SIA-KalmanNet: A Structurally Integrated Attention Kalman Filter for Multi-UAV Localization in Partially GNSS-Denied Environments

Cooperative localization is an essential task in multiple uncrewed aerial vehicle (UAV) networks, especially in environments with partial global navigation satellite system (GNSS) denial. By effectively integrating low-precision inertial navigation system (INS)-derived priors, inter-UAV relative distances, and sparse anchor-based measurements, the extended Kalman filter (EKF) can be employed for UAV localization. However, localization accuracy suffers under nonlinear dynamics and inaccurate knowledge of process and measurement noise statistics. To address these challenges, this article proposes a structurally integrated attention Kalman filter called SIA-KalmanNet for accurate and robust state estimation. By combining state-space models with attention-based neural networks in the Kalman flow, the estimator preserves the data efficiency and interpretability of traditional model-driven methods while implicitly learning second-order covariance matrices from data. Specifically, two networks are devised to learn the Kalman gain: the self-attention residual masked network (SA-RMN) and the self-cross attention residual masked network (SCA-RMN). Among them, SA-RMN is a lightweight network for end-to-end state estimation. SCA-RMN introduces masked cross-attention to adaptively fuse forward state features and backward historical correction information to obtain a more precise state estimate. Furthermore, a practical training strategy based on sliding window and causal masking is developed to ensure efficient training and real-time inference. The experimental results show that the proposed algorithm achieves superior localization performance compared to the traditional EKF and KalmanNets. Moreover, it exhibits strong robustness against INS drift and non-line-of-sight (NLOS)-induced distance errors, even in harsh environments where only a limited number of UAVs can access GNSS signals.