Localization is one of the most important research issues in Wireless Sensor Networks (WSNs). Recently, hop-count-based localization has been proposed as a cost-effective alternative to many expensive hardware-based localization algorithms. The basic idea of many hop-count-based localization algorithms is to seek a transformation from hop-count information to distance (e.g. DV-hop algorithm of Niculescu and Nath in Global Telecommunications Conference, vol. 5, pp. 2926–2931, 2001) or location (e.g. MDS algorithm of Shang et al. in International Symposium on Mobile Ad Hoc Networking and Computing, pp. 201–212, 2003) information. Traditionally, hop-counts between any pair of nodes can only take on integer value regardless of relative positions of nodes in the hop. We argue that by partitioning a node’s one-hop neighbor set into three disjoint subsets according to their hop-count values, the integer hop-count can be transformed into a real number accordingly. The transformed real number hop-count is then a more accurate representation of a node’s relative position than an integer-valued hop-count. In this paper, we present a novel algorithm termed HCQ (hop-count quantization) to perform such transformation. We then use the transformed real number hop-count to solve WSNs localization problems based on the MDS (multidimensional scaling) method. Simulation results show that the performance of the MDS algorithm using the real number hop-count outperforms those which use integer hop-count values.
