We propose a particle filter acoustic tracker to track multiple maneuvering targets using a state space formulation with a locally linear motion model. The observations are a batch of direction-of-arrival (DOA) estimates at various frequencies. The data likelihood incorporates the possibility of missing data as well as Spurious DOA observations. By imposing smoothness constraints on the target motion, the particle filter is able to avoid data association problems. To make the filter computationally efficient, a proposal strategy based on approximating the full posterior with Newton's method is employed. Computer simulations show the algorithm's performance.