Formation-Constrained Cooperative Localization for UAV Swarms in GNSS-Denied Environments

Cooperative localization is critical for UAV swarm operations in GNSS-denied environments. The backbone-listener scheme, using a small subset of agents as active backbone nodes and others as passive listeners, offers notable advantages in reducing communication overhead and enhancing swarm scalability. Building on this scheme, we propose a formation-constrained cooperative localization method to improve accuracy by integrating known formation geometry into the localization process. First, backbone node selection uses a formation-constrained greedy node activation (GNA) strategy with weighted distance fusion, combining measured and ideal formation distances to enable near-optimal selection aligned with formation structure. Second, listener node localization incorporates formation constraints into Chan's algorithm, paired with angle-of-arrival (AOA) refinement, to ensure estimated positions match expected inter-agent distances. Third, global optimization uses a gradient descent-based refinement to enforce formation constraints across all agent positions. Our theoretical derivations and simulations are limited to the two-dimensional (2D) case. Simulation results validate the proposed method's improved success rate, reliability, and stability. Its effectiveness is demonstrated across various formation types, with robust adaptability to asymmetric geometries shown to be a valuable feature for practical deployment.