Localisation of wireless nodes with partial connectivity in wireless sensor systems

Owing to their short communication range, wireless nodes in wireless sensor networks (WSNs) can exchange information with devices in their vicinity only. Thus, in sparse networks, the full connectivity of the network is rarely achieved. This renders a centralised approach towards localisation in WSNs useless. Moreover, the exploitation of a centralised algorithm for localisation compromises the scalability in dense networks. Thus, a decentralised, location-aware network with partial connectivity and hybrid (range and direction) measurements obtained between known sensors (reference sensors) and sensors at unknown locations (target sensors) is under focus. The decentralised location estimation is obtained using a linear least squares (LLS) approach and performance enhancements are achieved by introducing a weighing strategy to produce weighted least squares (WLS) estimates. This distributed estimation is made possible by designing a map stitching technique that forms the global map of the network from individual local maps of the wireless nodes without compromising the distributed nature of the network. In the analytical section of the study, theoretical mean squares error expression is derived for LLS estimation, and a Cramer–Rao lower bound is derived to bind the performance of the WLS solution. The algorithm's performance validation is conducted both theoretically and via simulations.