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This paper presents a Bayesian approach for tracking the directions-of-arrival (DOAs) of multiple wideband moving targets using a linear, passive sensor array, for use in smart antenna wireless applications, for example. A novel form of posterior distribution describing the parameters of the received signal is developed. The nuisance parameters (source amplitudes and variances) of this distribution are integrated out to form a more computationally efficient estimator. The desired parameters are then tracked using particle filtering techniques. Simulation results demonstrate the effectiveness and robustness of this method.