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Real-time muscle state estimation from EMG signals during isometric contractions using Kalman filters

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Abstract

State-space control of myoelectric devices and real-time visualization of muscle forces in virtual rehabilitation require measuring or estimating muscle dynamic states: neuromuscular activation, tendon force and muscle length. This paper investigates whether regular (KF) and extended Kalman filters (eKF), derived directly from Hill-type muscle mechanics equations, can be used as real-time muscle state estimators for isometric contractions using raw electromyography signals (EMG) as the only available measurement. The estimators’ amplitude error, computational cost, filtering lags and smoothness are compared with usual EMG-driven analysis, performed offline, by integrating the nonlinear Hill-type muscle model differential equations (offline simulations—OS). EMG activity of the three triceps surae components (soleus, gastrocnemius medialis and gastrocnemius lateralis), in three torque levels, was collected for ten subjects. The actualization interval (AI) between two updates of the KF and eKF was also varied. The results show that computational costs are significantly reduced (70x for KF and 17\(\times \) for eKF). The filtering lags presented sharp linear relationships with the AI (0–300 ms), depending on the state and activation level. Under maximum excitation, amplitude errors varied in the range 10–24% for activation, 5–8% for tendon force and 1.4–1.8% for muscle length, reducing linearly with the excitation level. Smoothness, measured by the ratio between the average standard variations of KF/eKF and OS estimations, was greatly reduced for activation but converged exponentially to 1 for the other states by increasing AI. Compared to regular KF, extended KF does not seem to improve estimation accuracy significantly. Depending on the particular application requirements, the most appropriate KF actualization interval can be selected.

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Acknowledgements

The author is gratefully acknowledged to Brazilian Federal Agencies CAPES, CNPq and FINEP, as well as to Rio de Janeiro State Agency FAPERJ, for financial support. The author thanks Prof. Liliam Oliveira for helping with data collection and statistical analysis.

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  1. Biomedical Engineering Program, Alberto Luiz Coimbra Institute for Graduate Studies and Research in Engineering (PEB/COPPE), Federal University of Rio de Janeiro, Av. Horacio Macedo 2030, Bloco H-338, Rio de Janeiro, 21941-914, Brazil

    Luciano L. Menegaldo

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Correspondence to Luciano L. Menegaldo.

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Menegaldo, L.L. Real-time muscle state estimation from EMG signals during isometric contractions using Kalman filters. Biol Cybern 111, 335–346 (2017). https://doi.org/10.1007/s00422-017-0724-z

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