# Does the Position of Foot-Mounted IMU Sensors Influence the Accuracy of Spatio-Temporal Parameters in Endurance Running?

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## Abstract

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## 1. Introduction

## 2. Methods

#### 2.1. Definition of Spatio-Temporal Parameters

#### 2.2. Data Set

- (1)
- Vector pair superior/inferior direction: The subjects were asked to stand still with both feet on the ground. Thus, the accelerometer of all sensors measured the gravitational acceleration in the sensor frame. The ${z}_{s}$-axis was defined as the corresponding vector in the shoe frame.
- (2)
- Vector pair medial/lateral direction: The subjects rotated their feet on a balance board, which only allowed for a rotation in the shoe frame’s sagittal plane. A gyroscope in the shoe frame measures the angular rate of the rotation on the medial/lateral axis. The medial/lateral axis of the shoe frame corresponds to the principle component of the angular rate data during rotation in the sensor frame. The ${x}_{s}$-axis was defined as the medial/lateral axis in the shoe frame.

#### 2.3. Algorithm

#### 2.3.1. Stride Segmentation

#### 2.3.2. Computation of Foot Trajectory

#### 2.3.3. Parameter Computation

#### 2.4. Evaluation

#### 2.4.1. Evaluation of Raw Data Similarity

#### 2.4.2. Evaluation of Spatio-Temporal Parameters

## 3. Results

#### 3.1. Results of Raw Data Similarity

#### 3.2. Results of Spatio-Temporal Parameters

## 4. Discussion

#### 4.1. Differences in Raw Data

#### 4.2. Temporal Parameters

#### 4.3. Spatial Parameters

#### 4.4. General Aspects

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

IMU | Inertial measurement unit |

IC | Initial contact |

TO | Toe off |

MS | Midstance |

## Appendix A. Trajectory Computation Plots

**Figure A1.**Acceleration $\overrightarrow{a}\left[t\right]$ and annular rate $\overrightarrow{\omega}\left[t\right]$ raw data of heel sensor.

**Figure A2.**Visualization of the gravity removal in the acceleration signal for a sample stride of the heel sensor. The upper plot shows the raw acceleration $\overrightarrow{a}\left[t\right]$ segmented from MS to MS measured by the accelerometer. The lower plot shows the gravity corrected acceleration signal ${\overrightarrow{a}}_{gc}\left[t\right]$ after rotating the raw acceleration by the quaternion sequence $\mathbf{q}\left[n\right]$ and removing gravity from the rotated signal. After the gravity removal, both the z-components of the acceleration at the first midstance ($t=0$ s) and the second midstance ($t=0.81$ s) have values close to zero.

**Figure A3.**Visualization of the dedrifting of the velocity after the first integration of the acceleration signal for a sample stride of the heel sensor. The upper plot shows the velocity $\overrightarrow{v}\left[t\right]$ before dedrifting. This signal displays that the velocity at the second midstance ($t=0.81$ s) is not zero. We enforce the velocity to be zero by dedrifing the velocity using a linear dedrifting function. The lower plot shows the velocity ${\overrightarrow{v}}_{dedrifted}\left[t\right]$ after dedrifting. Now, the velocity at the second MS is zero in all directions.

**Figure A4.**Visualization of the trajectory for a sample stride of the heel sensor. The upper plot shows the orientation $\overrightarrow{\alpha \left[t\right]}$ obtained by the quaternion based forward integration after converting the quaternions back to their angle representation. The lower plot shows the translation $\overrightarrow{s}\left[t\right]$ obtained by dedrifted double integration of the gravity corrected acceleration ${\overrightarrow{a}}_{gc}\left[t\right]$

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**Figure 3.**Visualization of sensor positions on the running shoes, the global coordinate system $({x}_{g},{y}_{g},{z}_{g})$, the shoe coordinate system $({x}_{s},{y}_{s},{z}_{s})$, and the individual sensor coordinate systems. When the foot is flat on the ground, the global and the shoe coordinate system are aligned.

**Figure 4.**Visualization of the functional calibration procedure. The first part of the functional calibration consisted of standing still with the foot flat on the ground in order to measure gravity. During the second part the subjects rotated their feet on a balance board to compute the medial/lateral axis using a principal component analysis.

**Figure 5.**Exemplary IMU data of one stride segmented from IC to IC for the four different sensor positions.

**Figure 6.**Visualization of the stride segmentation for the cavity sensor using the gyroscope signal in the sagittal plane ${\omega}_{x}\left[t\right]$. The fiducial points at swing phase ${n}_{SP}$ are local minima of the angular rate in the sagittal plane. The index ${n}_{IC}$ indicates the index of IC, which corresponds to the bias corrected local maximum after ${n}_{SP}$. The MS event ${n}_{MS}$ is at the minimum of the gyroscopic energy. The TO event at ${n}_{TO}$ is based on the second local maxima and a bias correction.

