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

Abstract

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.

Figures (6)

• Figure 1: Finalized TSKF architecture. The asynchronous correction path is routed externally to ensure zero overlap with control modules.
• Figure 2: During long-term acoustic interruption, the predicted variance boundary of the GP residual learner. Compared with uncompensated analytical position extraportion, GP can effectively suppress error drift.
• Figure 3: The timing diagram of the OOSM processing mechanism. The delay measurement is traced to the exact historical state ($t_{k-d}$) applied in the buffer, and the VHD principle is used to quickly push the generated correction forward to the current time ($t_k$) without interrupting the prediction of $t_{k+1}$.
• Figure 4: Dynamic acoustic propagation delay curve simulated via the Aqua-Sim FG framework. As the UUV travels further from the reference node, the plot confirms that our simulation accurately captures both the extreme communication latency (reaching up to $30$ s) and the realistic Gaussian measurement noise.
• Figure 5: Simulated UUV trajectory in the $X-Y$ plane. The delay-ignorant standard EKF diverges significantly (experiencing severe "pull-back" oscillations) when fusing measurements delayed by $>$$10$ s. Conversely, the proposed TSKF maintains robust adherence to the ground truth trajectory.