Skeletal muscle system has nonlinear dynamics and subject-specific characteristics. Thus, it is essential to identify unknown parameters from noisy biomedical signals to improve the modeling accuracy in neuroprosthetic control. The objective of this work is to develop an experimental identification method for subject-specific biomechanical parameters of a physiological muscle model which can be employed to predict the nonlinear force properties of stimulated muscle. Our previously proposed muscle model, which can describe multi-scale physiological system based on the Hill and Huxley models, was used for the identification. The identification protocols were performed on two rabbit experiments, where the medial gastrocnemius was attached to a motorized lever system to record the force by the nerve stimulation. The muscle model was identified using nonlinear Kalman filters: Sigma-Point and Extended Kalman Filter. The identified model was evaluated by comparison with experimental measurements in cross-validation manner. The feasibility could be demonstrated by comparison between the estimated parameter and the measured value. The estimates with SPKF showed 5.7% and 2.9% error in each experiment with 7 different initial conditions. It reveals that SPKF has great advantage especially for the identification of multi-scale muscle model which accounts for the high nonlinearity and discontinuous states between muscle contraction and relaxation process.