Multi-sensor estimation using energy harvesting and energy sharing

This paper investigates an optimal energy allocation problem for multi sensor estimation of a random source where sensors communicate their measurements to a remote fusion centre (FC) over orthogonal fading wireless channels using uncoded analog transmissions. The FC reconstructs the source using the best linear unbiased estimator (BLUE). The sensors have limited batteries but can harvest energy and also transfer energy to other sensors in the network. A distortion minimization problem over a finite-time horizon with causal and non-causal information is studied and the optimal energy allocation policy for transmission and sharing is derived. Several structural necessary conditions for optimality are presented for the two sensor problem with non-causal information and a horizon of two time steps. Numerical simulations are included to illustrate the theoretical results.