Joint distributed parameter and channel estimation in wireless sensor networks via variational inference

Wireless sensor networks (WSNs) have emerged as a viable candidate for a variety of applications including military surveillance, target tracking, process monitoring, etc. A central problem in WSN is the estimation of a source parameter through a network of distributed sensors. In this work, assuming an orthogonal access channel between the sensors and the fusion center (FC), the problem of joint distributed estimation of a source parameter and channel coefficients is considered. In order to ease the complexity involved in a direct maximization of the joint posterior density, a simpler suboptimal approach is proposed using the theory of variational inference, whereby an auxiliary distribution is obtained yielding minimum Kullback-Liebler (KL) divergence with the true posterior. This results in an iterative estimation algorithm that alternates between updating the channel coefficient vector distribution and the source parameter distribution. The iterative algorithm results in a non-increasing KL divergence at each iteration, and hence, converges in divergence. The algorithm is also particularized for the case when the sensors collect noiseless observations of the source parameter. The performance of the proposed algorithm is evaluated using numerical simulations.