Consensus-like algorithms for estimation of Gaussian mixtures over large scale networks

In this paper, we address the problem of estimating Gaussian mixtures in a sensor network. The scenario we consider is the following: a common signal is acquired by sensors, whose measurements are affected by standard Gaussian noise and by different offsets. The measurements can thus be statistically modeled as mixtures of Gaussians with equal variance and different expected values. The aim of the network is to achieve a common estimation of the signal, and to cluster the sensors according to their own offsets. For this purpose, we develop an iterative, distributed, consensus-like algorithm based on Maximum Likelihood estimation, which is well-suited to work in-network when the communication to a central processing unit is not allowed. Estimation is performed by the sensors themselves, which typically consist of devices with limited computational capabilities. Our main contribution is the analytical proof of the convergence of the algorithm. Our protocol is compared with existing methods via numerical simulations and the trade-offs between robustness, speed of convergence and implementation simplicity are discussed in detail.