The aim of this study was to validate a method based on the use of a WFLC adaptive filter approach, to obtain a drift-free estimate of the 3D orientation of a sensor attached to the lower trunk for a prolonged period of time during treadmill walking, from angular velocities recorded using only one IMU.
A tuning of the WFLC was initially performed, to find optimal values of its gains. A sensitivity analysis was then performed to assess the effects of changes in algorithm frequency weight w
, which is crucial for ensuring that equation 2, and hence the output of the proposed method, are not determinate. Results of this analysis showed that the outputs were always determinate for frequencies ranging between 0.1 Hz and 5 Hz, and that frequencies ranging from 1 Hz to 3 Hz led to very similar results. It has to be noted that these frequencies are actually those expected to be of interest when dealing with human locomotor tasks.
After the above tuning process, the method proved to be very accurate in estimating all the three angles, for all the observed speed conditions and also when the subjects were not walking at steady state. Interestingly, the convergence time of the algorithms, which generally depends on the signal properties, appeared to be negligible for the specific investigated application, as shown by the fact that the results obtained for the transition phases were almost identical to those obtained in the steady state phase (Table 1). This ability of the method to provide accurate angle estimations during non-periodic motion (acceleration and deceleration phases) and during short intervals of almost no motion (stopping phase) opens the way to future applications, such as uncontrolled walking.
The accuracy of the estimates of lower trunk bending in the sagittal (pitch) and frontal (roll) planes is similar to that obtained in a previous study using a properly optimized Kalman filter . A clear advantage of the proposed method is that, conversely from the previous approach, it uses only the angular velocity signals. Nevertheless, the Kalman filter approach is expected to be more robust for non-periodic motions than the proposed method, since it does not require any a-priori assumption about the signal characteristics.
It has been previously shown that when tracking signals that have a frequency content composed by many frequencies that are close to each other, the performance of the WFLC can be degraded . A Band-limited Multiple Fourier Linear Combiner (BMFLC) ,  can be used to overcome this problem. However, the BMFLC filter requires an a priori determined set of frequencies, which is not always available when dealing with human movement analysis applications [15, 16]. Numerical integration, as associated with WFLC-BMFLC adaptive filters, has been recently used successfully for tremor cancelation . This numerical approach, however, requires the use of a high-pass filter, which allows easy separation of the tremor oscillations (high frequency) from the voluntary motion (low frequency). Unfortunately, this approach is not suitable for lower trunk angular velocity data recorded during walking, when the determination of high-pass filter cut-off frequency is not straight forward due to the variability of walking speed and to the fact that most of the gyroscope signals power is within the low frequencies, which hinder the determination of a proper high-pass cut-off frequency
In conclusion, this study proved the effectiveness of the WFLC method in accurately reconstructing the 3D orientation of an IMU located on the lower trunk of a subject during treadmill walking. This method is expected to also perform satisfactorily for overground walking data. The small differences in the values of the measured angular velocities which might be observed between treadmill and level walking data, might require an adjustment of the identified values of the algorithm gains. Further studies are needed to test the suitability of the method for the assessment of pathological gaits and to examine the generalizability of the method to other “quasi-periodic” tasks, such as squatting, rowing, running, or swimming.