For the problem of tracking multiple targets, the joint probabilistic data association (JPDA) approach has shown to be very effective in handling clutter and missed detections. The JPDA, however, tends to coalesce neighboring tracks and ignores the coupling between those tracks. Fitzgerald [6] has shown that hypothesis pruning may be an effective way to prevent track coalescence. Unfortunately, this process leads to an undesired sensitivity to clutter and missed detections, and it does not support any coupling, To improve this situation, the paper follows a novel approach to combine the advantages of JPDA, coupling, and hypothesis pruning into new algorithms. First, the problem of multiple target tracking is embedded into one filtering for a linear descriptor system with stochastic coefficients. Next, for this descriptor system, the exact Bayesian and new JPDA filters are derived, Finally, through Monte Carlo simulations, it is shown that these new PDA tilters are able to handle coupling and insensitive to track coalescence, clutter, and missed detections.