Aiming at the cooperative localization problem for the dynamic UAV swarm in an anchor-limited environment, an adaptive Wasserstein filter (AWF) with distance-constrained bare bones self-recovery particles (CBBP) is proposed. Firstly, to suppress the cumulative error from the inertial navigation system (INS), a position-prediction strategy based on transition particles is designed instead of using inertial measurements directly, which ensures that the generated prior particles can better cover the ground truth and provide the uncertainties of nonlinear estimation. Then, to effectively quantify the difference between the observed and the prior data, the Wasserstein measure based on slice segmentation is introduced to update the posterior weights of the particles, which makes the proposed algorithm robust against distance-measurement noise variance under the strongly nonlinear model. In addition, to solve the problem of particle impoverishment caused by traditional resampling, a diversity threshold based on Gini purity is designed, and a fast bare bones particle self-recovery algorithm with distance constraint is proposed to guide the outlier particles to the high-likelihood region, which effectively improves the accuracy and stability of the estimation. Finally, the simulation results show that the proposed algorithm is robust against cumulative error in an anchor-limited environment and achieves more competitive accuracy with fewer particles.

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.

Target localization is a key technology for unmanned aerial vehicle (UAV) applications in various fields, such as target tracking and task planning. However, the accuracy of UAV localization is significantly affected by systematic and random errors in attitude data, and the nonlinearity of the measurement model, together with the unknown distribution of measurement noise. To achieve robust and precise localization in long-distance oblique scenarios based on dynamic platforms, this article proposes a Gaussian Mixture Filter-incorporated self-attention (SA) Residual Neural Network (GMAR) algorithm for target localization. Firstly, an end-to-end SA residual neural network (SA-ResNN) model is built to accurately model both systematic and random errors in attitude angle. The SA mechanism is innovatively introduced to enhance the global feature representation capability of the residual module. Then, the Gaussian mixture (GM) filter utilizes a GM model to model the prior and posterior probability density functions, which can effectively capture the uncertainty in the state probability density function under nonlinear measurement models and enhance the robustness of the localization system. Finally, simulations and flight experiments demonstrate that the proposed GMAR algorithm can significantly improve the localization accuracy and robustness of ground targets in long-distance oblique scenarios.