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As a generalized particle filtering, the box-particle filter (Box-PF) 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 multi-target tracking, called box-particle cardinality balanced multi-target multi-Bernoulli (Box-CBMeMBer) filter is presented in this paper. More important, to eliminate the negative effect of clutters in the estimation of the numbers of targets, an improved generalized likelihood is derived. 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 advantage of the Box-CBMeMBer filter over the SMC- CBMeMBer filter is that it reduces the number of particles significantly when they reach similar accurate results and therefore remarkably decreases the runtime. The numerical study demonstrates it.