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Track-before-detect (TBD) aims at tracking trajectories of a target prior to detection by integrating raw measurements over time. Many TBD algorithms have been developed in the literature, based on the Hough Transform, Dynamic Programming or Maximum Likelihood estimation. However these methods fail in the case of maneuvering targets and/or non straight-line motion, or become very computationally expensive when the SNR gets low. Other techniques are based on the so-called switching or jump-Markov state-space system (JMSS) model. However, a drawback of JMSS is that it is not possible to perform exact Bayesian restoration. As a consequence, one has to resort to approximations such as particle filtering (PF). In this paper we propose an alternative method to approximate the optimal filter, which does not make use of Monte Carlo approximation. Our method is validated by computer simulations.