Localization has been an important research issue in ubiquitous computing and wireless sensor networks (WSNs). From location-based services to autonomous mobile devices, location is prevalent in a wide range of applications. Localization methods for a mobile node vary from using GPS to localizing with respect to beacons with known locations, or using sensors like accelerometers and compasses. All of these solutions either require additional sensors in a node that reduce its battery life or require some kind of infrastructure and access to a database of anchor locations. Additionally, most solutions are for networks where nodes can communicate indiscriminately with each other. In this paper we introduce ReNLoc, a minimalistic anchor-free multilateration algorithm for 2D space (extendable to 3D space) with a centralized and a distributed version made for networks where the mobile nodes can only get range measurements to nodes with an unknown but fixed position that we call base nodes. The main assumption is that there is a minimum of three base nodes. ReNLoc takes advantage of geometric constraints that arise from the range measurements and represents them as sets on which we perform minimization over known geometric properties. We show that ReNLoc outperforms the commonly used multidimensional scaling (MDS) algorithm in a purely indirect ranging setup.