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.