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

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## Abstract

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## 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

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**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