Message Passing localisation algorithm combining BP with VMP for mobile wireless sensor networks

For large-scale wireless sensor networks (WSNs) with thousands of sensors, cooperative self-localisation is a key task and has caused extensive concerns. In this study, the authors propose a message passing algorithm for cooperative self-localisation of mobile WSNs by using belief propagation (BP) and variational message passing (VMP) on factor graphs. The sensors locate themselves through two steps: a prediction operation accounting for the sensors' mobility and a correction operation accounting for ranging measurements between neighbouring sensors. All the messages for computing and transmitting are restricted to be Gaussian to reduce communication overhead and computational complexity. According to the linear state-transition model and the non-linear ranging model, BP and VMP methods are employed to perform prediction and correction, respectively. Simulation results show that when the standard deviations of the prior distributions is small, the positioning accuracy of the proposed algorithm is comparable with that of sum-product algorithm over a wireless network (SPAWN) with much low communication overhead and computational complexity.