Medical and Biological Engineering and Computing

, Volume 43, Issue 1, pp 94–101 | Cite as

Quaternion-based strap-down integration method for applications of inertial sensing to gait analysis



The proposed strap-down integration method exploits the cyclical nature of human gait: during the gait swing phase, the quaternion-based attitude representation is integrated using a gyroscope from initial conditions that are determined during stance by an accelerometer. Positioning requires double time integration of the gravity-compensated accelerometer signals during swing. An interpolation technique applied to attitude quaternions was developed to improve the accuracy of orientation and positioning estimates by accounting for the effect of sensor bias and scale factor drifts. A simulation environment was developed for the analysis and testing of the proposed algorithm on a synthetic movement trajectory. The aim was to define the true attitude and positioning used in the computation of estimation errors. By thermal modelling, the changes of bias and scale factor of the inertial sensors, calibrated at a single reference temperature, were analysed over a range of ±10°C, for measurement noise standard deviations up to σg = 2.5° s−1 (gyroscope) and σa = 0.05 m s−1 (accelerometer). The compensation technique reduced the maximum root mean square errors (RMSEs) to: RMSEθ=14.6° (orientation) and RMSEd=17.7 cm (positioning) for an integration interval of one gait cycle (an improvement of 3° and 7 cm); RMSEθ=14.8° and RMSEd=30.0 cm for an integration interval of two gait cycles (an improvement of 11° and 262 cm).


Inertial sensing Gait analysis Strap-down integration Quaternion of rotation Computer simulations 


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Copyright information

© FMBE 2005

Authors and Affiliations

  1. 1.Scuola Superiore Sant'AnnaPisaItaly

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