While the unmanned aerial vehicles (UAVs) swarm travels under a dynamic environment, the cluster head (CH) switching is unavoidable due to the mitigation of mobility, quality of service, and energy consumption. If an attacker becomes the new CH, the entire swarm will be controlled and the sensitive data will be leaked. Unlike the other mobile networks with constant network connectivity, the authentication in the UAV swarm suffers from intermittent connection with the ground station under a hostile environment or spectrum constraint condition. Hence, this paper proposes a novel CH safeguarding mechanism enabled by edge intelligence utilizing a situational-aware authentication scheme. This low-latency mechanism provides extra security at the CH selection and switching without cloud server support. By adopting the unique cross-layer attributes, the system security is significantly improved based on the extracted multi-dimensional information. The Linear Discriminant Analysis (LDA) algorithm fuses the authentication decision accurately by projecting the high dimensional estimations into a low dimensional space for maximum separability by only keeping the necessary attributes. A situation-aware cross-layer attribute selection algorithm is developed to select a minimum number of attributes so that the time required for attribute estimation and computation overhead of authentication can be reduced. The simulation results demonstrate that our scheme performs better under a dynamic environment compared with the physical layer authentication scheme and some existing state-of-the-art authentication techniques.