  This paper presents two-hop relay gain-scheduling control in a Wireless
Sensor Network to estimate a static target prior characterized by Gaussian
probability distribution. The target is observed by a network of linear
sensors, whose observations are transmitted to a fusion center for carrying out
final estimation via a amplify-and-forward relay node. We are concerned with
the joint transmission power allocation for sensors and relay to optimize the
minimum mean square error (MMSE) estimator, which is deployed at the fusion
center. Particularly, such highly nonlinear optimization problems are solved by
an iterative procedure of very low computational complexity. Simulations are
provided to support the efficiency of our proposed power allocation.
