Background Low-altitude formation targets, including bird flocks and unmanned aerial vehicle (UAV) swarms, exhibit complex spatial configurations and rapidly changing internal structures. Accurate estimation of sub-object positions, orientations, extensions, and target counts is essential for radar-based situational awareness. Conventional multi-ellipsoidal tracking methods couple orientation and size within a random-matrix extension, limiting their response to rapid formation maneuvers.
Purpose This study aims to improve the estimation of dynamic formation structure and internal composition by developing an orientation-decoupled variational tracking method.
Methods The proposed multi-ellipsoidal orientation-decoupled group target tracking method (MEO-GTT) models each sub-object orientation independently as a Gaussian random variable. Its extension size is represented by a diagonal symmetric positive-definite matrix, while sub-object target counts are explicitly included as composition variables. A variational Bayesian procedure approximates the nonconjugate posterior induced by the nonlinear measurement model. It jointly estimates kinematic states, orientations, extension sizes, target counts, and measurement-to-sub-object associations. Performance was assessed through 200 Monte Carlo trials for a maneuvering V-shaped formation of 24 targets and through field measurements of 18 UAVs. The field data were collected using a high-resolution phased-array radar and evaluated against real-time kinematic positioning records. MEO-GTT was compared with conventional multi-ellipsoidal group target tracking (ME-GTT) under matched initialization and dynamic-model settings.
Results In simulations, MEO-GTT maintained lower orientation errors during coordinated turns, converged faster after maneuvers, and improved the stability of position and axis-length estimates. It also stably estimated the number of targets within each sub-object. In the field experiment, MEO-GTT reduced orientation root mean square error (RMSE) from 7.60 degrees to 4.77 degrees and axis-length RMSE from 9.23 m to 8.78 m. The reported execution time increased from 0.0461 s to 0.0923 s.
Conclusions Orientation-decoupled modeling improves structural tracking of maneuvering formation targets and supports simultaneous estimation of their internal composition. The method provides higher accuracy than conventional multi-ellipsoidal tracking at increased computational cost.
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