Neural Aided Kalman Filtering for UAV State Estimation in Degraded Sensing Environments

Accurate state estimation of nonlinear dynamical systems is fundamental to modern aerospace operations across the air, sea, and space domains. Reliable tracking and control require precise knowledge of a platform’s position and velocity state to predict near-term trajectories. Online tracking of adversarial remote-controlled unmanned aerial vehicles (UAVs) can be especially challenging due to agile nonlinear motion, noisy and sparse sensor measurement availability, and unknown control inputs, which violate key assumptions of classical Kalman filter variants and can degrade overall performance. These limitations motivate alternative approaches that capture control-induced nonlinear dynamics while remaining suitable for real-time deployment. Neural networks (NNs) can learn complex nonlinear relationships from data, but their lack of principled uncertainty quantification limits use in state estimation tasks where confidence bounds are critical. We address this using Bayesian Neural Networks (BNNs), which model uncertainty through distributions over network weights and produce predictive means and uncertainties via Monte Carlo sampling. Building on this capability, we propose the Bayesian Neural Kalman Filter (BNKF), a hybrid framework that couples a trained BNN with a Kalman filter correction step for robust online UAV state estimation. Unlike related neural Kalman approaches, BNKF produces full state predictions and incorporates Bayesian uncertainty directly into covariance propagation, improving robustness in high-noise regimes. We evaluate BNKF under varying radar noise levels and sampling rates using synthetic nonlinear UAV flight data. Fivefold cross-validation shows that BNKF outperforms Extended and Unscented Kalman Filters in accuracy, precision, and state containment under higher noise conditions. An ensemble variant (BNKFe) further improves precision in high-noise edge cases at the slight expense of accuracy, while overall runtime analysis confirms minimal inference overhead and the potential for real-time deployment feasibility.