INTRODUCTION: In ski cross, jumps represent key phases of the race. Therefore, it is essential that they are realistically depicted when creating a first-person virtual reality (VR) application to replay a race in an immersive way. Currently, when a VR application is based on real trajectories, these are mostly measured using a GNSS receiver in single point positioning (SPP) mode, which provides an accuracy of about 2 to 6 meters for the horizontal and vertical components, respectively. As a result, GNSS SPP altitudes are not usable for such applications. When the athlete is not in flight phase, the digital terrain model can be appropriately used to predict the athlete's altitude. However, when the athlete is jumping, it is necessary to obtain their trajectory in the air through an appropriate ballistic calculation. The objective of this work is therefore to propose a solution to determine the complete trajectory (including during jumps) of an athlete by merging GNSS SPP positions, a digital terrain model, and a ballistic model in order to create a smooth and immersive VR experience in a realistic 3D environment. METHODS: Two VR applications were developed. The first is a VR application to assist in the efficient determination of fused trajectories, and the second is an immersive first-person VR visualization for the ski cross track. To achieve this, a high-resolution 3D model of the ski cross track and its surroundings was generated using drone-based photogrammetric surveying. Additionally, the athletes' trajectories were measured using GNSS SPP technology. The first VR application allows users to visualize the track and interactively set the jump origins on each obstacle. The fused trajectory is displayed in real-time in an immersive and dynamic manner, and it can be adjusted on the fly if necessary. The trajectory fusion algorithm is based on control theory, combining GNSS horizontal data with ballistic calculations that account for gravity and simple aerodynamic effects. RESULTS/DISCUSSION: The initial results of the fusion algorithm are encouraging and have made it possible to determine realistic and usable trajectories for the VR application, benefiting both athletes and coaches. The VR application, which allows the adjustment of the jump-starting position as well as the initial impulse parameters, has proven to be effective and user-friendly. However, it would be feasible to automate some of these adjustments. The automation process and the data fusion for trajectory determination could also be improved by integrating data from accelerometers. CONCLUSION: The developed tools allow for the easy determination of ski cross athletes' trajectories by merging GNSS SPP data, a digital terrain model, and a simple ballistic model. The methodologies developed can also be applied to other disciplines, such as alpine skiing or ski jumping, where the vertical component of the trajectories measured by GNSS SPP technology is insufficient.
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