###### Abstract  
Navigation system performance degrades significantly in complex environments. It is important to analyze satellite visibility through 3D terrain modelling and separate the satellite signals propagated by NLOS to suppress the NLOS error. However, the traditional 3D terrain modelling visibility analysis method based on the pure terrain cover angle is only suitable for determining the visibility of GNSS satellites and may incorrectly separate LOS propagate measurement signals from members with low relative ranges and elevation angles under air-ground swarm conditions. To this end, this paper proposes a belief-propagating cooperative navigation method based on air-ground visibility analysis, which avoids mistakenly separating close-range LOS cooperative navigation signals by simultaneously considering the distances, elevation angles, and azimuths of the signal sources relative to the air-ground swarm members. The simulation shows that the cooperative navigation NLOS identification method based on air-ground visibility analysis proposed in this paper can more accurately realize the separation of NLOS signals under cooperative conditions than the traditional pure angular 3D terrain modelling visibility analysis method can, and the localization error of the members to be assisted is significantly reduced. air-ground swarms; cooperative navigation; belief propagation; visibility analysis; 3D terrain model 2024 16304202024/16/3042024/16/  
cooperative navigation for unmanned underwater submersibles. In 2017, [PERSON] from the University of Salento, Italy, proposed an extended Kalman filter colocalization method based on the antenna-measured angle of arrival (AOA), which combines inertial navigation and AOA signal fusion to effectively improve the co-localization accuracy of vehicles in urban environments [6]. The above co-localization method is mainly based on Kalman filtering, which constructs system state equations and measurement equations by taking member states as filtered state quantities and relative observation quantities. The method is simple in its engineering application and the algorithm runs stably. In addition, by establishing the cooperative network as a graph model and reasoning through the probabilistic graph model, swarm cooperative navigation can also be realized. In 2009, [PERSON] of MIT first proposed a distributed cooperative localization algorithm based on the sum-product algorithm for large-scale wireless network localization, laying a theoretical foundation for belief propagation cooperative localization [7]. To address the problem of cooperative navigation errors due to swarm clock errors, [PERSON] of the Vienna University of Technology proposed a nonparametric belief propagation cooperative localization algorithm for jointly estimating swarm positions and clock errors, which suppresses the effect of swarm clock errors on cooperative localization [8; 9]. Considering real-time iterative updating of swarm members' confidence, [PERSON] of Aalto University, Finland, proposed a cooperative localization method based on a posteriori linearized belief propagation, which uses the sigma point for the linearization between two nodes, thus reducing the number of dimensions and computations [10]. [PERSON] proposed an improved swarm cooperative localization method for the localization of collaborative UAVs in networks with GPS/INS/UWB interference, which allows normal sigma-point belief propagation in the presence of measurement interference [11]. In complex terrain environments, the accuracy of air-ground group localization is degraded by the fact that navigation and cooperative signals (e.g., satellite and radio signals) are often reflected by the nearby terrain, resulting in a non-line-of-sight (NLOS) effect. One study [12] weighted the satellite navigation positioning signals by the positioning signal carrier-to-noise ratio to reduce the weight of possible NLOS signals in the positioning solution to suppress the satellite navigation NLOS error.