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

Abstract

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.