Precise navigation is the key to guaranteeing the mission execution of unmanned aerial vehicle (UAV) swarms. Cooperative navigation (CN) realized through information interaction between UAVs can enhance the navigation performance of UAVs in complex environments. In this article, we construct a distributed CN framework that can fuse the measurements from various onboard navigation sensors and inter-UAV ranging based on factor graph (FG) and belief propagation (BP). In view of the computational efficiency, we propose a simplified Gaussian particle filter (GPF) for message passing and belief calculation, which reduces the computational load. The proposed algorithm is tested and verified using Monte Carlo simulations and flight test. The simulation results show that with similar positioning performance, the average processing time of the proposed algorithm is reduced by 88% compared to the sum-product algorithm for wireless network (SPAWN) algorithm.