Multi-fidelity Gaussian Process Learning for 3D Urban Radio Map Reconstruction from Sparse UAV Measurements

Reliable three-dimensional (3D) radio maps are a key enabler for low-altitude Unmanned Aerial Vehicle (UAV) operations in dense urban environments, since path planning, link adaptation, and coverage assessment all benefit from accurate spatial signal-quality estimates. Most existing radio-map studies, however, focus on two-dimensional estimation, rely on simulation-only benchmarks, or use Reference Signal Received Power (RSRP)-only metrics, which collectively fail to reflect actual deployment conditions. Real measurements, in contrast, are expensive to collect, sparse, and unevenly distributed across altitude layers. To bridge this gap, this paper develops a real-world 3D urban radio-map construction pipeline together with a multi-fidelity Gaussian process regression (mfGPR) estimator that fuses dense ray-tracing simulation (low fidelity) with sparse UAV measurements (high fidelity), and adopts the Third Generation Partnership Project (3GPP) cell-selection criterion (S-criterion) as the prediction target so that both received power and received quality are jointly captured. To use the limited high-fidelity budget more effectively, a two-stage sampling strategy is introduced, combining anisotropic farthest-point coverage with metric-driven densification.Experiments on a measurement campaign in an urban district of Macao show that, when averaged over sampling rates of 10%–100%, mfGPR reduces root-mean-square error (RMSE) by about 2.5decibels (dB) and mean absolute error (MAE) by about 1.9 dB and raises R2 by roughly 0.42 on the high-fidelity test set relative to the four single-fidelity baselines (inverse distance weighting (IDW), k-nearest neighbors (KNN), vanilla Gaussian process regression (GPR), and Kriging); the advantage is largest at the high-budget end, while at sparse rates the strongest classical baseline (Kriging or IDW under the proposed sampler) is within a few tenths of a dB. In the sparse-sampling regime that characterizes UAV campaigns, mfGPR also outperforms modern learning-based baselines (a deep neural network, a Conditional Neural Process, and Deep Kernel Learning), which tend to overfit the limited high-fidelity data, although these models become competitive at the full measurement budget. The trend holds across altitude layers and remains stable under simulation-bias perturbations of up to 10 dB. Ablations further show that the simulation prior and the sampling strategy contribute complementary, non-redundant gains. The proposed framework therefore offers a practical basis for 3D radio-map reconstruction in support of UAV-assisted communications.