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# Effect of inertial sensor redundancy on the accuracy of hip joint center localization

Camille Di Falco, Rachid Aissaoui, Nicola Hagemeister

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Camille Di Falco, Rachid Aissaoui, Nicola Hagemeister. Effect of inertial sensor redundancy on the accuracy of hip joint center localization. Multidisciplinary Biomechanics Journal, 2025, 50th congress of the., 10.46298/mbj.16145. hal-05191697v2

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Submitted on 23 Oct 2025

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Distributed under a Creative Commons Attribution 4.0 International License
# Effect of inertial sensor redundancy on the accuracy of hip joint center localization

Camille di Falco<sup>a, b*</sup>, Rachid Aissaoui<sup>a, b</sup>,
Nicola Hagemeister<sup>a, b</sup>

<sup>a</sup> Laboratoire d'Innovation Ouverte en technologies de la santé (LIO-ÉTS), Centre de Recherche du Centre Hospitalier de l'Université de Montréal (CRCHUM), 900 St-Denis, Montréal, QC H2X 0A9, Canada

<sup>b</sup> École de Technologie Supérieure, Département de génie des systèmes, 1100 rue Notre-Dame Ouest, Montréal, QC H21 2WS, Canada

*Corresponding author: camille.di-falco.1@ens.etmtl.ca

Received date: 03/04/2025

Accepted date: 27/06/2025

Publication date: 27/10/2025

**Keywords:** joint center estimation, inertial measurement unit (IMU), redundancy, calibration movement

© 2025 The Authors

Licence CC-BY 4.0

Published by Société de Biomécanique

## 1. Introduction

The estimation of joint centers (JC) is a crucial step in calibration methods for motion analysis, such as clinical knee kinematics assessment (Hagemeister et al., 2005). Moreover, inertial measurement units (IMUs) are increasingly used in motion analysis, with several studies investigating JC estimation using these sensors, such as for the shoulder (Crabolu et al., 2017) and hip (García-de-Villa, Jiménez-Martín, & García-Domínguez, 2021), respectively reporting accuracies of 2.1 ± 1 cm and 6.5 ± 0.1 cm. However, no IMU-based study has combined sacral and femoral motion for hip joint center (HJC) localization, nor assessed the effect of sensor redundancy (i.e., dual IMUs per anatomical segment) on localization accuracy. This study aims to investigate the impact of incorporating motion from multiple anatomical segments (sacrum and femur) and using dual IMUs per segment on the accuracy of HJC estimation. We hypothesize that combining multiple sensor locations and using redundancy can improve accuracy in estimating the HJC.

## 2. Methods

### 2.1 Participants

20 healthy able-bodied participants (13 women, 7 men; age 28.1 ± 7.5 years; height 172.2 ± 9.8 cm; body mass 69.5 ± 14.2 kg) participated in this study after providing written informed consent. Inclusion criteria required participants to be able to stand, perform single-leg movements, and walk on a treadmill for a total of 1 hour without pain or discomfort. Exclusion criteria

were any self-reported or diagnosed musculoskeletal or neurological disorders affecting the lower limbs.

### 2.2 Instrumentation

The sacral and femoral parts of the KneeKG system (Emovi Inc., Montreal, Canada) were respectively fixed on the sacrum and right knee of all participants to provide a reference for HJC estimation via reflective marker clusters, and to standardize the placement of four IMU sensors (MTw Awinda, Xsens Technologies). The KneeKG system is a reliable device that is now commonly used in clinics to monitor, as it effectively limits soft-tissue artifacts during 3D knee kinematic assessment. Two IMUs were fixed on each KneeKG part at predefined attachment sites designed to ensure fixed position and orientation relative to the corresponding marker cluster: “SacrIncl”, “SacrPlan” (sacral) and “FemLat”, “FemAnt” (femoral) (Fig. 1). The same 4 IMU were used, but their placement across the 4 fixed attachment sites was randomized between participants. Optical and inertial data were synchronized and recorded simultaneously at 100 Hz using a 12-camera Vicon system with Nexus software and the MT Manager software (Xsens), respectively.

### 2.3 Experimental protocol

After the KneeKG system was attached to the participants, they performed 3 trials of a 10-second circumduction movement at self-selected speed and amplitude, as this movement is clinically used for HJC estimation (Hagemeister et al., 2005).
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Sacral and femoral parts of the KneeKG, with IMUs SacIncl and SacPlan attached to the sacral part, and FemAnt and FemLat attached to the femoral part.</figcaption></figure>

Credit: Camille di Falco

## 2.4 Data processing

HJC estimation with the optical system (HJC<sub>opto</sub>) was calculated using the method proposed by (Siston & Delp, 2006), as it is the one implemented in the calibration approach of (Hagemeister et al., 2005).

HJC estimation with the inertial system (HJC<sub>imu</sub>) followed the approach of (Crabolu et al., 2017) for shoulder JC estimation, incorporating the use of dual IMUs per segment. We used the same angular velocity filtering technique as (Crabolu et al., 2017), but chose to also apply it to filter the free linear acceleration and angular acceleration signals.

## 2.5 Data analysis

Since HJC<sub>opto</sub> was obtained in the KneeKG femoral cluster of markers coordinate system (FCM-CS) and HJC<sub>imu</sub> in one femoral IMU coordinate system (IMU-CS), an optical probe was used to determine the relative position and orientation of each femoral IMU with respect to the FCM-CS. This allowed the comparison between the HJC<sub>opto</sub> and HJC<sub>imu</sub> within the same CS (FCM-CS). The error *d* was then computed as the distance norm between the 2 vectors as:

$$d = \| HJC_{opto} - HJC_{imu} \|$$

Where $\| \|$ denotes the Euclidean norm.

