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A box-particle filter (Box-PF) as a generalized particle filtering has a potential to process the measurements affected by bounded error of unknown distributions and biases. Inspired by the Box-PF, a novel implementation for multitarget tracking, called box-particle cardinality balanced multi-target multi-Bernoulli (Box-CBMeMBer) filter is presented in this paper. The approach can not only track multiple targets and estimate the unknown number of targets, but also handle three sources of uncertainty: stochastic, set-theoretic and data association uncertainty. The key advantage of the Box-CBMeMBer filter over the SMC-CBMeMBer filter is that it reduces the number of particles significantly when they reach the similar accurate results, leading to remarkablely decrease the runtime. Simulation results in the paper demonstrate it.