# Wearable Goniometer and Accelerometer Sensory Fusion for Knee Joint Angle Measurement in Daily Life

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Setup

**Figure 1.**Sensing prototype and sensor placement around the knee joint. (

**a**) A double-layer knitted piezoresistive fabrics (KPF) goniometer and two inertial measurement units (IMUs) were applied to the knee band; (

**b**) A geometrical scheme of the reference frames fixed with the body segments and the IMUs. The knee was simply modeled as a hinge joint, and the flexion-extension angle (θ) was defined as the angle between the two consecutive model segments (i.e., the angle between the x unit vectors of the ${\Psi}_{1}[{x}_{1},{y}_{1},{z}_{1}]$ and ${\Psi}_{2}[{x}_{1},{y}_{1},{z}_{1}]$ frames). IMU and accelerometer reference frames (${\Psi}_{{a}_{1}}[{x}_{{a}_{1}},{y}_{{a}_{1}},{z}_{{a}_{1}}]$ and ${\Psi}_{{a}_{2}}[{x}_{{a}_{2}},{y}_{{a}_{2}},{z}_{{a}_{2}}]$) are not aligned with the corresponding segment reference frame.

#### 2.1. KPF Goniometers

**Figure 2.**Schematic diagram of a double-layer KPF goniometer. The black stripes represent the two identical piezoresistive layers, while the gray stripe is the insulating layer. When the sensor is in the flat position, the resistance difference ($\Delta R$) between the two layers is zero. When the sensor is flexed, $\Delta R$ is proportional to the bending angle (θ), defined as the angle between the tangent planes to the sensor extremities (green dashed line in the picture).

#### 2.2. Accelerometer Alignment

**Figure 3.**The calibration procedure for the accelerometers. In the first step, using the accelerometer output only, acquired from a subject in standing position, the ${x}_{ai}$ axes of the accelerometer frame are aligned with the corresponding ${x}_{i}$ axis of the bone frames by computing the ${\widehat{\gamma}}_{i}$ and ${\widehat{\beta}}_{i}$ angles. In the second step, using data collected by the goniometer and the accelerometers in a dynamic acquisition, the remaining axes of the inertial frames are aligned with the corresponding axes of the frames fixed with the joint segments.

## 3. Fusion Algorithm

**Figure 4.**The goniometer/accelerometer fusion methods. The grey box represents the Kalman filter in its error state or indirect form.

#### 3.1. Estimation Procedure

## 4. Results

**Figure 5.**Dynamic comparison between our estimation technique and the reference measurement during contralateral monopodalic standing tasks with different knee flexion-extension velocities. The blue line represents our estimation, while the red line is the reference measurement. (

**a**) Slow knee flexion; (

**b**) Fast knee flexion.

**Figure 6.**Dynamic comparison between our estimation technique and the reference measurement during walking at different velocities. Velocities increase from (

**a**) to (

**d**). The blue line represents our estimation, while the red line is the reference measurement.

**Table 1.**Root mean square errors (RMSEs) obtained in the six trials for the various estimation methods. The first row ($RMS{E}_{hy}$) reports the errors of the hybrid system by applying the fusion technique described in this paper. The second and third rows show the textile goniometer ($RMS{E}_{g}$) and accelerometer ($RMS{E}_{acc}$) errors. The last two columns report the mean and standard deviation of the RMSE across the trials for the different measurement systems.

Slow Flexion | Fast Flexion | Walking No. 1 | Walking No. 2 | Walking No. 3 | Walking No. 4 | Average | Standard | |
---|---|---|---|---|---|---|---|---|

(Slowest) | (Fastest) | Value μ | Deviation σ | |||||

$RMS{E}_{hy}$ | 0.97${}^{\circ}$ | 3.50${}^{\circ}$ | 1.07${}^{\circ}$ | 1.6${}^{\circ}$ | 2.1${}^{\circ}$ | 2.5${}^{\circ}$ | 1.96${}^{\circ}$ | 0.96${}^{\circ}$ |

$RMS{E}_{g}$ | 5.12${}^{\circ}$ | 4.60${}^{\circ}$ | 5.40${}^{\circ}$ | 4.6${}^{\circ}$ | 5.5${}^{\circ}$ | 5.7${}^{\circ}$ | 5.15${}^{\circ}$ | 0.47${}^{\circ}$ |

$RMS{E}_{acc}$ | 1.48${}^{\circ}$ | 10${}^{\circ}$ | 5.80${}^{\circ}$ | 6.7${}^{\circ}$ | 7.1${}^{\circ}$ | 8.2${}^{\circ}$ | 6.55${}^{\circ}$ | 2.87${}^{\circ}$ |

