Unmanned aerial vehicles (UAVs) are increasingly employed in civil applications due to their ease of use and adaptability. This paper proposes a distributed navigation strategy for a formation of UAVs in post-avalanche search-and-rescue (SAR) operations. Formations offer a more efficient approach than single UAVs in dynamic and complex operational environments. Additionally, they can distribute different sensors, reducing payload and increasing robustness and overall efficiency. The proposed navigation algorithm relies on the Kalman filter (KF) based on consensus to distribute state estimation, and internodal transformation theory to improve system scalability, preserving the dynamic equivalence between the global and local models. The effectiveness of this approach was tested in two realistic scenarios, resulting in the ability to detect victims and maintain situational awareness while avoiding unsearched areas. The proposed approach offers a promising alternative to human-intensive SAR missions.