Distributed implementations of the Expectation-Maximization (EM) algorithm reported in literature have been proposed for applications to solve specific problems. In general, a primary requirement to derive a distributed solution is that the structure of the centralized version enables the computation involving global information in a distributed fashion. This paper treats the problem of distributed estimation of Gaussian densities by means of the EM algorithm in wireless sensor networks using diffusion strategies, where the information is gradually diffused across the network for the computation of the global functions. The low-complexity implementation presented here is based on a two time scale operation for information averaging and diffusion. The convergence to a fixed point of the centralized solution has been studied and the appealing results motivates our choice for this model. Numerical examples provided show that the performance of the distributed EM is, in practice, equal to that of the centralized scheme.
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