— This paper proposes a new tracking algorithm within a 3D-SLAM framework that takes segmented range images as observations. The framework has two layers: the local layer tracks the view path and correspondences across the image sequence, using ambiguous landmark surfaces, and provides multiple hypotheses. The global layer conjectures and closes loops. We analyze the effect of different local trackers on the global layer. An interpretation tree (IPT) is compared to a new algorithm, Orthogonal Surface Assignment (OSA), which attempts to track a building coordinate system. OSA is specialized to man-made work spaces. But our indoor experiments, performed with a rotating laser scanner, show clear advantages over the more general IPT: OSA covers the more relevant portion of the solution space, avoids the accumulation of rotation errors, and can estimate a unique translation in cases where IPT fails.