This paper presents a novel approach to range-based cooperative localization for robot swarms in GPS-denied environments, addressing the limitations of current methods in noisy and sparse settings. We propose a robust multi-layered localization framework that combines shadow edge localization techniques with the strategic deployment of UAVs. This approach not only addresses the challenges associated with nonrigid and poorly connected graphs but also enhances the convergence rate of the localization process. We introduce two key concepts: the S1-Edge approach in our distributed protocol to address the rigidity problem of sparse graphs and the concept of a powerful UAV node to increase the sensing and localization capability of the multi-robot system. Our approach leverages the advantages of the distributed localization methods, enhancing scalability and adaptability in large robot networks. We establish theoretical conditions for the new S1-Edge that ensure solutions exist even in the presence of noise, thereby validating the effectiveness of shadow edge localization. Extensive simulation experiments confirm the superior performance of our method compared to state-of-the-art techniques, resulting in up to 95\% reduction in localization error, demonstrating substantial improvements in localization accuracy and robustness to sparse graphs. This work provides a decisive advancement in the field of multi-robot localization, offering a powerful tool for high-performance and reliable operations in challenging environments.

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