Skip to main content

Three-Dimensional Human Kinematic Estimation Using Magneto-Inertial Measurement Units


This chapter deals with the estimation of human kinematics using magneto and inertial sensing technology. A magneto-inertial measurement unit typically embeds a triaxial gyroscope, a triaxial accelerometer, and a triaxial magnetic sensor in the same assembly. By combining the information provided by each sensor within a sensor fusion framework, it is possible to determine the unit orientation with respect to a common global coordinate system. Recent advances in the construction of microelectromechanical system devices have made possible the manufacturing of small and light devices. These advances have widened the range of possible applications to include areas such as human movement. This chapter aims at providing the reader with a picture of the state of the art in the measurement and estimation methods for the description of human joint kinematics using magneto-inertial sensing technology. In the first section, fundamental concepts of rigid body kinematics are introduced with special reference to magneto-inertial measurements. Then a short description of the operational characteristics of accelerometers, gyroscopes, and magnetometers is provided. The third section reports theory and methods for the estimation of the orientation and position of magneto-inertial measurement units along with the implementation of a Kalman filter for 3D orientation estimate as an example. In the last section, a critical review of the most common methodologies for the joint kinematic estimation is reported.


  • Joint mechanics
  • Acceleration
  • Angular velocity
  • Orientation
  • Position
  • Multi-segmental model
  • Multibody
  • Anatomical coordinate system
  • Joint kinematics
  • Wearable sensors
  • Kalman filter
  • Pose

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5



Anatomical landmark identification


Angle Random Walk


Anatomical coordinate system


Body-fixed coordinate system


Center of rotation


Coordinate system


Degree of freedom


Extended Kalman filter




Kalman filter


Global coordinate system


Inertial measurement unit


MIMU coordinate system


Microelectromechanical systems


(Magneto)-inertial measurement unit


Manual Unit Alignment


Nano-electromechanical systems


Velocity Random Walk

〈⋅, ⋅〉:

Dot product between vectors


Quaternion multiplication


Skew-symmetric operator


  • Barbour N, Schmidt G (2001) Inertial sensor technology trends. IEEE Sensors J 1:332–339

    CrossRef  Google Scholar 

  • Bergamini E, Ligorio G, Summa A, Vannozzi G, Cappozzo A, Sabatini AM (2014) Estimating orientation using magnetic and inertial sensors and different sensor fusion approaches: accuracy assessment in manual and locomotion tasks. Sensors 14:18625–18649

    CrossRef  Google Scholar 

  • Biryukova EV, Roby-Brami A, Frolov AA, Mokhtari M (2000) Kinematics of human arm reconstructed from spatial tracking system recordings. J Biomech 33:985–995

    CrossRef  Google Scholar 

  • van den Bogert AJ, Smith GD, Nigg BM (1994) In vivo determination of the anatomical axes of the ankle joint complex: an optimization approach. J Biomech 27:1477–1488

    CrossRef  Google Scholar 

  • Bouvier B, Duprey S, Claudon L, Dumas R, Savescu A (2015) Upper limb kinematics using inertial and magnetic sensors: comparison of sensor-to-segment calibrations. Sensors 15:18813–18833

    CrossRef  Google Scholar 

  • Bregler C, Malik J (1998) Tracking people with twists and exponential maps. In: Proceedings of 1998 I.E. computer society conference on computer vision pattern recognition (Cat. No.98CB36231), pp 8–15

    Google Scholar 

  • Camomilla V, Bergamini E, Fantozzi S, Vannozzi G (2015) In-field use of wearable magneto-inertial sensors for sports performance evaluation. In: 33rd international conference on biomechanics in sport, pp 1–4

    Google Scholar 

  • Cappozzo A, Catani F, Della Croce U, Leardini A (1995) Position and orientation in space of bones during movement. Clin Biomech 10:171–178

    CrossRef  Google Scholar 

  • Cereatti A, Margheritini F, Donati M, Cappozzo A (2010) Is the human acetabulofemoral joint spherical? J Bone Joint Surg Br 92:311–314