## 5. Discussion

**Figure 7.**Signal comparison between the angle reconstruction by the accelerometers (green dotted line), the goniometer (black dotted line), the hybrid system (accelerometer + goniometer, blue solid line) and the reference measurement. (

**a**) Walking; (

**b**) Fast flexion.

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Veltink, P.H.; Rossi, D.D. Wearable technology for biomechanics: E-Textile or micromechanical sensors. IEEE Eng. Med. Biol. Mag.
**2010**, 29, 37–43. [Google Scholar] [CrossRef] [PubMed] - Interaction. Available online: http://cordis.europa.eu/project/rcn/100699_en.html (accessed on 6 November 2015).
- Tognetti, A.; Lorussi, F.; Carbonaro, N.; De Rossi, D.; De Toma, G.; Mancuso, C.; Paradiso, R.; Luinge, H.; Reenalda, J.; Droog, E.; et al. Daily-life monitoring of stroke survivors motor performance: The interaction sensing system. In Proceedings of the 2014 36th Annual International Conference of the IEEE, Chicago, IL, US, 26–30 August 2014.
- Zhu, R.; Zhou, Z. A real-time articulated human motion tracking using tri-axis inertial/magnetic sensors package. IEEE Trans. Neural Syst. Rehabil. Eng.
**2004**, 12, 295–302. [Google Scholar] [CrossRef] [PubMed] - Roetenberg, D.; Luinge, H.J.; Baten, C.; Veltink, P.H. Compensation of magnetic disturbances improves inertial and magnetic sensing of human body segment orientation. IEEE Trans. Neural Syst. Rehabil. Eng.
**2005**, 13, 395–405. [Google Scholar] [CrossRef] [PubMed] - Picerno, P.; Cereatti, A.; Cappozzo, A. Joint kinematics estimate using wearable inertial and magnetic sensing modules. Gait Posture
**2008**, 28, 588–595. [Google Scholar] [CrossRef] [PubMed] - Sabatini, A.M. Estimating three-dimensional orientation of human body parts by inertial/magnetic sensing. Sensors
**2011**, 11, 1489–1525. [Google Scholar] [CrossRef] [PubMed] - O’Donovan, K.J.; Kamnik, R.; O’Keeffe, D.T.; Lyons, G.M. An inertial and magnetic sensor based technique for joint angle measurement. J. Biomech.
**2007**, 40, 2604–2611. [Google Scholar] [CrossRef] [PubMed] - Savage, P.G. Strapdown inertial navigation integration algorithm design part 1: Attitude algorithms. J. Guid. Control Dyn.
**1998**, 21, 19–28. [Google Scholar] [CrossRef] - Luinge, H.J.; Veltink, P.H.; Baten, C.T. Ambulatory measurement of arm orientation. J. Biomech.
**2007**, 40, 78–85. [Google Scholar] [CrossRef] [PubMed] - Roetenberg, D.; Slycke, P.J.; Veltink, P.H. Ambulatory position and orientation tracking fusing magnetic and inertial sensing. IEEE Trans. Biomed. Eng.
**2007**, 54, 883–890. [Google Scholar] [CrossRef] [PubMed] - Yuan, Q.; Chen, I.M. Human velocity and dynamic behavior tracking method for inertial capture system. Sens. Actuators A Phys.
**2012**, 183, 123–131. [Google Scholar] [CrossRef] - Xsens. Available online: www.xsens.com/en/general/mtw (accessed on 6 November 2015).
- Roetenberg, D.; Luinge, H.; Slycke, P. XSens MVN: Full 6DOF Human Motion Tracking Using Miniature Inertial Sensors. Available online: www.xsens.com/wp-content/uploads/2013/12/MVN_white_paper1.pdf (accessed on 6 November 2015).
- Zhang, J.T.; Novak, A.C.; Brouwer, B.; Li, Q. Concurrent validation of XSens MVN measurement of lower limb joint angular kinematics. Physiol. Meas.
**2013**, 34, N63. [Google Scholar] [CrossRef] [PubMed] - Muro-de-la Herran, A.; Garcia-Zapirain, B.; Mendez-Zorrilla, A. Gait analysis methods: An overview of wearable and non-wearable systems, highlighting clinical applications. Sensors
**2014**, 14, 3362–3394. [Google Scholar] [CrossRef] [PubMed] - Liu, T.; Inoue, Y.; Shibata, K.; Shiojima, K.; Han, M. Triaxial joint moment estimation using a wearable three-dimensional gait analysis system. Measurement
**2014**, 47, 125–129. [Google Scholar] [CrossRef] - INSENCO. Available online: www.insenco-j.com. (accessed on 6 November 2015).
- Tech Gihan. Available online: http://www.tecgihan.co.jp/english/p7.htm (accessed on 6 November 2015).
