The main drawback today for range-based indoor localization is the requirement of a sufficient amount of fixed reference nodes within radio range of the user. However, these reference nodes, called anchors, are expensive and require professional maintenance. Using ultra-wideband in an indoor environment, the number of anchors can be reduced to one when reflections are taken into account. With the help of a floorplan it is possible to obtain a set of virtual anchors that can be associated with the reflections. In this paper, a low-complex twostep algorithm is proposed that is able to accurately estimate the user positions using a single anchor. In a first step, the algorithm tries to estimate a number of rigid structures using the noisy inter-node distances and tries to fit this structure in the room by exploiting the measured reflections. It is shown that the presented algorithm can provide positioning accuracy similar to multi-anchor localization algorithms, even in scenarios with many unwanted scatterers and non-line-of-sight.