ARC: Adaptive Robust Joint State and Covariance Estimation

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.

State estimation is a key component in model-based control of walking robots and, more broadly, applicable wherever hidden variables must be inferred. The Kalman filter is widely used to estimate floating-base position and velocity by fusing multiple sensing modalities. However, tuning noise parameters is challenging and typically requires expert knowledge. Moreover, fixed noise parameters are unsuitable for varying gaits and environments. We propose an online adaptation strategy for the process noise covariance matrix Q and the measurement noise covariance matrix R. Specifically, we introduce a filter residual and innovation-based covariance adaptation method for legged robot state estimation and evaluate it against a baseline approach relying on IMU and foot force measurements. The proposed adaptation is implemented within an Invariant Extended Kalman Filter (InEKF) fusing IMU and leg kinematics. Experiments on indoor and outdoor datasets with a Unitree Go2 quadruped show that adapting R is sufficient and improves accuracy by 25% for the trotting gait compared to the fixed-tuned InEKF. Finally, the proposed residual-based adaptation achieves comparable performance to the foot force approach, without requiring foot force measurements or additional parameter tuning.

Radar-Inertial Odometry (RIO) based on the Extended Kalman Filter (EKF) relies on accurate extrinsic calibration between the radar and the Inertial Measurement Unit (IMU) and is sensitive to disturbances, as large linearization errors can degrade performance or even cause divergence. To address these limitations, this letter proposes an Equivariant Filter (EqF) for RIO based on a Lie group symmetry that geometrically couples navigation states and IMU biases, extending it to incorporate radar-IMU extrinsic calibration and multi-state constraint updates. This equivariant formulation inherently preserves consistency and enhances robustness, enabling reliable state estimation even under poor or completely wrong initialization of calibration states. Real-world experiments on two different Uncrewed Aerial Vehicles (UAVs) show that the proposed EqF-RIO achieves state-of-the-art accuracy under correct extrinsic calibration and offers improved convergence under large calibration errors, where the conventional EKF-RIO fails. Evaluation code is open-sourced.