    CrossRef  Google Scholar 

  • Cereatti A, Trojaniello D, Della Croce U (2015) Accurately measuring human movement using magneto-inertial sensors: techniques and challenges. In: 2015 I.E. international symposium on inert sensors system proceedings, pp 1–4

    Google Scholar 

  • Churchill DL, Incavo SJ, Johnson CC, Beynnon BD (1998) The transepicondylar axis approximates the optimal flexion axis of the knee. Clin Orthop Relat Res 356:111–118

    Google Scholar 

  • Cooper G, Sheret I, McMillian L, Siliverdis K, Sha N, Hodgins D et al (2009) Inertial sensor-based knee flexion/extension angle estimation. J Biomech 42:2678–2685

    CrossRef  Google Scholar 

  • Corke PI (2007) A simple and systematic approach to assigning Denavit-Hartenberg parameters. IEEE Trans Robot 23:590–594

    CrossRef  Google Scholar 

  • Crabolu M, Pani D, Raffo L, Cereatti A (2016) Estimation of the center of rotation using wearable magneto-inertial sensors. J Biomech 49:3928–3933

    CrossRef  Google Scholar 

  • Cutti AG, Giovanardi A, Rocchi L, Davalli A, Sacchetti R (2008) Ambulatory measurement of shoulder and elbow kinematics through inertial and magnetic sensors. Med Biol Eng Comput 46:169–178

    CrossRef  Google Scholar 

  • Cutti AG, Ferrari A, Garofalo P, Raggi M, Cappello A, Ferrari A (2010) “Outwalk”: a protocol for clinical gait analysis based on inertial and magnetic sensors. Med Biol Eng Comput 48:17–25

    CrossRef  Google Scholar 

  • Dumas R, Chèze L (2007) 3D inverse dynamics in non-orthonormal segment coordinate system. Med Biol Eng Comput 45:315–322

    CrossRef  Google Scholar 

  • El-Sheimy N, Hou H, Niu X (2008) Analysis and modeling of inertial sensors using Allan variance. IEEE Trans Instrum Meas 57:140–149

    CrossRef  Google Scholar 

  • Favre J, Aissaoui R, Jolles BM, de Guise JA, Aminian K (2009) Functional calibration procedure for 3D knee joint angle description using inertial sensors. J Biomech 42:2330–2335

    CrossRef  Google Scholar 

  • Frigo C, Rabuffetti M, Kerrigan DC, Deming LC, Pedotti A (1998) Functionally oriented and clinically feasible quantitative gait analysis method. Med Biol Eng Comput 36:179–185

    CrossRef  Google Scholar 

  • Grood ES, Suntay WJ (1983) A joint coordinate system for the clinical description of three-dimensional motions: application to the knee. J Biomech Eng 105:136–144

    CrossRef  Google Scholar 

  • Koning BHW, van der Krogt MM, Baten CTM, Koopman BFJM (2013) Driving a musculoskeletal model with inertial and magnetic measurement units. Comput Methods Biomech Biomed Eng 5842:37–41

    Google Scholar 

  • Ligorio G, Sabatini AM (2015) A novel Kalman filter for human motion tracking with an inertial-based dynamic inclinometer. IEEE Trans Biomed Eng 62:2033–2043

    CrossRef  Google Scholar 

  • Ligorio G, Sabatini AM (2016) Dealing with magnetic disturbances in human motion capture: a survey of techniques. Micromachines 7:1–17

    Google Scholar 

  • Luinge HJ, Veltink PH, Baten CTM (2007) Ambulatory measurement of arm orientation. J Biomech 40:78–85

    CrossRef  Google Scholar 

  • Madgwick SOH, Harrison AJL, Vaidyanathan R (2011) Estimation of IMU and MARG orientation using a gradient descent algorithm. IEEE Int Conf Rehabil Robot 2011:5975346.

