This paper describes an algorithm that exploits multipath propagation for position estimation of mobile receivers. We apply a novel algorithm based on recursive Bayesian filtering, named Channel-SLAM. This approach treats multipath components as signals emitted from virtual transmitters which are time synchronized to the physical transmitter and static in their positions. Contrarily to other approaches, Channel-SLAM considers also paths occurring due to multiple numbers of reflections or scattering as well as the combination. Hence, each received multipath component increases the number of transmitters resulting in a more accurate position estimate or enabling positioning when the number of physical transmitters is insufficient. Channel-SLAM estimates the receiver position and the positions of the virtual transmitters simultaneously, hence, the approach does not require any prior information such as a room-layout or a database for fingerprinting. The only prior knowledge needed is the physical transmitter position as well as the initial receiver position and moving direction. Based on simulations, the position precision of Channel-SLAM is evaluated by a comparison to simplified algorithms and to the posterior Cramér-Rao lower bound. Furthermore, the paper shows the performance of Channel-SLAM based on measurements in an indoor scenario with only a single physical transmitter.