- Luinge, H.J.; Veltink, P.H. Measuring orientation of human body segments using miniature gyroscopes and accelerometers. Med. Biol. Eng. Comput.
**2005**, 43, 273–282. [Google Scholar] [CrossRef] [PubMed] - De Vries, W.; Veeger, H.; Baten, C.; van der Helm, F. Magnetic distortion in motion labs, implications for validating inertial magnetic sensors. Gait Posture
**2009**, 29, 535–541. [Google Scholar] [CrossRef] [PubMed] - Bachmann, E.R.; Yun, X.; Brumfield, A. Limitations of attitude estimnation algorithms for inertial/magnetic sensor modules. IEEE Robot. Autom. Mag.
**2007**, 14, 76–87. [Google Scholar] [CrossRef] - Seel, T.; Raisch, J.; Schauer, T. IMU-based joint angle measurement for gait analysis. Sensors
**2014**, 14, 6891–6909. [Google Scholar] [CrossRef] [PubMed] - De Rossi, D.; Carpi, F.; Lorussi, F.; Paradiso, R.; Scilingo, E.; Tognetti, A. Electroactive fabrics and wearable man-machine interfaces. Wearable Electron. Photonics
**2005**, 4, 59–80. [Google Scholar] - Gibbs, P.T.; Asada, H.H. Wearable conductive fiber sensors for multi-axis human joint angle measurements. J. NeuroEng. Rehabil.
**2005**, 2, 7. [Google Scholar] [CrossRef] [PubMed][Green Version] - Mattmann, C.; Clemens, F.; Tröster, G. Sensor for measuring strain in textile. Sensors
**2008**, 8, 3719–3732. [Google Scholar] [CrossRef] - Gioberto, G.; Dunne, L. Theory and characterization of a top-thread coverstitched stretch sensor. In Proceedings of the 2012 IEEE International Conference on Systems, Man, and Cybernetics (SMC), Seoul, Korea, 14–17 October 2012.
- Vanello, N.; Hartwig, V.; Tesconi, M.; Ricciardi, E.; Tognetti, A.; Zupone, G.; Gassert, R.; Chapuis, D.; Sgambelluri, N.; Scilingo, E.P.; et al. Sensing glove for brain studies: design and assessment of its compatibility for fMRI with a robust test. IEEE/ASME Trans. Mechatron.
**2008**, 13, 345–354. [Google Scholar] [CrossRef] - Tognetti, A.; Lorussi, F.; Mura, G.D.; Carbonaro, N.; Pacelli, M.; Paradiso, R.; Rossi, D.D. New generation of wearable goniometers for motion capture systems. J. Neuroeng. Rehabil.
**2014**, 11, 56. [Google Scholar] [CrossRef] [PubMed] - Carbonaro, N.; Mura, G.D.; Lorussi, F.; Paradiso, R.; de Rossi, D.; Tognetti, A. Exploiting wearable goniometer technology for motion sensing gloves. IEEE J. Biomed. Health Inform.
**2014**, 18, 1788–1795. [Google Scholar] [CrossRef] [PubMed] - Dalle Mura, G.; Lorussi, F.; Tognetti, A.; Anania, G.; Carbonaro, N.; Pacelli, M.; Paradiso, R.; de Rossi, D. Piezoresistive goniometer network for sensing gloves. In Proceedings of the XIII Mediterranean Conference on Medical and Biological Engineering and Computing, Sevilla, Spain, 25–28 September 2013.
- Dejnabadi, H.; Jolles, B.M.; Aminian, K. A new approach to accurate measurement of uniaxial joint angles based on a combination of accelerometers and gyroscopes. IEEE Trans. Biomed. Eng.
**2005**, 52, 1478–1484. [Google Scholar] [CrossRef] [PubMed] - Favre, J.; Jolles, B.; Aissaoui, R.; Aminian, K. Ambulatory measurement of 3D knee joint angle. J. Biomech.
**2008**, 41, 1029–1035. [Google Scholar] [CrossRef] [PubMed] - Liu, T.; Inoue, Y.; Shibata, K. Development of a wearable sensor system for quantitative gait analysis. Measurement
**2009**, 42, 978–988. [Google Scholar] [CrossRef] - Takeda, R.; Tadano, S.; Natorigawa, A.; Todoh, M.; Yoshinari, S. Gait posture estimation using wearable acceleration and gyro sensors. J. Biomech.
**2009**, 42, 2486–2494. [Google Scholar] [CrossRef] [PubMed] - Cooper, G.; Sheret, I.; McMillian, L.; Siliverdis, K.; Sha, N.; Hodgins, D.; Kenney, L.; Howard, D. Inertial sensor-based knee flexion/extension angle estimation. J. Biomech.
**2009**, 42, 2678–2685. [Google Scholar] [CrossRef] [PubMed] - Ferrari, A.; Cutti, A.G.; Garofalo, P.; Raggi, M.; Heijboer, M.; Cappello, A.; Davalli, A. First in vivo assessment of Outwalk: A novel protocol for clinical gait analysis based on inertial and magnetic sensors. Med. Biol. Eng. Comput.
**2010**, 48, 1–15. [Google Scholar] [CrossRef] [PubMed] - Smartex srl. Available online: www.smartex.it (accessed on 6 November 2015).
- Taccini, N.; Loriga, G.; Pacelli, M.; Paradiso, R. Wearable monitoring system for chronic cardio-respiratory diseases. In Proceedings of the 30th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Vancouver, BC, Canada, 20–25 August 2008.
