Distributionally Robust Kalman Filter Under Likelihood Model Mismatch From an Optimization Perspective— Part II: Extension and Application to Cooperative Localization

Cooperative localization enhances positioning performance by exploiting relative measurements and information exchange within a swarm system. Fully distributed cooperative localization, wherein each agent maintains and shares only its local state information, is particularly attractive due to its low communication overhead and strong scalability. However, the lack of correlation information prevents fully distributed cooperative localization from precisely maintaining likelihood model and leads to an inherent likelihood model mismatch problem, which causes inconsistent and inaccurate relative measurement update. To address this issue, the robust filtering method proposed in the companion paper (Part I) is considered to reduce the sensitivity of the state estimation to the likelihood model mismatch and improve the estimation consistency and accuracy. To better balance estimation accuracy and consistency, this robust filtering method is further extended by incorporating the$\gamma$-divergence, which enables a tunable trade-off between the estimation accuracy and consistency through the parameter$\gamma$. Based on this extension, a fully distributed cooperative localization framework is developed. A theoretical analysis is conducted to elucidate the impact of the tunable parameter$\gamma$on estimation accuracy and consistency. Extensive simulations, dataset evaluations, and real-world experiments validate the effectiveness of the proposed approach and demonstrate its advantages over existing state-of-the-art cooperative localization methods.