targets, targets’ transitional probability model, and observation probability. The experiment results show good performance of our proposed filter for multiple targets tracking.

Keywords:

• particle filter
• jump Markov nonlinear system
• Bayes estimation
• multi-targets tracking

Acknowledgements

This study was supported in part by the Key Project of the National Nature Science Foundation of China (no. 61 134 009), the National Nature Science Foundation of China (no. 60 975 059), Specialised Research Fund for the Doctoral Program of Higher Education from Ministry of Education of China (no. 20 090 075 110 002), Specialised Research Fund for Shanghai Leading Talents and Project of the Shanghai Committee of Science and Technology (nos. 11XD1400100, 11JC1400200, 10JC1400200, 10DZ0506500).