Distributed localisation of sensors with partially overlapping field-of-views in fusion networks

We consider geographically distributed sensor platforms with limited field of views (FoVs) networked together in order to cover a larger surveillance region. Each sensor has a partially overlapping FoV with its neighbours, and, collects both target originated and spurious measurements. We are interested in estimating the locations of the sensors in a network coordinate system using only these measurements. The parameter likelihood of the problem, however, does not scale with the number of sensors as its evaluation requires joint multi-sensor filtering. We propose an approximate likelihood which provides scalability by building upon local single sensor filtering, and, is capable of handling partially overlapping coverage for a pair of sensors. Such scalable approximations for fully overlapping sensor coverages have been recently introduced in a cooperative self-calibration framework in which they are used with pairwise Markov random fields as edge potentials. We use the proposed likelihoods within this framework for distributed self-localisation of sensors in the partially overlapping FoVs case. We provide explicit formulae for the likelihoods and a Monte Carlo algorithm which consists of consecutive likelihood updates and belief propagation steps for estimation --all performed as distributed message passings across the network. We demonstrate the estimation accuracy achieved through simulations with multiple objects and complex measurement~models.