In this paper we show the results of an experimental assessment of an indoor localization system based on a Wireless Sensor Network. The estimated position of a target node embedded in the monitored environment is obtained by running of the Relative Span Exponentially Weighted Localization (REWL) algorithm, a novel localization procedure recently proposed in the literature. The inputs of the algorithm are the Received Signal Strength (RSS) measurements collected in a real indoor scenario. A description of the developed system and a metrological characterization of the proposed technique is presented in this paper.