**Figure 7.**Visualization of angle computation for a sample stride from the cavity sensor. The angles are depicted from ${n}_{IC}$ ($t=0$ s) to ${n}_{TO}$ ($t=0.32$ s). The sole angle is defined as the rotation in the sagittal plane between IC and MS. As the orientation is initialized with zero at MS, the sole angle is the angle at ${n}_{IC}$. The range of motion is defined as the difference between the maximum and minimum (red dots) of the angle in the frontal plane during ground contact.

**Figure 8.**Results of the evaluation of the Pearson’s correlation coefficients between the IMU raw signals. Each box visualizes the correlation coefficients between two sensors for all the strides in x, y, and z direction. The box plots also display the median of the correlations (median line), the IQR (box), and the 5 and 95 percentiles (whiskers). The upper plot depicts the correlation of the full strides, the middle plot the correlations during the ground contact phase, and the lower plot the correlations during the swing phase.

**Figure 9.**Visualization of the error for (

**a**) stride length and (

**b**) the acceleration at the zero-velocity update for the four different sensor positions in different speed ranges.

Name | Mounting |
---|---|

Cavity | Cavity cut in the sole of the shoe under the arch |

Instep | Mounted with suiting clip to laces of the shoe |

Lateral | Mounted with tape laterally under ankle |

Heel | Mounted with tape on heel cap |

**Table 2.**Number of trials and recorded strides per velocity range. During the data acquisition, we controlled for speed and the subjects only changed the velocity range, if the required number of trials in the previous (slower) velocity range was reached.

Velocity Range (m/s) | Number of Trials | Number of Strides |
---|---|---|

2–3 | 10 | 962 |

3–4 | 10 | 558 |

4–5 | 15 | 544 |

5–6 | 15 | 362 |

**Table 3.**Median error and IQR of the error for the parameters stride time, ground contact time, stride length, average stride velocity, sole angle, and range of motion compared to the motion capture system.

Cavity | Heel | Instep | Lateral | |||||
---|---|---|---|---|---|---|---|---|

Median | IQR | Median | IQR | Median | IQR | Median | IQR | |

Stride time (ms) | −0.5 | 6.9 | 0.0 | 8.4 | 0.4 | 7.6 | 0.3 | 8.6 |

Ground contact time (ms) | −11.0 | 37.6 | −1.3 | 29.5 | −22.6 | 37.5 | −1.7 | 29.0 |

Sole angle (${}^{\circ}$) | 1.6 | 7.2 | −6.1 | 5.1 | 2.1 | 5.8 | −5.9 | 5.1 |

Range of motion (${}^{\circ}$) | 0.0 | 2.8 | 1.2 | 2.9 | 2.3 | 3.3 | 1.4 | 3.0 |

Stride length (cm) | 0.3 | 8.5 | −8.3 | 14.7 | −5.6 | 15.1 | −3.3 | 9.7 |

Avg. stride velocity (m/s) | 0.0 | 0.1 | −0.1 | 0.2 | −0.1 | 0.2 | 0.0 | 0.1 |

**Table 4.**Median error and IQR of the error for the parameters sole angle without the bias correction for IC.

Cavity | Heel | Instep | Lateral | |||||
---|---|---|---|---|---|---|---|---|

Median | IQR | Median | IQR | Median | IQR | Median | IQR | |

Sole angle (${}^{\circ}$) | 6.8 | 10.2 | −2.9 | 6.8 | 6.7 | 7.0 | −2.4 | 6.7 |

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**MDPI and ACS Style**

Zrenner, M.; Küderle, A.; Roth, N.; Jensen, U.; Dümler, B.; Eskofier, B.M.
Does the Position of Foot-Mounted IMU Sensors Influence the Accuracy of Spatio-Temporal Parameters in Endurance Running? *Sensors* **2020**, *20*, 5705.
https://doi.org/10.3390/s20195705

**AMA Style**

Zrenner M, Küderle A, Roth N, Jensen U, Dümler B, Eskofier BM.
Does the Position of Foot-Mounted IMU Sensors Influence the Accuracy of Spatio-Temporal Parameters in Endurance Running? *Sensors*. 2020; 20(19):5705.
https://doi.org/10.3390/s20195705

**Chicago/Turabian Style**

Zrenner, Markus, Arne Küderle, Nils Roth, Ulf Jensen, Burkhard Dümler, and Bjoern M. Eskofier.
2020. "Does the Position of Foot-Mounted IMU Sensors Influence the Accuracy of Spatio-Temporal Parameters in Endurance Running?" *Sensors* 20, no. 19: 5705.
https://doi.org/10.3390/s20195705