Compressed delayed-information projection for six-degree-of-freedom underwater vehicle navigation under delayed acoustic positioning

In Global Navigation Satellite System (GNSS)-denied underwater environments, individual unmanned underwater vehicles (UUVs) suffer from unbounded dead-reckoning drift, making collaborative navigation (CN) crucial for accurate state estimation. However, the severe communication delay inherent in underwater acoustic channels poses serious challenges to real-time state estimation. Traditional filters, such as Extended Kalman Filters (EKFs) or Unscented Kalman Filters (UKFs), usually block the main control loop while waiting for delayed data, or effectively discard Out-of-Sequence Measurements (OOSMs), resulting in serious drift. To address this, we propose an Asynchronous Two-Speed Kalman Filter (TSKF) enhanced by a novel projection mechanism, which we term Variational History Distillation (VHD). The proposed architecture decouples the estimation process into two parallel threads: a fast-rate thread that utilizes Gaussian Process (GP) compensated dead reckoning to guarantee high-frequency real-time control, and a slow-rate thread dedicated to processing asynchronously delayed collaborative information. By introducing a Finite-Length Circular State Buffer (FLCSB), the algorithm applies delayed measurements to their corresponding historical states, and utilizes a VHD-based projection to fast-forward the correction to the current time without computationally heavy recalculations. Simulation results demonstrate that the proposed TSKF maintains a trajectory error comparable to computationally intensive batch-optimization methods under severe delays (up to 30,s). Executing in sub-millisecond time, it significantly outperforms standard EKF/UKF. The results demonstrate an effective control, communication, and computing (3C) co-design that significantly enhances the resilience of autonomous marine automation systems.

We present a safety-oriented framework for autonomous underwater vehicles (AUVs) that improves localization accuracy, enhances trajectory prediction, and supports efficient search operations during communication loss. Acoustic signals emitted by the AUV are detected by a network of fixed buoys, which compute Time-Difference-of-Arrival (TDOA) range-difference measurements serving as position observations. These observations are subsequently fused with a Kalman-based prediction model to obtain continuous, noise-robust state estimates. The combined method achieves significantly better localization precision and trajectory stability than TDOA-only baselines. Beyond real-time tracking, our framework offers targeted search-and-recovery capability by predicting post-disconnection motion and explicitly modeling uncertainty growth. The search module differentiates between continued navigation and propulsion failure, allowing search resources to be deployed toward the most probable recovery region. Our framework fuses multi-buoy acoustic data with Kalman filtering and uncertainty propagation to maintain navigation accuracy and yield robust search-region definitions during communication loss.

The reliable operation of Unmanned Underwater Vehicle (UUV) clusters is highly dependent on continuous acoustic communication. However, this communication method is highly susceptible to intermittent interruptions. When communication outages occur, standard state estimators such as the Unscented Kalman Filter (UKF) will be forced to make open-loop predictions. If the environment contains unmodeled dynamic factors, such as unknown ocean currents, this estimation error will grow rapidly, which may eventually lead to mission failure. To address this critical issue, this paper proposes a Variational History Distillation (VHD) approach. VHD regards trajectory prediction as an approximate Bayesian reasoning process, which links a standard motion model based on physics with a pattern extracted directly from the past trajectory of the UUV. This is achieved by synthesizing ``virtual measurements'' distilled from historical trajectories. Recognizing that the reliability of extrapolated historical trends degrades over extended prediction horizons, an adaptive confidence mechanism is introduced. This mechanism allows the filter to gradually reduce the trust of virtual measurements as the communication outage time is extended. Extensive Monte Carlo simulations in a high-fidelity environment demonstrate that the proposed method achieves a 91% reduction in prediction Root Mean Square Error (RMSE), reducing the error from approximately 170 m to 15 m during a 40-second communication outage. These results demonstrate that VHD can maintain robust state estimation performance even under complete communication loss.