The online estimation of the joint angle based on the gravity acceleration using the accelerometer and gyroscope in the wireless networks

  • Zhen Ding
  • Chifu Yang
  • Jiantao Ma
  • JianGuo Wei
  • Feng JiangEmail author


This study aims at the online estimation of the hip and knee angle in the sagittal plane for the motion surveillance only using the tri-axis accelerometers and gyroscopes of IMU, without considering the magnetic disturbance. The proposed method utilizes the projection of gravity acceleration on each sensor coordinate system to estimate the joint angle which rotating around the horizontal axis and approximately horizontal axis. With the third row of the rotation matrix independent of the yaw angle, the proposed method first calculates the projection of the gravity acceleration on each IMU sensor coordinate system only using accelerometer and gyroscope. And then, the rotation matrix between two adjacent coordinate systems is directly calculated. After evaluating the body to sensor rotation matrix, the rotation matrix between two adjacent body segments can be calculated, ultimately. Two types of experiments are adopted in the paper. The results show that the proposed method obtains the outstanding performance with the RMSE lower than 0.8 deg in the horizontal rotation experiment. In the limb joint experiment, the RMSE of the hip joint is lower than 3.12 deg, while the RMSE of the knee joint is lower than 3.83 deg for all predefined locomotion modes. The characteristic of our approach is that it can be run online without any parameter adjustment and additional time latency while ensuring estimation accuracy.


IMU Wireless networks Gravity acceleration Joint angle 



This research was supported by national key research and development plan 2018YFC0832105 and 2018YFC0806800.


  1. 1.
    Brodie M, Walmsley A, Page, W (2008)Google Scholar
  2. 2.
    Bell-Jenje T, Olivier B, Wood W, Rogers S, Green A, McKinon W (2016) Manual Therapy 21:256CrossRefGoogle Scholar
  3. 3.
    Cutti AG, Ferrari A, Garofalo P, Raggi M, Cappello A, Ferrari A (2010) Med Biol Eng Comput 48(1):17CrossRefGoogle Scholar
  4. 4.
    Dejnabadi H, Jolles BM, Aminian K (2005) IEEE Trans Biomed Eng 52(8):1478. CrossRefGoogle Scholar
  5. 5.
    Din S, Ahmad A, Paul A, Rho S (2018) J Parallel Distrib Comput 118:34CrossRefGoogle Scholar
  6. 6.
    Fong DTP, Chan YY (2010) Sensors 10(12):11556CrossRefGoogle Scholar
  7. 7.
    Gośliński J, Nowicki M, Skrzypczyński P (2015) IEEE Sensors J 15(7):3781CrossRefGoogle Scholar
  8. 8.
    Hassan EA, Jenkyn TR, Dunning CE (2007) J Biomech 40(4):930CrossRefGoogle Scholar
  9. 9.
    Kim Y, Jung S, Ji S, Hwang E, Rho S (2018) Multimed Tools Appl 78(3):3009–3043CrossRefGoogle Scholar
  10. 10.
    Laidig D, Schauer T, Seel T (2017) In: 2017 International Conference on Rehabilitation Robotics (ICORR), pp 971–976.
  11. 11.
    Liu K, Liu T, Shibata K, Inoue Y (2009) In: 2009 International Conference on Mechatronics and Automation, pp 3065–3069.
  12. 12.
    Madgwick, SOH, pp 32Google Scholar
  13. 13.
    Madgwick S (2010) Report x-io Univ Bristol (UK) 25:113Google Scholar
  14. 14.
    Mahony R, Hamel T, Pflimlin JM (2008) IEEE Trans Autom Control 53(5):1203. CrossRefGoogle Scholar
  15. 15.
    Millor N, Lecumberri P, Gomez M, Martínez-ramirez A, Izquierdo M (2014) IEEE Trans Neural Syst Rehab Eng 22(5):926CrossRefGoogle Scholar
  16. 16.
    Mohanraj V, Sakthivel R, Paul A, Rho S (2018) Int J Parallel Prog 46(5):904CrossRefGoogle Scholar
  17. 17.
    Palermo E, Rossi S, Marini F, Patanè F, Cappa P (2014) Measurement 52:145. CrossRefGoogle Scholar
  18. 18.
    Picerno P, Cereatti A, Cappozzo A (2008) Gait Posture 28(4):588. CrossRefGoogle Scholar
  19. 19.
  20. 20.
    Roetenberg D, Luinge HJ, Baten CT, Veltink PH (2005) IEEE Trans Neural Syst Rehab Eng 13(3):395CrossRefGoogle Scholar
  21. 21.
    Roetenberg D, Baten CT, Veltink PH (2007) IEEE Trans Neural Syst Rehab Eng 15(3):469CrossRefGoogle Scholar
  22. 22.
    Seel T, Raisch J, Schauer T (2014) Sensors 14(4):6891CrossRefGoogle Scholar
  23. 23.
    Shuster MD, Oh SD (1981) J Guid Control Dyn 4(1):70Google Scholar
  24. 24.
    Takeda R, Tadano S, Natorigawa A, Todoh M, Yoshinari S (2009) J Biomech 42(15):2486CrossRefGoogle Scholar
  25. 25.
    Vitali RV, Cain SM, McGinnis RS, Zaferiou AM, Ojeda LV, Davidson SP, Perkins NC (2017) Sensors 17(9):1970CrossRefGoogle Scholar
  26. 26.
    Yadav N, Bleakley C (2014) Sensors 14(11):20008CrossRefGoogle Scholar
  27. 27.
    Yun X, Bachmann ER, McGhee RB (2008) IEEE Trans Instrum Meas 57(3):638–650. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mechatronics EngineeringHarbin Institute of TechnologyHarbinChina
  2. 2.School of Computer Science and TechnologTianjin UniversityTianjinChina
  3. 3.School of Computer Science and TechnologyHarbin Institute of TechnologyHarbinChina
  4. 4.Pengcheng LabratoryShenzhenChina

Personalised recommendations