Graph Laplacian-Based Sequential Smooth Estimator for Three-Dimensional RSS Map

In wireless links between ground stations and UAVs (Unmanned Aerial Vehicles), wireless signals may be attenuated by obstructions such as buildings. A three-dimensional RSS (Received Signal Strength) map (3D-RSS map), which represents a set of RSSs at various reception points in a three-dimensional area, is a promising geographical database that can be used to design reliable ground-to-air wireless links. The construction of a 3D-RSS map requires higher computational complexity, especially for a large 3D area. In order to sequentially estimate a 3D-RSS map from partial observations of RSS values in the 3D area, we propose a graph Laplacian-based sequential smooth estimator. In the proposed estimator, the 3D area is divided into voxels, and a UAV observes the RSS values at the voxels along a predetermined path. By considering the voxels as vertices in an undirected graph, a measurement graph is dynamically constructed using vertices from which recent observations were obtained and their neighboring vertices, and the 3D-RSS map is sequentially estimated by performing graph Laplacian regularized least square estimation.