An Optimization-Based Method for Relative Pose Estimation for Collaborating UAVs Using Observed Predefined Trajectories

Accurate relative pose estimation between unmanned aerial vehicles (UAVs) is a key requirement for cooperative navigation, formation control, and swarm operation in GNSS-denied environments. In multi-UAV systems, monocular vision is attractive due to its low weight and power requirements; however, bearing-only measurements can lead to angular ambiguities, particularly under symmetric or planar target motion. This paper presents a geometric framework for monocular relative pose estimation using observed known motion patterns, rather than relying on complex distributed system architectures. The method exploits trajectory-induced geometric constraints by back-projecting the observed image-plane trajectory of a target UAV into three-dimensional space and tracing rays from the camera center toward a geometrically parameterized reference trajectory. Relative pose parameters are refined through nonlinear optimization using Levenberg–Marquardt, enabling accurate estimation under noisy conditions. Beyond the estimation framework, the influence of cooperative trajectory geometry on angular observability is investigated through simulation experiments. The results indicate that planar collaborative motion may induce angular ambiguity despite numerical convergence, whereas introducing modest out-of-plane excitation through three-dimensional trajectories significantly improves observability. In addition to simulation-based evaluation, a limited real-world flight experiment is conducted to qualitatively validate the observed ambiguity patterns under practical sensing conditions. In particular, three-dimensional eight-shaped trajectories are shown to significantly suppress large angular outliers and improve estimation robustness without increasing computational complexity, providing validated guidance for active trajectory design to ensure observability in vision-based aerial scenarios.