Cooperative Localization in WSNs Using Gaussian Mixture Modeling: Distributed ECM Algorithms

We study cooperative sensor network localization in a realistic scenario where the underlying measurement errors more probably follow a non-Gaussian distribution; the measurement error distribution is unknown without conducting massive offline calibrations; and non-line-of-sight identification is not performed due to the complexity constraint and/or storage limitation. The underlying measurement error distribution is approximated parametrically by a Gaussian mixture with finite number of components, and the expectation-conditional maximization (ECM) criterion is adopted to approximate the maximum-likelihood estimator of the unknown sensor positions and an extra set of Gaussian mixture model parameters. The resulting centralized ECM algorithms lead to easier inference tasks and meanwhile retain several convergence properties with a proof of the "space filling" condition. To meet the scalability requirement, we further develop two distributed ECM algorithms where an average consensus algorithm plays an important role for updating the Gaussian mixture model parameters locally. The proposed algorithms are analyzed systematically in terms of computational complexity and communication overhead. Various computer based tests are also conducted with both simulation and experimental data. The results pin down that the proposed distributed algorithms can provide overall good performance for the assumed scenario even under model mismatch, while the existing competing algorithms either cannot work without the prior knowledge of the measurement error statistics or merely provide degraded localization performance when the measurement error is clearly non-Gaussian.