This article presents MTT-<inline-formula><tex-math notation="LaTeX">\text{SE}\mathopen {}(3)\mathclose {}</tex-math></inline-formula>, a vision-based multiple-target tracking algorithm for targets that evolve on the special Euclidean group <inline-formula><tex-math notation="LaTeX">\text{SE}\mathopen {}(3)\mathclose {}</tex-math></inline-formula> in dense clutter. The target state consists of the pose in <inline-formula><tex-math notation="LaTeX">\text{SE}\mathopen {}(3)\mathclose {}</tex-math></inline-formula> and the twist of the vehicle. Contributions of the article include the development of a robust track initialization scheme designed on <inline-formula><tex-math notation="LaTeX">\text{SE}\mathopen {}(3)\mathclose {}\times \mathbb {R}^{6}</tex-math></inline-formula>, and a track-to-track association and fusion algorithm to merge similar tracks evolving on <inline-formula><tex-math notation="LaTeX">\text{SE}\mathopen {}(3)\mathclose {}\times \mathbb {R}^{6}</tex-math></inline-formula>. The performance of MTT-<inline-formula><tex-math notation="LaTeX">\text{SE}\mathopen {}(3)\mathclose {}</tex-math></inline-formula> is verified in hardware by simultaneously tracking three multirotors using a stationary monocular camera. The results are compared to a multiple-target tracking algorithm that uses linear, time-invariant nearly constant velocity, acceleration, and jerk models, where it is shown that MTT-<inline-formula><tex-math notation="LaTeX">\text{SE}\mathopen {}(3)\mathclose {}</tex-math></inline-formula> improves several traditional tracking metrics.