ST-DCL: A Spatio-Temporally Decoupled Cooperative Localization Method for Dynamic Drone Swarms

In GPS-denied environments, the spatio-temporal coupling of errors caused by dynamic network topologies poses a fundamental challenge to cooperative localization, presenting existing methods with a dilemma: approaches pursuing global optimization lack dynamic adaptability, while those focusing on local adaptation struggle to guarantee global convergence. To address this challenge, this paper proposes ST-DCL, a cooperative localization framework based on a novel principle of closed-loop spatio-temporal decoupling. The core of ST-DCL comprises two modules: a Dynamic Weighted Multidimensional Scaling (DW-MDS) optimizer, responsible for providing a globally consistent coarse estimate with provable convergence, and a specially designed Spatio-Temporal Graph Neural Network (ST-GNN) corrector, tasked with compensating for local nonlinear errors. The DW-MDS effectively suppresses interference from historical errors via an adaptive sliding window and confidence weights derived from our error propagation model. The key innovation of the ST-GNN lies in its two newly designed components: a Dynamic Topological Attention Module for actively modulating neighbor aggregation to inhibit spatial error diffusion, and a Dilated Causal Convolution Module for modeling long-term temporal dependencies to curb error accumulation. These two modules form a closed loop via a confidence feedback mechanism, working in synergy to achieve continuous error suppression. Theoretical analysis indicates that the framework exhibits bounded-error convergence under dynamic topologies. In simulations involving 200 nodes, velocities up to 50 m/s, and 15% NLOS links, the ST-DCL achieves a normalized root mean square error (NRMSE) of 0.0068, representing a 21% performance improvement over state-of-the-art methods. The practical efficacy and real-time capability are further validated through real-world flight experiments with a 10-UAV swarm in complex, GPS-denied scenarios.