A novel distributed variational approximation method for density estimation in sensor networks

In this paper, a consensus filter based distributed variational Bayesian (CFBDVB) algorithm is developed for distributed density estimation. Sensor measurements are assumed to be statistically modeled by a finite mixture model for which the CFBDVB algorithm is used to estimate the parameters, including means, covariances and weights of components. This algorithm is based on three steps: (1) calculating local sufficient statistics at every node, (2) estimating a global sufficient statistics vector using a consensus filter, (3) updating parameters of the finite mixture model based on the global sufficient statistics vector. Scalability and robustness are two advantages of the proposed algorithm. Convergence of the CFBDVB algorithm is also proved using Robbins-Monro stochastic approximation method. Finally, to verify performance of CFBDVB algorithm, we perform several simulations of sensor networks. Simulation results are very promising.