Electromyography (EMG) has been widely used as control commands for prosthesis, powered exoskeletons and rehabilitative robots. In this paper, an EMG-driven state space model is developed to estimate continuous joint angular displacement and velocity, demonstrated by elbow flexion/ extension. The model combines the Hill-based muscle model with the forward dynamics of joint movement, in which kinematic variables are expressed as a function of neural activation levels. EMG features including integral of absolute value and waveform length are then extracted, and two quadratic equations which associate the kinematic variables with EMG features are constructed to represent the measurement equation. The proposed model are verified by extensively experiments, where the angular movements of human elbow joint are estimated only using the EMG signals, and the estimations are compared with the IMU measurements to validate the accuracy. As a demonstration, a robotic arm is commanded to follow the human elbow movement estimated by the proposed model, which shows the possibility of EMG-based robotic assisted rehabilitation.