Gaussian belief propagation for distributed simultaneous localization and tracking in wireless sensor networks

In this paper, we propose a distributed simultaneous localization and tracking (SLAT) algorithm in wireless sensor networks. Belief propagation (BP) algorithm is applied on the factor graph which represents the factorization of the joint posterior distribution function. Due to the nonlinearity between the observations and location variables, closed-form expression of messages cannot be obtained by directly applying BP on factor graph. We resort to the Taylor expansion to approximate the nonlinear terms. Accordingly, Gaussian messages and the beliefs of the location variables can be derived. Due to the noncooperation of the target, the posterior position distribution has to be calculated by sensors distributively. We propose to use an average consensus algorithm to estimate the parameters of the target´s posterior position distribution. Monte Carlo simulations showed that the proposed SLAT algorithm performs close to the particle-based BP algorithm, with significantly lower computational complexity and communication overhead, which makes it very attractive in practical applications.