In Global Navigation Satellite System (GNSS)-denied environments, swarm unmanned aerial vehicle (UAV) systems face the challenge of losing absolute localization information, which in turn leads to a rapid dispersion of system navigation errors. To this end, this paper proposes a consensus-enhanced particle filter algorithm using error constraints and quantum particle swarm optimization (C-EC-QPF) for cooperative navigation of swarm UAVs. The proposed method abandons the traditional weight concept in particle filters and introduces an error constraints enhanced quantum particle swarm optimization (QPSO) during the resampling stage, effectively mitigating particle impoverishment and sample size dependency. Additionally, the consensus algorithm is employed to optimize inter-UAV information exchange during cooperative navigation, enabling effective fusion of swarm navigation information on top of filtering, thereby enhancing overall navigation performance. Simulation results show that compared with other improved particle filter methods, the method proposed in this paper improves positioning accuracy for swarm UAVs in GNSS-denied environments and exhibits superior robustness.