This paper presents a relative positioning method, called "multi-hop positioning", which is suitable for raw GPS data collected by densely deployed L1 GPS receivers. The wireless sensor network employing an affordable L1 GPS receiver has been developed by the authors for monitoring displacement of large civil structures with high spatial resolution. In general, relative positioning of GPS sensors are performed between a single reference point and sensor nodes. On the other hand, in the newly developed approach, relative positioning is performed between all pair of sensor nodes in the network. Then, the best set of relative position vectors is selected to determine the location of sensor nodes. Experiments have been conducted using 53 sensor nodes equipped with an affordable L1 GPS receiver and the collected data are analysed by using the proposed method in a post-processing manner. The results show that the success rate of relative position estimate is considerably improved compared with the conventional approach.