Convergence-Guaranteed Parametric Bayesian Distributed Cooperative Localization

Belief propagation (BP) is a popular message passing algorithm for distributed cooperative localization. However, due to the nonlinearity of measurement functions, BP implementation has no closed-form expression and requires message approximations. While nonparametric BP can be used, it suffers from a high computational complexity, thus being impractical in energy-constrained networks. In this paper, a parametric Bayesian method with Gaussian BP implementation is proposed for distributed cooperative localization. With linearization of the Euclidean norm in ranging measurements, the joint posterior distribution of agents' locations is successively approximated with a sequence of high-dimensional Gaussian distributions. At each iteration of the successive Gaussian approximation, vector-valued Gaussian BP is further adopted to compute the marginal distributions of agents' locations in a distributed way. It is proved by the principle of majorization-minimization that the proposed successive Gaussian approximation is guaranteed to converge, and the sequence of the estimated agents' locations converges to a stationary point of the objective function of the maximum a posteriori estimation. Furthermore, although cooperative localization involves loopy network topologies, in which convergence property of Gaussian BP is generally unknown, it is proved in this paper that vector-valued Gaussian BP converges, making the proposed parametric BP-based method being the first one achieving convergence guarantee. Compared to the nonparametric BP counterpart, the proposed method has a much lower computational complexity and communication overhead. Simulation results demonstrate that the proposed method achieves a superior performance in localization accuracy compared to existing cooperative localization methods.