Delay-Compensated EKF and Adaptive Delay Threshold Weighting for AUV–MDS Docking

This study tackles real-time state estimation for autonomous underwater vehicle (AUV)–mobile docking station (MDS) cooperation over low-bandwidth, high-latency, jitter-dominated acoustic links, with the goal of turning delayed/out-of-sequence measurements (OOSM) into consistent and informative constraints without sacrificing online operation. We propose an integrated scheme centered on a delay-compensated extended Kalman filter (DC-EKF): a ring buffer enables backward updates and forward replay so that OOSM are absorbed strictly at their physical timestamps; a data-driven delay threshold is learned from “effective information gain” combined with normalized estimation error squared (NEES) filtering; and dynamic confidence, derived from innovation statistics, delay, and signal-to-noise ratio (SNR) proxies, scales the measurement noise to adapt fusion weights. Simulations show the learned delay threshold converges to about 6.4 s (final 6.35 s), error spikes are suppressed, and the overall position root-mean-square error (RMSE) is 5.751 m; across the full data stream, 1067 station measurements were accepted and 30 rejected, and the fusion weights shifted smoothly from inertial measurement unit (IMU)-dominant to station-dominant (≈0.16/0.84) over time. On this basis, a cooperative augmented EKF (Co-Aug-EKF) is added as a lightweight upper layer for unified-frame cooperative estimation, further improving relative consistency. The results indicate that the framework reliably maps delayed acoustic measurements into closed-loop useful information, significantly enhancing estimator stability and docking readiness, while remaining practical to deploy and readily extensible.