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Inference in 3D articulated human body tracking is challenging due to the high dimensionality and nonlinearity of the parameter-space. We propose a particle filter with Rao-Blackwellisation which marginalizes part of the state variables by exploiting the correlation between the right-side and the left-side joint Euler angles. The correlation is naturally induced by the symmetric and repetitive patterns in specific human activities. A novel algorithm is proposed to learn the correlation from the training data using partial least square regression. The learned correlation is then used as motion prior in designing the Rao-Blackwellised particle filter, which estimates only one group of state variables using the Monte Carlo method, leaving the other group being exactly computed through an analytical filter that utilizes the learned motion correlation. We evaluate the effectiveness of the motion correlation for 3D articulated human body tracking. The accuracy of the proposed 3D tracker is quantitatively assessed based on the distance between the true and the estimated marker positions. Extensive experiments with multi-camera walking sequences from the HumanEva-I/II data set show that (i) the proposed tracker achieves significantly lower estimation error than both the annealed particle filter and the standard particle filter; and (ii) the learned motion correlation generalizes well to motion performed by subjects other than the training subject.