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The tracking problem of maneuvering target with an assumption that the maneuver is unknown and its acceleration has some abrupt changes is treated by formulating a general (nonlinear, non-Gaussian) state space model with the system model to describe the target dynamics and observation model to represent a measurement process of the target position. The Bayesian switching structure model, which includes a set of possible models and switches among them, is used to cope with the unknown maneuver. The heavy-tailed uni-modal distribution, e.g. Cauchy distribution, is also used for the system noise to accomplish good performance of tracking both the constant period and abrupt changing time point of acceleration. The Monte Carlo filter, which is a kind of particle filter that approximates state distribution by many particles in state spare, is used for state estimation of the model. A simple simulation study shows an improvement of performance by the proposed model comparing with a Gaussian case of the Bayesian switching structure model.