This paper represents the problem of tracking multiple maneuvering targets from possibly missing and false measurements as one of filtering for a jump-linear descriptor system with stochastic i.i.d. coefficients. This particular representation serves as an instrument in the characterization of the exact Bayesian filter. Subsequently, novel finite dimensional filter algorithms are developed through introducing approximations to the exact Bayesian solution. One filter approximation assumes conditionally Gaussian density of the joint target state given the joint target maneuver mode and the algorithm is referred to as joint IMM coupled PDA (JIMMCPDA). The specialty of this filter algorithm is that both the IMM step and the PDA step are performed jointly over the modes and states of all targets. Subsequently, the CPDA track-coalescence-avoiding hypothesis pruning approach of [Blom & Bloem (2000). Probabilistic data association avoiding track coalescence. IEEE Transactions of Automatic Control, 45, 247-259] is extended to bring the joint target modes into account. The resulting filter algorithm is referred to as track-coalescence-avoiding joint IMM coupled PDA. The two novel algorithms are compared to IMMJPDA and IMMPDA through Monte Carlo simulations. (c) 2005 Elsevier Ltd. All rights reserved.