# Experimental Validation of Real-Time Ski Jumping Tracking System Based on Wearable Sensors

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Measurement Systems

#### 2.1.1. Wearable Real-Time Tracking System (WRRTS)

#### 2.1.2. Official Distance Measurements

#### 2.1.3. Camera Measurements (ccc Software GmbH)

#### 2.1.4. Total Station Tracking (QDaedalus System)

#### 2.2. Venue

#### 2.3. Evaluation

#### 2.3.1. Synchronization

#### 2.3.2. Statistical Analysis

## 3. Results

#### 3.1. Official Video Distance

#### 3.2. Camera Measurements (ccc Software GmbH)

#### 3.2.1. Projection of 3D WRRTS Measurements into the 2D Image Plane

#### 3.2.2. Comparison of 3D WRRTS Position Measurements with 3D Camera Vectors

#### 3.2.3. Comparison of 3D WRRTS Position Measurements with 3D QDaedalus Measurements

#### 3.2.4. Comparison of 3D WRRTS Angle Measurements with 3D Camera Vectors

## 4. Discussion

#### 4.1. Jumping Distance

#### 4.2. Projection of 3D WRRTS Measurements into the 2D Image Plane

#### 4.3. Comparison of 3D WRRTS Position Measurements with 3D Camera Vectors

#### 4.4. Comparison of 3D WRRTS Angle Measurements with 3D Camera Vectors

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

dGNSS | differential Global Navigation Satellite System |

FIS | Fédération Internationale de Ski |

IMU | inertial measurement unit |

LoA | limit of agreement |

MAE | mean absolute error |

PTZ | pan–tilt–zoom |

SEM | standard error of the mean |

UWB | ultra-wideband |

WRTTS | wearable real-time tracking system |

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**Figure 1.**Definition of the local coordinate system with respect to the ski jumping hill. The origin of the coordinate system is the middle of the edge of the jump-off platform. With respect to the jumping direction, the axes are defined as: X-axis: horizontal, forward, Y-axis: horizontal, left, Z-axis: vertical, upward. Additionally, the setup at the ski jumping hill is presented. This includes the positions of the antennas of the WRRTS, the total stations of the QDaedalus system, the cameras, and the 3D models of the ski jumping in-run and landing hill.

**Figure 2.**Attachment of the wearable tracker on top of the binding of the skis. The tracker is mounted on top of the regular ski jumping binding in front of the foot (tracker in white).

**Figure 3.**Example for the manual determination of the official video-based jumping distance. The red lines are the calibrated projection of the official jumping distance (to the jump-off platform). The blue line corresponds to the determined jumping distance.

**Figure 4.**Example for the manual labeling of the tracker positions and skis for the cameras next to the jumping hill.

**Figure 5.**Example of the manual labeling of the V-angle 2 s after the crossing of the jump-off platform. The PTZ camera is mounted at the top of the in-run.

**Figure 6.**Bland–Altman plot for the comparison jumping distance determined with the WRRTS and the official video distance.

**Figure 7.**Projection of the WRRTS position data onto the video of the camera at 18 m after take-off. The cyan curve shows the trajectory of the WRRTS tracker placed on the binding of the left foot. The magenta curve shows the trajectory of the right tracker. The numbers indicate the corresponding 3D coordinates in meters. Coordinates as depicted in Figure 1.

**Figure 8.**Bland–Altman plot for the comparison of the X-coordinate determined with the WRRTS and camera vectors.

**Figure 9.**Bland–Altman plot for the comparison of the Z-coordinate determined with the WRRTS and camera vectors.

**Figure 10.**The left part shows a scatter plot for the comparison of the three-dimensional position measured with the WRRTS and QDaedalus tracking. The distance on the X-axis is the mean distance of WRRTS and QDaedalus to the jump-off platform. The histogram of the projection of the distance between both measurement methods is visualized in the right part. The fitted beta distribution is also plotted in the projection.

**Figure 11.**The left part shows the Bland–Altman plot for the comparison of the angle measured with the WRRTS and the angle determined in the camera images from the side along the jumping hill. The right part shows the projected histogram of the difference as well as the fitted Student’s t-distribution. The gray arrows and numbers at the top of the plot indicate three measured angles out of the plot’s range.

**Figure 12.**Bland–Altman plot for the comparison of the projected V-angle measured with the WRRTS and the PTZ camera.

**Table 1.**Bias, SEM, and precision of the X- and Z-coordinate determined with the WRRTS and camera vectors for every camera individually.

Coordinate | Metric | Camera Position | ||||
---|---|---|---|---|---|---|

0 m | 8 m | 18 m | 45 m | 60 m | ||

X | bias [m] | −0.001 | −0.0086 | −0.008 | −0.088 | −0.077 |

SEM [m] | 0.001 | 0.0005 | 0.001 | 0.004 | 0.005 | |

precision [m] | 0.01 | 0.007 | 0.02 | 0.05 | 0.06 | |

Z | bias [m] | −0.001 | −0.048 | −0.026 | −0.151 | −0.108 |

SEM [m] | 0.002 | 0.003 | 0.004 | 0.007 | 0.007 | |

precision [m] | 0.02 | 0.03 | 0.06 | 0.08 | 0.08 |

**Table 2.**MAE between the WRRTS and the respective reference system for all parameters investigated in this study.

Parameter | Accuracy (MAE) |
---|---|

jumping distance | $0.46\text{}\mathrm{m}$ |

3D position | $0.12\text{}\mathrm{m}$ |

lateral angle | $0.8{}^{\xb0}$ |

V-angle | $3.4{}^{\xb0}$ |

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**MDPI and ACS Style**

Link, J.; Guillaume, S.; Eskofier, B.M.
Experimental Validation of Real-Time Ski Jumping Tracking System Based on Wearable Sensors. *Sensors* **2021**, *21*, 7780.
https://doi.org/10.3390/s21237780

**AMA Style**

Link J, Guillaume S, Eskofier BM.
Experimental Validation of Real-Time Ski Jumping Tracking System Based on Wearable Sensors. *Sensors*. 2021; 21(23):7780.
https://doi.org/10.3390/s21237780

**Chicago/Turabian Style**

Link, Johannes, Sébastien Guillaume, and Bjoern M. Eskofier.
2021. "Experimental Validation of Real-Time Ski Jumping Tracking System Based on Wearable Sensors" *Sensors* 21, no. 23: 7780.
https://doi.org/10.3390/s21237780