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This paper proposes a marginal multi-object Bayesian filter with multiple hypotheses to track multiple objects in the presence of object appearing and object disappearing, missed detection and clutter. This filter delivers the probability of existence and probability density function of each object. A mathematical model for searching K-best hypotheses is set up by the maximization of the generalized joint likelihood ratios of hypotheses, which results in a 2-dimensional assignment problem. The K-best hypotheses can be acquired by using the Murty algorithm to solve the 2-dimensional assignment problem. According to the K-best hypotheses, the existence probabilities and probability density functions of objects are formed. Furthermore, an implementation of this filter for a linear Gaussian system is developed and is extended to nonlinear observations. Experimental result demonstrates that the proposed filter outperforms other available filters at various numbers of clutter and different detecting probabilities. [ABSTRACT FROM AUTHOR]