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We study target tracking with wireless sensor networks in its most basic form, assuming a binary sensing model in which each sensor can return only 1-bit information regarding target's presence or absence in its sensing range. A novel, real-time and distributed target tracking algorithm for imperfect binary sensing models is proposed, which is an extension of our previous work on the ideal binary sensing model. The algorithm estimates target's location, velocity and trajectory in a distributed and asynchronous manner. Extensive simulations show that our algorithm achieves high performance and outperforms other algorithms in terms of accuracy of the estimation of target's location, velocity and trajectory.