VRPF: A Fine-Grained 3D Radar Power-Density Computation Framework Based on Photogrammetric City Models for Urban Observation

Radar is critical for urban security against Unmanned Aerial Vehicles (UAVs), yet signal occlusion caused by dense buildings and complex urban structures remains a major challenge for coverage assessment. Existing approaches commonly rely on 2D maps or 2.5D Digital Surface Models (DSMs), which have difficulty representing vertical facades, vegetation, bridges, overhanging structures, and void spaces. These geometric limitations can introduce errors in radar occlusion determination and direct-path power-density estimation. Full 3D ray-tracing methods offer high fidelity, but their multi-path modeling and material-parameter requirements can be costly for large oblique photogrammetric city meshes. To address this problem, this paper proposes the Visible Radar Power-Density Field (VRPF), a 3D radar power-density field computation framework based on high-resolution oblique photogrammetric models. The method constructs a reusable spatial index for large numbers of triangular facets and performs two-stage occlusion queries: rapid Axis-Aligned Bounding Box (AABB) pruning followed by ray-triangle intersection tests. Together, these components enable efficient direct-path power-density calculation while accounting for line-of-sight occlusion in complex urban scenes. Qualitative and quantitative experiments show that VRPF better preserves occlusion boundaries around building edges, vegetation, and elevated structures than DSM-based baselines. VRPF also requires less time for repeated occlusion queries than a conventional 3D BVH ray-casting baseline while maintaining highly consistent radar-signal occlusion determinations. With 32 threads, VRPF computes power density for 108 target points in 5.92 s, about 2.66× faster than the 1 m DSM method. These results indicate that VRPF provides a practical balance between geometric fidelity and computational efficiency for direct-path radar power-density assessment with urban geometric occlusion.