###### Abstract  
The advent of 5G technology has facilitated the adoption of private cellular networks in industrial settings. Ensuring reliable coverage while maintaining certain requirements at its boundaries is crucial for successful deployment yet challenging without extensive measurements. In this article, we propose the leveraging of unmanned aerial vehicles (UAVs) and Gaussian processes (GPs) to reduce the complexity of this task. Physics-informed mean functions, including a detailed ray-tracing simulation, are integrated into the GP models to enhance the extrapolation performance of the GP prediction. As a central element of the GP prediction, a quantitative evaluation of different mean functions is conducted. The most promising candidates are then integrated into an informative path-planning algorithm tasked with performing an efficient UAV-based cellular network mapping. The algorithm combines the physics-informed GP models with Bayesian optimization and is developed and tested in a hardware-in-the-loop simulation. The quantitative evaluation of the mean functions and the informative path-planning simulation are based on real-world measurements of the 5G reference signal received power (RSRP) in a cellular 5G-SA campus network at the Port of Lubeck, Germany. These measurements serve as ground truth for both evaluations. The evaluation results demonstrate that using an appropriate mean function can result in an enhanced prediction accuracy of the GP model and provide a suitable basis for informative path planning. The subsequent informative path-planning simulation experiments highlight these findings. For a fixed maximum travel distance, a path is iteratively computed, reducing the flight distance by up to 98 % while maintaining an average root-mean-square error of less than 6 dBm when compared to the measurement trials. unmanned aerial vehicle; drone; path planning; mapping; mobile network; 5G; Bayes methods; Gaussian processes +
Footnote †: journal: Sensors  
0000-0001-998-0000-0001-9989-9999-9999-9999-9999-9999-9999-99999-9999-99999-99999-99999-99999-99999-99999-99999-99999-99999-99999-99999-99999-99999-99999-99999-99999-99999-99999-99999-99999-999999-99999-99999-99999 physical network due to unmodeled structures and obstacles or other sources of error [2]. Monitoring and structured measurement of the physical network using an unmanned aerial vehicle (UAV) can provide insights into unforeseen weak spots that can be avoided by changing the antenna orientation or adding new antennas to the network if necessary. This helps to improve its performance and reliability. Furthermore, compliance with legal limits on signal strength, especially at the boundaries of the network site, can also be confirmed with such measurements. To avoid missing important locations, i.e., areas with insufficient coverage or areas exceeding legal limits, the UAV's flight path usually follows a dense grid while flying at low speed. However, such a flight path contradicts the battery-power limitation of common multicopter configurations for UAVs. To the best of our knowledge, previous structured cellular network coverage measurements conducted using a UAV have been limited to small one- or two-dimensional measurement areas (cf., [3]). For instance, [PERSON] et al. [4] and [PERSON] [5] presented only one-dimensional measurements in a 4G LTE network, while [PERSON] et al. [6] conducted two-dimensional measurements in a 5G network. To average out measurement noise, they stopped at waypoints along the measurement trajectory and considered only the average measurement at those waypoints, applying natural neighbor interpolation to the cluster centroids and their means to create a two-dimensional map. [PERSON] et al. [7] and [PERSON] et al. [8] showed that Gaussian Processes (GPs) are beneficial for predicting signal strengths in mobile networks. GPs are nonparametric, kernel-based probabilistic models that can incorporate prior information about an unknown function by means of their mean and covariance function [9].