  • McGinnis RS, Perkins NC (2013) Inertial sensor based method for identifying spherical joint center of rotation. J Biomech 46:2546–2549

    CrossRef  Google Scholar 

  • Picerno P, Cereatti A, Cappozzo A (2008) Joint kinematics estimate using wearable inertial and magnetic sensing modules. Gait Posture 28:588–595

    CrossRef  Google Scholar 

  • Prentice MJ (1986) Orientation statistics without parametric assumptions. J R Stat Soc Ser B 48:214–222

    MathSciNet  MATH  Google Scholar 

  • Roetenberg D, Luinge H, Slycke P (2013) Xsens MVN: Full 6DOF Human Motion Tracking Using Miniature Inertial Sensors. In: Xsens Technologies, whitepaper, version 3:1–9.

    Google Scholar 

  • Sabatini AM (2011) Estimating three-dimensional orientation of human body parts by inertial/magnetic sensing. Sensors 11:1489–1525

    CrossRef  Google Scholar 

  • Seel T, Schauer T, Raisch J (2012) Joint axis and position estimation from inertial measurement data by exploiting kinematic constraints. In: 2012 IEEE international conference on control applications (CCA). Part of 2012 IEEE multi-conference on systems and control, Dubrovnik, 3–5 Oct 2012, pp 45–49

    Google Scholar 

  • Seel T, Raisch J, Schauer T (2014) IMU-based joint angle measurement for gait analysis. Sensors 14:6891–6909

    CrossRef  Google Scholar 

  • Shuster MD (1993) A survey of attitude representations. J Astronaut Sci 41:439–517

    MathSciNet  Google Scholar 

  • Skog I, Händel P, Nilsson J-O, Rantakokko J (2010) Zero-velocity detection – an algorithm evaluation. IEEE Trans Biomed Eng 57:2657–2666

    CrossRef  Google Scholar 

  • Slajpah S, Kamnik R, Munih M (2014) Kinematics based sensory fusion for wearable motion assessment in human walking. Comput Methods Prog Biomed 116:131–144

    CrossRef  Google Scholar 

  • Sommer HJ, Miller NR (1980) A technique for kinematic modeling of anatomical joints. J Biomech Eng 102:311–317

    CrossRef  Google Scholar 

  • Taetz B, Bleser G, Miezal M (2016) Towards self-calibrating inertial body motion capture. 19th Int Conf Informa Fusion 1751–1759

    Google Scholar 

  • Titterton DH, Weston JL (2004) Strapdown inertial navigation technology. Editor AIAA Educ. Ser., Reston

    CrossRef  Google Scholar 

  • Veeger HEJ (2000) The position of the rotation center of the glenohumeral joint. J Biomech 33:1711–1715

    CrossRef  Google Scholar 

  • Waldron K, Schmiedeler J (2008) Kinematics. Springer Handbook of Robotics, pp 9–33

    Google Scholar 

  • Wells D, Cereatti A, Camomilla V, Donnelly C (2015) A calibration procedure for mimu sensors allowing for the calculation of elbow angles. In: 33rd international conference on biomechanics in sports, Poitiers

    Google Scholar 

  • Woodman OJ (2007) An introduction to inertial navigation. Cambridge University Press, Cambridge

    Google Scholar 

  • Wu G, Siegler S, Allard P, Kirtley C, Leardini A, Rosenbaum D et al (2002) ISB recommendation on definitions of joint coordinate system of various joints for the reporting of human joint motion – part I: ankle, hip, and spine. J Biomech 35:543–548

    CrossRef  Google Scholar 

  • Wu G, Van Der Helm FCT, Veeger HEJ, Makhsous M, Van Roy P, Anglin C et al (2005) ISB recommendation on definitions of joint coordinate systems of various joints for the reporting of human joint motion – part II: shoulder, elbow, wrist and hand. J Biomech 38:981–992

    CrossRef  Google Scholar 

  • Yazdi N, Ayazi F, Najafi K (1998) Micromachined inertial sensors. Proc IEEE 86:1640–1658

    CrossRef  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Andrea Cereatti .

Rights and permissions

Reprints and Permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this entry

Verify currency and authenticity via CrossMark

Cite this entry

Cereatti, A., Della Croce, U., Sabatini, A.M. (2018). Three-Dimensional Human Kinematic Estimation Using Magneto-Inertial Measurement Units. In: Handbook of Human Motion. Springer, Cham.

Download citation