This document discusses cooperative sensor network localization using Gaussian mixture modeling and expectation-conditional maximization (ECM) algorithms. It proposes using a Gaussian mixture to approximate the unknown non-Gaussian measurement error distribution. Centralized ECM algorithms are developed for parameter estimation with proofs of convergence properties. Distributed ECM algorithms are also created to improve scalability, using average consensus to update the Gaussian mixture model locally. Computer tests show the distributed algorithms can perform well even with model mismatch and unknown error statistics, outperforming alternatives.

1. Cooperative Localization in WSNs Using Gaussian Mixture Modeling:
Distributed ECM Algorithms
Abstract:
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. Tomeet 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

2. 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.