Residual-Corrected Variable-Interval Kalman Filtering for Channel Load Estimation in SPMA-Based Multi-Hop UAV Ad Hoc Networks

In multi-hop UAV ad hoc networks, three-dimensional high mobility, strong line-of-sight interference and a hard saturation constraint on control-plane broadcasting distinguish the channel load estimation problem from its terrestrial counterpart: the HELLO broadcast interval cannot be shortened arbitrarily, so the channel occupancy statistics (COS) required by the statistical priority-based multiple access (SPMA) protocol must be inferred from observations that are asynchronous and separated by long idle gaps. The existing SMA-KF filtering method adopts a first-order random-walk prediction model and lacks trend-tracking capability, and thus easily produces systematic lag when the channel load changes with a trend; directly introducing data-driven compensation, in turn, brings the risk of closed-loop estimation divergence under long gaps. To this end, this paper proposes a residual-corrected variable-interval Kalman filtering (RC-VKF) method for channel load estimation. The method builds a closed-loop recursive framework with the variable-interval Kalman filter while retaining the capability to quantify state uncertainty; it constructs residual labels only from the node’s local packet observations and adopts recursive least squares to perform incremental online training of the corrector, without any offline ground-truth dataset; it designs a confidence gating mechanism driven by the gap duration, under which the correction term gradually withdraws when the gap is extra long and the algorithm automatically degenerates into a covariance-bounded Kalman filter, thereby guaranteeing the stability of the closed-loop estimation at the architectural level. Closed-loop simulation results of a multi-hop network show that, compared with SMA-KF, the proposed RC-VKF method achieves a consistent improvement in estimation accuracy under different traffic intensities and HELLO broadcast periods; meanwhile, it can effectively suppress the large estimation errors in the 95th-percentile tail and improve the reliability of the SPMA transmission decision; when observations become extremely sparse, the correction term is withdrawn by the confidence gate and the estimator degrades gracefully to the filtering kernel; within the bounded gap range assumed in the stability analysis, its accuracy is essentially that of the filtering kernel, and beyond that range, the estimate reduces to the hold-based prediction instead of diverging.