A study on band-pass filtering for calculating foot displacements from accelerometer and gyroscope sensors

As a promising alternative to laboratory-constrained video capture systems in studies of human movement, inertial sensors (accelerometers and gyroscopes) are recently gaining popularity. Secondary quantities such as velocity, displacement and joint angles can be calculated through integration of acceleration and angular velocities. It is broadly accepted that this procedure is significantly influenced by accumulative errors due to integration, arising from sensor noise, non-linearities, asymmetries, sensitivity variations and bias drifts. In this paper, we assess the effectiveness of applying band-pass filtering to raw inertial sensor data under the assumption that sensor drift errors occur in the low frequency spectrum. The normalized correlation coefficient rho of the Fast Fourier Transform (FFT) spectra corresponding to vertical toe acceleration from inertial sensors and from a video capture system as a function of digital band-pass filter parameters is compared. The Root Mean Square Error (RMSE) of the vertical toe displacement for 30 second walking windows is calculated for 2 healthy subjects over a range of 4 walking speeds. The lowest RMSE and highest cross correlation achieved for the slowest walking speed of 2.5Km/h was 3.06cm and 0.871 respectively, and 2.96cm and 0.952 for the fastest speed of 5.5Km/h.