Why (n + 1)th-hop neighbours are more important than nth-hop ones for localisation in multi-hop WSNs

For range-free localisation in a wireless sensor network (WSN), the importance of indirect anchor neighbours of an unknown node has been underestimated in the past. In this reported work, for the unknown node, we show that its (n + 1)th-hop anchor neighbours are more useful than its nth-hop ones. By employing a theoretical model to analyse the possible localisation area (PLA) of the unknown node, it is found that the PLA and the hop count are negatively correlated, which indicates that (n + 1)th-hop anchor neighbours can provide more information to more accurately localise the unknown node. Meanwhile, the property of convergence of the theoretical model means that localisation accuracy cannot be unlimitedly improved with increasing hop counts. In the simulations, the presented theory is verified.