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A particle-based track-before-detect filtering algorithm is presented. This algorithm incorporates the Swerling family of target amplitude fluctuation models in order to capture the effect of radar cross-section changes that a target would present to a sensor over time. The filter is designed with an existence variable, to determine the presence of a target in the data, and an efficient method of incorporating this variable in a particle filter scheme is developed. Results of the algorithm on simulated data show a significant gain in detection performance through accurately modelling the target amplitude fluctuations.