  This paper studies the problem of multi-agent cooperative localization of a
common reference coordinate frame in $\mathbb{R}^3$. Each agent in a system
maintains a body-fixed coordinate frame and its actual \textit{frame
transformation} (translation and rotation) from the global coordinate system is
unknown. The mobile agents aim to determine their \textit{trajectories of
rigid-body motions} (or the frame transformations, i.e., rotations and
translations) with respect to the global coordinate frame up to a common frame
transformation by using local measurements and information exchanged with
neighbors. We present two frame localization schemes which compute the
rigid-body motions of the agents with asymptotic stability and finite-time
stability properties, respectively. Under both localization laws, the estimates
of the frame transformations of the agents converge to the actual frame
transformations almost globally and up to an unknown constant transformation
bias. Finally, simulation results are provided.