## 3. Results and discussion

Table 1 shows the error *d* in HJC estimation for all tested IMU combinations, averaged across all 20 participants.

First, it should be noted that our results are in agreement with those of (García-de-Villa et al., 2021), who implemented the approach of (Crabolu et al., 2017) for the hip joint. However, our results show a considerably improved accuracy, as they reported an average error of 6.5 ± 0.1 cm using a single femoral IMU, whereas we obtained a notably lower error of 2.6 ± 1 cm with the FemLat IMU. This improvement is partly due to the use of the KneeKG system, as well as to the filtering of all three inertial signals, including angular velocity, free linear acceleration, and angular acceleration.

Our results also show that adding sacral motion to femoral movement does not necessarily improve HJC estimation. This is consistent with the findings of (Crabolu et al., 2017), who reported that incorporating scapular motion alongside arm movement did not enhance shoulder JC estimation, despite the difference in joint anatomy.

<table><caption>**Table 1.** Mean and Standard Deviation (Std) of error *d* for all IMU combinations tested</caption><thead><tr><th>IMU combination</th><th>Mean d (cm)</th><th>Std d (cm)</th></tr></thead><tbody><tr><td>FemLat</td><td>2.61</td><td>1.04</td></tr><tr><td>FemAnt</td><td>3.37</td><td>0.95</td></tr><tr><td>2 Fem</td><td>2.91</td><td>0.96</td></tr><tr><td>FemAnt, SacPlan</td><td>4.28</td><td>1.62</td></tr><tr><td>FemAnt, SacIncl</td><td>5.09</td><td>2.24</td></tr><tr><td>FemLat, SacPlan</td><td>4.72</td><td>2.23</td></tr><tr><td>FemLat, SacPlan</td><td>4.60</td><td>1.73</td></tr><tr><td>FemLat, 2 Sacr</td><td>3.53</td><td>1.40</td></tr><tr><td>FemAnt, 2 Sacr</td><td>3.74</td><td>1.49</td></tr><tr><td>2 Fem, SacPlan</td><td>4.10</td><td>1.57</td></tr><tr><td>2 Fem, SacIncl</td><td>4.88</td><td>2.21</td></tr><tr><td>2 Fem, 2 Sacr</td><td>3.47</td><td>1.48</td></tr></tbody></table>

"2 Fem" refers to the use of both FemLat and FemAnt IMUs, while "2 Sacr" refers to the use of both SacPlan and SacIncl IMUs.

Credit: Camille di Falco
Additionally, using multiple, redundant IMUs per
anatomical segment (femur or sacrum) does not enhance
accuracy either. This result may be partly explained by
the filtering method used, which might not be optimal
for inertial data measured from IMUs fixed to the
sacrum, where the amplitude of movement is lower
compared to femoral IMUs.

Furthermore, the lowest HJC estimation error is
consistently achieved with the FemLat IMU for each
three trials of all twenty subjects. Randomly assigning
the IMU to the 4 attachment sites allowed us to isolate
the effect of sensor placement on estimation accuracy,
independent of the intrinsic characteristics of a par-
ticular IMU, such as drift or sensitivity to magnetic
interference.

It should be noted that the self-selected nature of the
movement led to a wide range of execution strategies,
some resembling those of clinical populations. Future
work should include individuals with musculoskeletal
impairments to further validate the method's clinical
applicability.

4. Conclusions

These findings are clinically relevant, as they suggest
that a single IMU on the femur could be sufficient for
a hip joint center estimation. This could simplify the
initial calibration step in lower limb kinematics analysis.

Acknowledgements

The authors thank Clément Ghazouani, research assis-
tant at LIO-ÉTS, for his valuable assistance with data
collection.

Conflict of Interest Statement

None to declare.

Contributor Roles

RA: Writing- review & editing, Validation, Supervision.
NH: Writing- review & editing, Validation, Supervision,
Funding acquisition. CdF: Writing- original draft,
Visualization, Validation, Methodology, Investigation,
Formal analysis, Conceptualization.

Funding

Funding was obtained from the Alliance program of
CRSNG (ALLRP 565212 – 21).

References

Crabolu, M., Pani, D., Raffo, L., Conti, M., Crivelli, P., & Cereatti, A. (2017). In vivo estimation of the shoulder joint center of rotation using magneto-inertial sensors: MRI-based accuracy and repeatability assessment. *BioMedical Engineering OnLine, 16*(1), 34. https://do.org/10.1186/s12938-017-0324-0

García-de-Villa, S., Jiménez-Martín, A., & García-Domínguez, J. J. (2021). Novel IMU-based adaptive estimator of the center of rotation of joints for movement analysis. *IEEE Transactions on Instrumentation and Measurement, 70*, 1–11. https://do.org/10.1109/TIM.2021.3073688

Hagemeister, N., Parent, G., Van de Putte, M., St-Onge, N., Duval, N., & de Guise, J. (2005). A reproducible method for studying three-dimensional knee kinematics. *Journal of Biomechanics, 38*(9), 1926–1931. https://doi.org/10.1016/j.jbiomech.2005.05.013

Siston, R. A., & Delp, S. L. (2006). Evaluation of a new algorithm to determine the hip joint center. *Journal of Biomechanics, 39*(1), 125–130. doi: 10.1016/j.jbiomech.2004.10.032