Maximum Likelihood Localization Using A Priori Position Information of Inaccurate Anchors

Localization in wireless sensor networks has become an attractive research field in recent years. Most studies focus on the mitigation of measurement noise by assuming the positions of anchors are perfectly known, which may become impractical due to some inevitable errors in the observations of anchors´ positions. This paper addresses the problem by taking into account the a priori position information of inaccurate anchors. Considering that the maximum likelihood (ML) algorithm suffers from the intractable integrals involved, we resort to expectation maximization (EM) algorithm to solve this problem iteratively. The a posteriori probability of the anchor position is approximated by circularly symmetric Gaussian distribution, with parameters optimized by minimizing Kullback-Leibler divergence of the two distributions. Building on this approximation, we are able to derive the expectation step in closed form. Particle swarm optimization is then followed to perform the maximization step. Numerical results demonstrate that the proposed EM estimator is less sensitive to the anchors´ uncertainties and it significantly outperforms the traditional ML estimator which ignores the prior information of anchors.