The calculation of marginal association probabilities is the major computational bottleneck in the Joint
Probabilistic Data Association Filter (JPDAF). In this paper, we investigate approximations for the marginal associations that simplify the (computational complex) original association model in order to obtain efficient algorithms. In this context, we first discuss the Bakhtiar-Alavi algorithm and the Linear Multitarget Integrated Probabilistic Data Association (LMIPDA) algorithm. Second, we propose a fast novel approximation that exploits systematic combinations of the JPDAF measurement model with the Probabilistic Multi-Hypothesis Tracker (PMHT) measurement model. The discussed methods are evaluated by means of a tracking scenario with a high number of closely-spaced targets.