Journal of Applied Mathematics
Volume 2012 (2012), Article ID 584140, 25 pages
Research Article

Convergence Analysis for the SMC-MeMBer and SMC-CBMeMBer Filters

1Ministry of Education Key Laboratory for Intelligent Networks and Network Security (MOE KLINNS), School of Electronics and Information Engineering, Xi'an Jiaotong University, Xi'an 710049, China
2Software Engineering School, Xi'an Jiaotong University, Xi’an 710049, China

Received 27 February 2012; Revised 15 May 2012; Accepted 22 May 2012

Academic Editor: Qiang Ling

Copyright © 2012 Feng Lian et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The convergence for the sequential Monte Carlo (SMC) implementations of the multitarget multi-Bernoulli (MeMBer) filter and cardinality-balanced MeMBer (CBMeMBer) filters is studied here. This paper proves that the SMC-MeMBer and SMC-CBMeMBer filters, respectively, converge to the true MeMBer and CBMeMBer filters in the mean-square sense and the corresponding bounds for the mean-square errors are given. The significance of this paper is in theory to present the convergence results of the SMC-MeMBer and SMC-CBMeMBer filters and the conditions under which the two filters satisfy mean-square convergence.