Spatial Correlation-Aided Multi-Source Asynchronous Kalman Filter for SPMA Channel Occupancy Statistics Estimation in Multi-Hop UAV Ad Hoc Networks

초록

In multi-hop UAV ad hoc networks employing the Statistical Priority-based Multiple Access (SPMA) protocol, the HELLO broadcast interval cannot be arbitrarily shortened due to the inherent upper bound on the per-slot transmission probability of each node in saturated networks, which fundamentally limits the estimation accuracy of Channel Occupancy Statistics (COS). To address this problem, this paper proposes a spatial correlation-aided multi-source asynchronous Kalman filtering method, abbreviated as SMA-KF. On the basis of conventional COS broadcasting, SMA-KF introduces two complementary observation sources: COS measurements piggybacked on data packets, and spatially correlated observations from common neighbors compensated by historical biases. These three types of observations are integrated into a unified Kalman filtering framework, and a state-space model suitable for asynchronous intermittent observations is constructed. Theoretical analysis verifies the convergence of the algorithm. Simulation results demonstrate that the proposed algorithm significantly outperforms the EWMA and TW algorithms across all test scenarios, and achieves overall lower error than BiLSTM. Under the extremely sparse observation condition with a HELLO broadcast interval of 600 slots, the Normalized Root Mean Square Error (NRMSE) of SMA-KF is 28.28%, which is 32.8% and 26.2% lower than those of EWMA (42.11%) and TW (38.33%), respectively. In the heavy-traffic scenario with an average data packet arrival interval of 20 slots, the NRMSE of SMA-KF is as low as 4.80%, whereas those of EWMA and TW are 17.49% and 15.40%, respectively, corresponding to reductions of 72.6% and 68.8%. In comparison with BiLSTM, SMA-KF achieves lower NRMSE in five out of seven traffic configurations, while BiLSTM exhibits only marginal and statistically insignificant advantages in the remaining two configurations. Link interruption experiments show that SMA-KF maintains NRMSE between 5.68% and 10.40% across the entire meaningful interruption coverage range of 0% to 53%, consistently outperforming all benchmark algorithms. Moreover, SMA-KF consistently achieves the lowest estimation error under varying node mobility speeds. Parameter sensitivity analysis confirms that SMA-KF maintains stable performance across a wide range of parameter values. These results validate the effectiveness of multi-source observation fusion and spatial cooperative estimation in improving both the accuracy and robustness of COS estimation. © 2026 by the authors.

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