High-Efficiency Urban 3D Radio Map Estimation Based on Sparse Measurements

Recent widespread applications for unmanned aerial vehicles (UAVs) – from infrastructure inspection to urban logistics – have prompted an urgent need for high-accuracy three-dimensional (3D) radio maps. However, existing methods designed for two-dimensional radio maps face challenges of high measurement costs and limited data availability when extended to 3D scenarios. To tackle these challenges, we first build a real-world large-scale 3D radio map dataset, covering over 4.2 million <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\rm {{m}}^{3}$</tex-math></inline-formula> and over 4 thousand data points in complex urban environments. We propose a Gaussian Process Regression-based scheme for 3D radio map estimation, allowing us to realize more accurate map recovery with a lower RMSE than state-of-the-art schemes by over 2.5dB. To further enhance data efficiency, we propose two methods for training point selection, including an offline clustering-based method and an online maximum a posterior (MAP)-based method. Extensive experiments demonstrate that the proposed scheme not only achieves full-map recovery with only 2% of UAV measurements, but also sheds light on future studies on 3D radio maps.