- Carbonaro, N.; Greco, A.; Anania, G.; Dalle Mura, G.; Tognetti, A.; Scilingo, E.P.; de Rossi, D.; Lanata, A. Unobtrusive Physiological and Gesture Wearable Acquisition System: A Preliminary Study on Behavioral and Emotional Correlations. In Proceedings of the First International Conference on Global Health Challenges, Venezia, Italia, 21–26 October 2012.
- Roumeliotis, S.; Sukhatme, G.; Bekey, G.A. Circumventing dynamic modeling: Evaluation of the error-state kalman filter applied to mobile robot localization. In Proceedings of the 1999 IEEE International Conference on Robotics and Automation, Detroit, MI, US, 10–15 May 1999.
- Panich, S. Indirect kalman filter in mobile robot application. J. Math. Stat.
**2010**, 6, 381–384. [Google Scholar] [CrossRef] - Luinge, H.J.; Veltink, P.H. Measuring orientation of human body segments using miniature gyroscopes and accelerometers. Med. Biol. Eng. Comput.
**2005**, 43, 273–282. [Google Scholar] [CrossRef] [PubMed] - Kortier, H.G.; Sluiter, V.I.; Roetenberg, D.; Veltink, P.H. Assessment of hand kinematics using inertial and magnetic sensors. J. Neuroeng. Rehabil.
**2014**, 11, 70. [Google Scholar] [CrossRef] [PubMed] - Kortier, H.; Antonsson, J.; Schepers, H.; Gustafsson, F.; Veltink, P. Hand pose estimation by fusion of inertial and magnetic sensing aided by a permanent magnet. IEEE Trans. Neural Syst. Rehabil. Eng.
**2014**, 23, 796–806. [Google Scholar] [CrossRef] [PubMed] - Grewal, M.S.; Weill, L.R.; Andrews, A.P. Global Positioning Systems, Inertial Navigation, and Integration; John Wiley & Sons: Hoboken, NJ, US, 2007. [Google Scholar]
- Hansson, G.; Mikkelsen, S. Kinematic evaluation of occupational work. Adv. Occup. Med. Rehabil.
**1997**, 3, 57–69. [Google Scholar] - Yen, T.Y.; Radwin, R.G. Comparison between using spectral analysis of electrogoniometer data and observational analysis to quantify repetitive motion and ergonomic changes in cyclical industrial work. Ergonomics
**2000**, 43, 106–132. [Google Scholar] [CrossRef] [PubMed] - Johnson, P.W.; Jonsson, P.; Hagberg, M. Comparison of measurement accuracy between two wrist goniometer systems during pronation and supination. J. Electromyogr. Kinesiol.
**2002**, 12, 413–420. [Google Scholar] [CrossRef] - Reinschmidt, C.; van den Bogert, A.; Lundberg, A.; Nigg, B.; Murphy, N.; Stacoff, A.; Stano, A. Tibiofemoral and tibiocalcaneal motion during walking: external vs. skeletal markers. Gait Posture
**1997**, 6, 98–109. [Google Scholar] [CrossRef]

© 2015 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Tognetti, A.; Lorussi, F.; Carbonaro, N.; De Rossi, D.
Wearable Goniometer and Accelerometer Sensory Fusion for Knee Joint Angle Measurement in Daily Life. *Sensors* **2015**, *15*, 28435-28455.
https://doi.org/10.3390/s151128435

**AMA Style**

Tognetti A, Lorussi F, Carbonaro N, De Rossi D.
Wearable Goniometer and Accelerometer Sensory Fusion for Knee Joint Angle Measurement in Daily Life. *Sensors*. 2015; 15(11):28435-28455.
https://doi.org/10.3390/s151128435

**Chicago/Turabian Style**

Tognetti, Alessandro, Federico Lorussi, Nicola Carbonaro, and Danilo De Rossi.
2015. "Wearable Goniometer and Accelerometer Sensory Fusion for Knee Joint Angle Measurement in Daily Life" *Sensors* 15, no. 11: 28435-28455.
https://doi.org/10.3390/s151128435