Extended Kalman filtering for state estimation of a Hill muscle model

The objectives of this study are five-fold: (i) design an extended Kalman filter (EKF) for the single-muscle and two-muscle Hill models; (ii) design an EKF for unknown-input estimation of the muscle models; (iii) investigate the detectability of the muscle models; (iv) examine the robustness of the EKF to modeling errors; and (v) improve state estimation by incorporating physical constraints into the estimator. Two noisy measurements are available for state estimation: muscle length, which is measured from joint angles; and muscle activation, which is measured from electromyography sensors. Simulation results verify that the EKF is an effective approach for estimation of the activation signals and the states of the system if the system is detectable; the EKF outperforms the high gain observer; and the EKF is robust to modeling errors. The standard deviations of the estimation errors are in the range 0.01–0.1 mm for the muscle lengths, which is one to two orders of magnitude more accurate than the measurements. The standard deviations of the dimensionless muscle activation estimation errors are in the range 0.01–0.02, which is one order of magnitude more accurate than the measurements. A projection approach accounts for constraints to further improve the estimates.