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Underwater surveillance using passive sonar and track-before-detect technology requires accurate models of the tracked signal and the background noise. However, in an underwater environment, the signal channel is time-varying and prior knowledge about the spatial distribution of the background noise is unavailable. In this paper, an autoregressive model that captures a time-varying signal level caused by multi-path propagation is presented. In addition, a multi-source model is proposed to describe spatially distributed background noise. The models are used in a Bernoulli filter track-before-detect framework and evaluated using both simulated and sea trial data. The simulations demonstrate clear improvements in terms of target loss and improved ability to discern the target from the noisy background. An evaluation of the track-before-detect algorithm on the sea trial data indicates a performance gain when incorporating the proposed models in underwater surveillance and tracking problems.