Localization is particularly challenging when the environment has mixed line-of-sight (LOS) and non-LOS paths and even more challenging if the anchors’ positions are also uncertain. In the situations in which the parameters of the LOS-NLOS propagation error model and the channel states are unknown and uncertainties for the anchors exist, the likelihood function of a localizing node is computationally intractable. In this paper, assuming the knowledge of the prior distributions of the error model parameters and that of the channel states, we formulate the localization problem as the maximization problem of the posterior distribution of the localizing node. Then we apply variational distributions and importance sampling to approximate the true posterior distributions and estimate the target’s location using an asymptotic minimum mean-square-error (MMSE) estimator. Furthermore, we analyze the convergence and complexity of the proposed variational Bayesian localization (VBL) algorithm. Computer simulation results demonstrate that the proposed algorithm can approach the performance of the Bayesian Cramer-Rao bound (BCRB) and outperforms conventional algorithm
