Positioning with high precision and reliability can be provided by 5G cellular networks in environments where satellite positioning is not available or reliable. The accuracy that can be achieved by classical methods like triangulation and trilateration however degrades significantly under non line of sight (NLOS) conditions. The problem can be mitigated with increasingly dense deployments of network transmission and reception points (TRPs), but that is both impractical and costly. As an alternative, this study investigates if multipath propagation of radio signals can be exploited to improve positioning accuracy and reduce the necessary deployment density. With 3GPP Rel. 17 new signaling support has been introduced to report the propagation delay, corresponding to the length, of multiple paths between the user equipment (UE) and a network TRP. The length of a multipath can, in combination with a partially known map of the environment, give additional information about the UE position. In this study we develop multipath-assisted tracking algorithms and evaluate their performances in realistic simulations using 3GPP standardized positioning reference signals and measurements in an indoor factory environment. Our evaluations show that multipath-assisted algorithms can achieve an accuracy below 0.9 m in 90% of the cases, which is more than tenfold better than a conventional LOS based algorithm. Moreover, one algorithm variant also shows an ability to track a UE using very few TRPs.