## 4 Discussion  
As shown in Section 3, the kinematic information from the sacral crest and knee can most accurately estimate both the anterior and mediolateral MoSs. The sacral crest was anticipated to be a suitable estimation point owing to its proximity to the center of body mass (\(\pi_{\text{com}}\)), which is used for MoS calculations. Further, the positions of the feet can be accurately predicted using the motion of the center of mass [42; 43], implying that only the kinematic information near the center of mass is satisfactory to predict the MoSs. Following the sacral crest, the xiphisternum, T10 vertebra, and great trochanter are the feature points closest to the center of body mass. However, the estimation accuracies for the xiphisternum and T10 did not match that of the sacral crest. This discrepancy could be attributed to the separation of the xiphisternum and T10 from the center of body mass by several spinal and coastal bones, potentially weakening their motion correlation with the sacral crest. The great trochanter, despite its proximity to the center of body mass, proved to be the least suitable point for MoS estimation, similar to the toe. This may be because the femur, prominently featuring the great trochanter, moves independently from the pelvis, which comprises the sacral crest, rendering it less relevant for MoS estimations. Contrarily, the femoral lateral epicondyle, another prominent feature of the femur, achieved estimation accuracies comparable to the sacral crest. A possible explanation for this is that the great trochanter is located near the instant center of rotation of the femur [44], where its translational motion is minimal and hence less contributory to MoS estimation. The knee, along with the sacral crest, was identified as a suitable point for estimating the MoS. This suitability may stem from the position of the knee, which captures motion information from both the center of body mass and toe, as it is located between them. In healthy individuals, the knee is almost fully extended at the moment of heel contact [45], rendering its motion information valuable for predicting foot position. The position marker of the knee, attached to the femoral lateral epicondyle, does not capture information regarding the abduction and adduction movements of the knee joint. However, unexpectedly, the knee also proved effective for estimating the mediolateral MoS. This finding necessitates further investigation to elucidate the underlying mechanisms in future studies. The toe was unsuitable, although it is used for computing the MoS. This is potentially because the toe does not include significant kinematic information during the stance phase. As shown in Figure 4j, the right toe rarely moves for approximately 40% of the gait cycle. Notably, the typical stance phase occupies 60% of the gait cycle [46; 47], but the toe continues to move immediately after the heel contact. Further, during the swing phase, the ankle joint can move freely in the air or at least without the restriction caused by the contact with the ground, although such motions are used to determine the toe clearance [48; 49; 50]. Figure 10: Examples of gait motions with the highest (rigid curves) and smallest (dotted curves) scores for each principal motion to estimate the anterior MoS. Ankle motions in the air may not be directly linked to the MoS that is computed referring to the foot position during the stance phase. Collectively, the toe is reasonably judged as an unsuitable point to estimate the MoS. This study identifies two body points--the sacral crest and knee--as suitable for estimating the anterior and mediolateral MoSs based on their kinematic information. When attaching the IMUs to these points using a cloth bandage, areas near joints where the attachment may loosen during extended periods of walking should be avoided. In practice, IMUs are typically affixed near the knee, either on the femoral or tibial parts [10; 51; 52; 53].