**4. Discussion**

The main objective of this study was to compare the accuracy and reproducibility of lower limb joint angles computed from IMUs following di fferent functional calibration methods. The study showed that applying a functional calibration movement before IMU-based lower limb kinematic assessment allowed for a fairly accurate measurement of gait movements. Except for the squat calibration movement, only small discrepancies were observed between functional calibration movements during a walking task, with a peak mean error of 3.6◦ for any joint in any plane of movement. Overall, the absolute reproducibility was similar for the three planes, but relative reproducibility was higher in the sagittal plane, with a mean standard error of measurement of less than 1.1◦ observed between multiple repetitions of the same functional calibration movement. A comparable overall performance was observed for di fferent calibration movements, although each movement reported variable merits for di fferent joints and planes of movement. Although the highest accuracy was observed in straight walking with a mean error of 2.2◦, more complex gait movements tended to provide larger but limited errors, with a mean error of 3.5◦ for a step ascent, 5.4◦ for a step descent, and 4.7◦ for crossing an obstacle.

#### *4.1. Accuracy of Di*ff*erent Calibration Methods during Straight Walking*

The accuracy reported in this study during straight walking ranged from 1.1◦ to 3.6◦ for RMSE and from 0.2◦ to 3.4◦ for ΔROM, which is comparable to the mean error below 3◦ reported when using marker clusters on segments [22] rather than markers on anatomical landmarks [23–25]. Indeed, both methods reported di fferent joint kinematics and accounted di fferently for errors of markers placement, soft tissue artefacts, and biomechanical model calculations [22]. The functional calibration of the optical system did not influence the accuracy, indicating that the reference frame obtained for each segmen<sup>t</sup> with the functional calibration movements were close to the optical reference frame. As the magnetometer was not used in the AHRS algorithm, the DRIFT was controlled to be acceptable (mean of 2.3◦) for such short experiments. The drift was slightly higher in the more distal joints, probably due to the higher speed of the movements [26,27]. The drift was slightly lower in the sagittal plane, probably because the drift in this plane was better compensated by the sensor fusion algorithm. Although a mean error under 2◦ has been obtained on a single-joint movement [13], the accuracy obtained with our multi-joint model is acceptable for most clinical gait applications [8].

While the tilted and extension calibration movements provided a higher accuracy in the hip and ankle kinematics compared to the knee, walking calibration movements reported a higher accuracy for distal joints, whatever the walking speed. This observation can be supported by (1) a greater variability in the knee kinematics during the tilted and extension movements compared to straight walking and (2) higher accelerations of the distal relative to the proximal segments during walking. This observation also showed that the reference frame for each segmen<sup>t</sup> can be equally determined via a rotational movement recorded by the gyroscopes or via a translational movement recorded by the accelerometers contained in each IMU. The accuracy obtained in slow walking also validates the use of this functional calibration movement in similar conditions, which is often encountered in pathological gaits or in older adults [28].

The lower accuracy reported for the knee and ankle via the squat calibration movement could be explained by the lower movement amplitude of the shank and foot segments during this calibration movement. Indeed, the smaller amplitude-to-noise ratio probably resulted in an erroneous definition of the reference frame, leading to kinematic crosstalk [29]. This result also showed that functional movements exploring a wide range of segmen<sup>t</sup> orientation tended to provide more accurate segmen<sup>t</sup> reference frames.

#### *4.2. Reproducibility of Calibration Movements*

Reproducibility was excellent in 65% of the tested joints and motion planes, good in 24%, acceptable in 10%, and poor in 1 observation out of 84. Concerning di fferences between calibration movements, the walking calibration movement produced the highest reproducibility and SEM% for the ankle, while the other functional calibration movements produced higher reproducibility indices for the pelvis and hip joints. The lower reproducibility at the ankle for the segment-rotation-based movements could be explained by the di fficulty in reproducing movements purely in the sagittal plane. This observation also supports previous results showing that the variable position of the foot a ffects the functional calibration when using di fferent static postures [12]. The use of more guidance or more repetitions of the calibration movements could improve the reproducibility by (1) avoiding parasitic movements of the feet out of the sagittal plane and (2) decreasing the impact of any parasitic movement on the definition of the rotation axis. However, in order to limit the complexity and burden of the functional calibration movements, the walking calibration movement remains a remarkably convenient alternative since it o ffers a good to excellent reproducibility (though lower than other movements for the proximal joints), with a very simple and ecological movement. Caution may be needed for subjects having an impaired walking pattern, e.g., a subject walking with the feet pointing outwards.

A higher reproducibility was observed in the sagittal plane compared to the frontal plane. This could be explained by the higher range of motion in the sagittal plane during walking, leading to more kinematic crosstalk in the other planes measured and/or by the fact that the functional calibrations mainly generated segmen<sup>t</sup> movements in the sagittal plane. The combination of the higher variability and smaller ROM in the frontal plane during walking led to a higher SEM% in this plane, as also shown in upper limb anteroposterior reaching tasks [19]. Higher SEM% values inevitably require higher changes to detect meaningful functional changes, e.g., after therapy. The reproducibility of calibration movements in the frontal plane should be explored for the assessment of functional outcomes involving larger movements in the frontal plane.

#### *4.3. Accuracy across Di*ff*erent Gait Movements*

More complex gait movements tended to provide larger errors than a peak mean RMSE of 3.6◦ and a peak mean ΔROM of 3.4◦ for straight walking. Indeed, the peak mean errors obtained in the sagittal plane for a step ascent of 3◦, 5◦, and 5◦ for hip, knee, and ankle, respectively, correspond to errors in elevation angles of 5◦, 4◦, and 4◦ previously reported for the same joints [30]. Similarly, the peak mean ΔROM of 6.4◦ obtained for the stair ascent and of 4.6◦ for the stair descent are comparable to the errors previously reported for healthy subjects (peak error of 4.1◦ for a stair ascent and 4.8◦ for a stair descent) [31]. Therefore, before implementing inertial sensors in a complex, real-life context, the accuracy should be established in such a context rather than extrapolated from simpler gait movements recorded in controlled lab conditions.

#### *4.4. Limitations and Perspectives*

This study focused on healthy adults and this could be a limitation in case the functional calibration movements proposed here would be used with patients with a limited range of motion or who have parasitic movements that may hinder an accurate and reproducible calibration movement. The transferability to the elderly or to patients with motion disabilities should be assessed in further studies.

The IMU magnetometer was voluntarily omitted in this study in order to avoid ferromagnetic disturbances. The recordings in this study were limited in time due to the short time required to execute the investigated movements. The drift resulting from longer records [32] could be limited by using the IMU magnetometer or algorithms that constantly fuse the segment's angular velocity and linear acceleration via known kinematic relations between segments [33].

Although a high accuracy for the lower limb joint angles has been obtained by using only the gyroscope signals, our methods could be improved by also accounting for the segmen<sup>t</sup> accelerations [9,34], which can be used to locate the joint centers and improve the robustness of the segmen<sup>t</sup> orientations [35]. Another approach consists in using a hinge joint model and kinematic constraints to develop automatic or so-called "plug and play" calibrations [9,36]. This less restrictive method may facilitate clinical applications where patients with motion disabilities cannot be expected to perform precise prescribed calibration movements.
