Characterizing the Operating Envelope of an Anomaly-Aware Adaptive EKF for GNSS-Denied USV Formation Relative Localization

Unmanned surface vehicle (USV) formations operating under GNSS denial require accurate relative localization using proprioceptive sensors and inter-vehicle ranging. This paper presents an anomaly-aware adaptive extended Kalman filter for four-USV formations using inertial measurements, compass, and ultra-wideband ranging, and systematically characterizes its operating envelope. Observability analysis establishes that S-curve maneuvering achieves structural rank 24, with only global translation unobservable, while straight-line motion leads to a rank deficiency of exactly seven dimensions All four gyroscope biases remain observable under both trajectories. The proposed filter integrates chi-square testing, cumulative sum (CUSUM) detection, and bias drift rate monitoring to trigger coordinated R adaptation and Q-boost mechanisms. Controlled experiments spanning outlier magnitudes and drift rates reveal three performance regimes, clean conditions with equivalent performance across all variants, moderate outliers [3σd,10σd] where the proposed method achieves 4.8–13.4% improvement, and extreme outliers where all robust methods converge. Critically, pure bias drift experiments expose a structural limitation of single-hypothesis, residual domain robustification within the tested drift range—all variants exhibit equivalent performance across the tested drift rates, analytically attributable to Kalman gain partitioning that distributes innovations between position and bias subspaces. The characterized operating envelope establishes that robust mechanisms provide measurable benefits for transient anomalies but encounter hard boundaries under persistent drift conditions, with all variants converging to equivalent performance across the tested range, necessitating multi-hypothesis or constraint-based approaches.