###### Abstract
The common simplification of the GP mean to a zero function is not well suited for extrapolation because the posterior mean converges to zero in areas with fewer measurements. Thus, [PERSON] et al. [7] and [PERSON] et al. [8] incorporated path loss and fading effects into GP mean and covariance, respectively. However, to the best of our knowledge, in the case of UAV mapping and path planning, it has not yet been investigated how the mean function influences the GP prediction performance. In this work, we present novel and comprehensive three-dimensional 5G signal strength measurements in volumes of up to \(1.7\times 10^{4}\) m\({}^{3}\) within a cellular campus network at the largest German harbor on the Baltic Sea, the Skandinavienkai of the Port of Lubeck, Germany. We show that GP regression is suitable for predicting missing information and identifying regions that require further examination. Furthermore, GPs inherently provide uncertainty estimates with any prediction. This approach also enables larger three-dimensional measurement areas to be surveyed despite limited flight time. Instead of stopping at waypoints to average out measurement noise (cf., [6]), the GP models the measurement noise as Gaussian white noise. The first main contribution of this article is the extension of the idea of [PERSON] et al. [7] by analyzing the influence of different physics-informed mean priors of varying complexity, including a full ray-tracing simulation, as the GP mean function. In order to address the sequential nature of data collection in a realistic UAV mapping application, we evaluate the performance using a more natural (and challenging) split between training and testing data points. We purposefully use the data points from the measurement data in the order they were collected instead of random points from the entire training set. The second main contribution is the application of a GP model with physics-informed mean functions as a basis for informative path planning (IPP) of the UAV flight path. The IPP problem, also known as robotic information gathering (cf., [10]), is concerned with planning the trajectory of a robot, i.e., a UAV, with a measurement unit to collect informative measurements for efficient mapping of a search space with as few measurements or as short a path length as possible. Available approaches include continuous IPP using Bayesian optimization [11; 12], evolutionary strategies [13], and iterative candidate selection approaches [10; 14], which differ in their sampling and selection strategies. The algorithms for a continuous IPP proposed by [PERSON], [PERSON], and [PERSON] using continuous splineswith numerous free parameters [11] or partially observable Markov decision processes (POMDPs) [12] are too computationally complex for online path planning onboard a UAV. In the candidate selection method proposed by [PERSON] et al. [10; 14], a utility function based on mutual information is maximized. However, a fixed target is approached, making it unfit for a mapping task. For this reason, we choose to draw random candidate points across the search area and select the candidate with the highest expected reward. Similarly, the expected entropy of each point was used as a reward by [PERSON] et al. [10] for their active sampling strategy, but the measurements collected along the path to that point were omitted. We present a novel combined algorithm that defines a continuous informative path within a three-dimensional search area using a fixed maximum total length of all segments. Different configurations of the approach are assessed in a real-time hardware-in-the-loop simulation using the M300 UAV platform by DJI (Shenzhen, China). The third central contribution of this paper is the development of a UAV-based 5G measurement system that accurately performs a three-dimensional mapping of a 5G network site within the premises of the Port of Lubeck using physics-informed GP-based data processing.