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As it widely exists in applications as diverse as biomechanics, motion capture and robot control, the fundamental problem of articulated skeleton fitting, which is to fit an articulated skeleton to k frames of corresponding raw joint points under the fixed-bone-length constraint, is proposed in this paper. With different parametrization of the articulated skeleton, three types of potential solutions to the above problem are presented and compared. Special cases for this problem, including that generated under joint trajectory smoothness constraints and from weighted joints, are also discussed and analyzed. Based on the joint location parametrization and the sparse matrix techniques, we propose an efficient and accurate articulated skeleton fitting method (JLP2). Elaborate experiments and interesting applications in motion capture are presented to show its effectiveness.