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A Rao-Blackwellised particle filter is used in the estimation of the parameters of a linear stochastic state space model. The proposed method combines the particle filtering technique with a Kalman filter using marginalisation so as to make full use of the analytically tractable structure of the model. Simulation studies are performed on a simple illustrative example and the results demonstrate the effectiveness of the proposed method in comparison with the conventional extended-Kalman-filter-based method. The proposed method is then applied in the estimation of the parameters in a railway vehicle dynamic model for condition monitoring and the desired results have been obtained.