The problem of maintaining tracks of multiple maneuvering targets from unassociated measurements is formulated as a problem of estimating the hybrid state of a Markov jump linear system from measurements made by a descriptor system with independent, identically distributed (i.i.d.) stochastic coefficients. This characterization is exploited to derive the exact equation for the Bayesian recursive filter, to develop two novel Sampling Importance Resampling (SIR) type particle filters, and to derive approximate Bayesian filters which use for each target one Gaussian per maneuver mode. The two approximate Bayesian filters are a compact and a track-coalescence avoiding version of Interacting Multiple Model Joint Probabilistic Data Association (IMMJPDA). The relation of each of the four novel filter algorithms to the literature is well explained. Through Monte Carlo simulations for a two target example, these four filters are compared to each other and to the approach of using one IMMPDA filter per target track. The Monte Carlo simulation results show that each of the four novel filters clearly outperforms the IMMPDA approach. The results also show under which conditions the IMMJPDA type filters perform close to exact Bayesian filtering, and under which conditions not.