**3. Results**

The pelvis orientation and the joint angles during a time-normalized typical gait stride at a self-selected speed of 1 <sup>m</sup>·s<sup>−</sup><sup>1</sup> are illustrated in Figure 3 for measurements with the IMUs and with the optical system using the walking functional calibration (Calibration movement 4a). The traces displayed a classical movement pattern as indicated by the similarity between both set of measurements, with a mean RMSE value lower than 5◦ for all joints in all planes.

#### *3.1. Assessment of the IMU Accuracy*

The mean differences between measurements from the IMUs and from the optical system, as well as the factors affecting this difference, are presented in Table 1. The highest mean error was observed at the knees and at the ankles, bilaterally, as shown by the RMSE between 3.0◦ and 4.1◦ and by the ΔROM between 1.9◦ and 5.1◦ in any plane of motion. The generalized linear model also indicated that these differences were significantly linked to the functional calibration movement; see the details in Figure 4. These errors were also significantly associated with the methods of determination of the IMUs reference frame, although to a lesser extent: the mean (SD) RMSE was 2.3◦ (1.7◦) when the vertical axis was aligned to the gravity vector and 3.0◦ (3.1◦) when the lateral axis was aligned to the segmen<sup>t</sup> rotation axis. The errors were not significantly linked to the two different methods used to compute the 3D kinematics from the optical system (lab frame or computed through the functional calibration). Table 1 also shows that the DRIFT was largely independent of the factors considered in the generalized linear model.



The variation of the RMSE across di fferent functional calibration movements is illustrated in Figure 4. While the RMSE varied between approximately 1◦ and 6◦ for most joints, planes of motion, and functional calibration movements, it was larger for the "squat" calibration movement, especially at the knee and ankle where the upper confidence limit of the RMSE reached up to 8◦ and the upper confidence limit ΔROM reached up to 10◦ or more. Tilted, extension, and walking functional calibration movements tended to provide less accurate measurements at the knee. Walking functional calibration movements tended to report more accurate angles for distal lower limb joints, although without a clear visible impact on the ROM accuracy. After excluding the "squat" movement, the mean accuracy for all other calibration movements is summarized in Table 2, indicating a mean RMSE of less than 2◦ at the pelvis, less than 3◦ at the hip and ankle, and less than 4◦ at the knee with a trend for larger errors in the frontal plane. The mean errors were smaller in ΔROM. DRIFT values at the hips and at other lower limb joints in the sagittal plane were on average under 2.7◦, while higher mean values up to 4.9◦ were observed at the knee and at the ankle in the frontal and transverse planes.


**Table 2.** Summary of the accuracy without the squat calibration movement and with reference frames aligned with gravity.

Bold values indicate angles >3◦.

#### *3.2. Assessment of the IMU Reproducibility*

The mean ROM recorded for each joint in each plane of motion during one walking test movement are presented in Table 3, together with the reproducibility indices computed across repetitions of each calibration movement. The mean ROM displayed symmetrical values for both limbs and classical movement amplitudes for walking at 1 <sup>m</sup>·s<sup>−</sup>1. Overall, the mean reproducibility was excellent for all calibration movements in the sagittal plane (ICC: 0.96–0.99) and it was good to excellent in the transverse plane (ICC: 0.87–0.93). In the frontal plane, the mean reproducibility was good for all calibration movements (ICC: 0.79–0.86), except for walking, which had an acceptable reproducibility on average (ICC: 0.63) due to the low ICC observed for the hip and knee. The reproducibility was uniformly good to excellent across the calibration movements, except for the walking movement, which reported slightly lower reproducible movement amplitudes for proximal joints (as low as ICC = 0.76 for the hip compared to ICC = 0.94 for any other movement) and slightly higher reproducibility in distal joints (as high as ICC = 0.91 for the ankle compared to ICC = 0.82 for other movements). For all functional calibration movements, whatever the joint, the mean SEM was within 1.2◦ in all planes, although the mean SEM remained generally higher at the knee (0.9◦) and ankle (1.8◦) compared to the hip (0.6◦) and pelvis (0.1◦). This resulted in acceptable variations between movements, as shown by a mean SEM% of 1.8% in the sagittal plane, 4.8% in the transverse plane, and 7.9% in the frontal plane, where articular amplitudes were smaller for all lower limb joints.

#### *3.3. Assessment of Accuracy in Di*ff*erent Test Movements*

The functional calibration movements that provided the highest accuracy were the tilted and extension movements, as well as walking at a self-selected speed (mean RMSE for all joints, respectively: 2.5◦, 2.3◦, 2.2◦). Since these calibration movements provided a comparable performance for the functional calibration of the IMU, the mean accuracy with the walking functional calibration was computed for the measurement of the four gait test movements, namely walking, ascending or descending one step, and stepping over an obstacle, when considering the lateral axis of the reference frame perpendicular to the gravity vector (as similar accuracies were obtained when considering it parallel to the axis of the segmen<sup>t</sup> rotation during the functional calibration). The mean accuracy obtained with the functional calibration movements retained is presented in Table 4. The RMSE and ΔROM were both smaller than 6◦ for ascending a step and smaller than 13◦ for descending it. For stepping over an obstacle, the RMSE reached 13◦ but the ΔROM had maximum values of only 4◦. Notably, the accuracy of the IMU measurements were higher in walking than in other gait movements, where larger inaccuracies were observed, especially for a step ascent (both ankles in the sagittal plane and back leg hip in the frontal plane), for a step descent (all joints of both legs), and for stepping over an obstacle (all joints of both legs excluding the pelvis), although the error was generally within 5◦ and only rarely exceeded 10◦.

**Figure 4.** Accuracy across functional calibration movements (1. Tilted to stand, 2. Extension, 3. Squat, 4a. Walking (1 ± 0.1 <sup>m</sup>·s−1), 4b. Walking fast (1.5 ± 0.1 <sup>m</sup>·s−1), 4c. Walking slow (0.6 ± 0.1 <sup>m</sup>·s−1)). Error bars are the confidence interval means at 95%.



Bold values indicate SEM% > 10%, ROM: range of motion, SD: standard deviation, ICC: intraclass correlation coefficient, SEM: standard error of measurement, SEM%: standard error of measurement in proportion to the mean.


