Nodes localization with inaccurate anchors via EM algorithm in wireless sensor networks

Due to the inevitable errors introduced by means of observations and estimation algorithms, anchors' locations are usually not accurate in practical applications. This paper proposes an Expectation-Maximization (EM)-based localization algorithm with inaccurate anchors and noisy range measurements in wireless sensor networks. A circularly symmetric Gaussian distribution is used to approximate the a posteriori distribution of anchor's position uncertainty by minimizing the Kullback-Leibler (KL) divergence, building on which, we are able to derive a close-form expression of the expectation step (E-step). Then, a gradient method is followed in the maximization step (M-step) to find the solution which maximizes the E-step. Simulation results show that the EM estimator for localization can mitigate the impact of the anchors' position uncertainties and outperforms the approximated Maximum Likelihood (ML) estimator which ignores the anchors' position uncertainties.