WRAP: Wasserstein-Robust Adaptive Plug-in for Robot 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 $19.8\mathrm{\%}$ and $27.4\mathrm{\%}$ relative to the nominal ESKF; an isotropic ablation reaches $19.5\mathrm{\%}$, 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.