Wireless Sensor Networks (WSNs) refer to a group of spatially deployed devices which are used to monitor or detect phenomena, and have the ability to relay sensed data and signalling wirelessly. Positioning information in WSNs is absolutely crucial to perform tasks such as intelligent routing, data aggregation and data collection optimally. A need exists for localisation algorithms which are scalable, distributed, energy efficient and easy to deploy. This research proposes a beaconless Cluster-based Radial Coordinate Establishment (CRCE) positioning algorithm to locate sensor nodes relative to a local coordinate system. The system does not make use of Global Positioning System (GPS) or any other method to provide apriori position information for a set of nodes prior to the CRCE process. The objective of CRCE is to reduce energy consumption while providing a scalable coordinate establishment method for use in WSNs. To reduce energy consumption during the node positioning process, the research focuses on minimising the number of message exchanges in the network by implementing a cluster-based network topology and utilising the potential of geographically distributed processors. A radial coordinate convergence process is proposed to achieve scalability as the number of sensors in the network increases. Three other localisation algorithms are investigated and compared to CRCE to identify the one best suited for coordinate establishment in WSNs. Two of these comparison algorithms are published in the literature and the other is a modified version of one of the published algorithms. The results show a significant decrease in the number of messages that are necessary to establish a network-wide coordinate system successfully, ultimately making it more scalable and energy efficient. In addition, position based algorithms, such as location based routing, can be deployed on top of CRCE. / Dissertation (MEng (Computer Engineering))--University of Pretoria, 2006. / Electrical, Electronic and Computer Engineering / unrestricted