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 σ_g = 2.5° s⁻¹ (gyroscope) and σ_a = 0.05 m s⁻¹ (accelerometer). The compensation technique reduced the maximum root mean square errors (RMSEs) to: RMSE_θ=14.6° (orientation) and RMSE_d=17.7 cm (positioning) for an integration interval of one gait cycle (an improvement of 3° and 7 cm); RMSE_θ=14.8° and RMSE_d=30.0 cm for an integration interval of two gait cycles (an improvement of 11° and 262 cm).