Normalizing Flow-Enhanced Message Passing for Multirobot Collaborative Localization

Robotic localization under changing sensing conditions can suffer from biased errors and miscalibrated covariances. We present WRAP, an adapter-agnostic Wasserstein-robust plug-in for nonlinear extended Kalman filter (EKF) and error-state Kalman filter (ESKF) stacks. A causal module supplies time-varying effective process and measurement statistics; a mean-preserving Wasserstein local update then computes least-favorable covariances and a robust gain without changing the propagation model, residual, or retraction. This separates mean adaptation from covariance robustification and uses distinct radii for propagation and sensing. On 18 UWB--IMU sequences held out from adapter training, adapter-only and WRAP reduce mean 3-D position RMSE by $19.8\%$ and $27.4\%$ relative to the nominal ESKF; an isotropic ablation reaches $19.5\%$, linking the incremental gain to directional process-covariance redistribution. An in-sample GNSS--INS study shows that mean adaptation provides most of the accuracy gain, while DR improves consistency and mitigates over-tightened classical covariance estimates. The robust solve takes 0.05 ms for UWB and 2.92 ms for GNSS on a Jetson Orin Nano.

Multi-robot localization that is accurate and consistent is imperative for downstream tasks such as planning and control. Centralized filtering approaches optimally fuse all available sensor measurements of the team. However, a centralized solution is rarely implementable due to hardware, communication, and computational constraints. Distributed approaches deploy a filter on each robot to estimate their own state and neighbours' states using inter-robot communication. This paper proposes a consistent, communication-efficient, and consensus-based distributed filtering framework that shares both preintegrated odometry and relevant shared states among communicating robots. The proposed method is validated in simulated and experimental scenarios, showing near centralized performance in accuracy, and especially in consistency, compared to the current state-of-the-art decentralized approach.

State estimation is a fundamental requirement in robotics, where the accurate determination of a robot's state is essential for stable operation despite inherent process disturbances and sensor noise. Traditionally, this is achieved through Kalman filtering, providing a statistically optimal estimate by balancing predictive models with noisy measurements. In the context of robotic swarms, the challenge shifts from individual accuracy to collective coordination, where the integration of global dynamics can significantly enhance the precision of the entire group. Existing estimation techniques rely on centralized processing or heavy communication protocols to reach a global consensus, which are frequently impractical in real-world deployments. Here we show that a localized, "greedy" approach to distributed state estimation (termed "Greedy Kalman-Swarm") allows individual robots to leverage relative inter-robot sensing for improved accuracy without requiring full data availability or global communication. Simulations in communication-constrained environments show robots can effectively integrate all currently available neighbor data at each iteration to refine their internal states, yet remain robust and functional even when data is missing. This results in a performance profile that strikes a balance between the low overhead of independent estimation and the high accuracy of centralized systems, specifically under harsh or dynamic environmental conditions. Our results demonstrate that global state awareness can be emergent rather than enforced, providing a scalable framework for maintaining swarm cohesion in unpredictable terrains. We anticipate that this decentralized methodology will serve as a foundation for more resilient autonomous systems, particularly in search-and-rescue or space exploration missions where reliable, high-bandwidth communication cannot be guaranteed.