An Asynchronous Two-Speed Kalman Filter for Real-Time UUV Cooperative Navigation Under Acoustic Delays

In GNSS-denied underwater environments, individual unmanned underwater vehicles (UUVs) suffer from unbounded dead-reckoning drift, making collaborative navigation 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 (EKF) or Unscented Kalman Filters (UKF), usually block the main control loop while waiting for delayed data, or completely discard Out-of-Sequence Measurements (OOSM), 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 State Buffer, the algorithm applies delayed measurements (t-T) 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 trajectory Root Mean Square Error (RMSE) 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.

Communication Outage-Resistant UUV State Estimation: A Variational History Distillation Approach

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.