When an unmanned aerial vehicles (UAV) swarm is used for edge computing, and high-speed data transmission is required, accurate tracking of the UAV swarm’s centroid is of great significance for the acquisition and synchronization of signal demodulation. Accurate centroid tracking can also be applied to accurate communication beamforming and angle tracking, bringing about a reception gain. Group target tracking (GTT) offers a suitable framework for tracking the centroids of UAV swarms. GTT typically involves accurate modeling of target maneuvering behavior and effective state filtering. However, conventional coordinate-uncoupled maneuver models and multi-model filtering methods encounter difficulties in accurately tracking highly maneuverable UAVs. To address this, an innovative approach known as 3DCDM-based GRU-MM is introduced for tracking the maneuvering centroid of a UAV swarm. This method employs a multi-model filtering technique assisted by a gated recurrent unit (GRU) network based on a suitable 3D coordinate-coupled dynamic model. The proposed dynamic model represents the centroid’s tangential load, normal load, and roll angle as random processes, from which a nine-dimensional unscented Kalman filter is derived. A GRU is utilized to update the model weights of the multi-model filtering. Additionally, a smoothing-differencing module is presented to extract the maneuvering features from position observations affected by measurement noise. The resulting GRU-MM method achieved a classification accuracy of 99.73%, surpassing that of the traditional IMM algorithm based on the same model. Furthermore, our proposed 3DCDM-based GRU-MM method outperformed the Singer-KF and 3DCDM-based IMM-EKF in terms of the RMSE for position estimation, which provides a basis for further edge computing.