Distributed Estimation with Analog Forwarding in Energy-Harvesting Wireless Sensor Networks

Distributed estimation is examined for energyharvesting wireless sensor networks, where the energy available at the sensors are converted entirely from ambient sources. Here, each sensor takes a local measurement of the common parameter of interest and, by adopting an analog-forwarding transmission strategy, forwards a scaled version of it to the fusion center. A sensor transmits in a given time slot only if its available energy is sufficient to support the transmission of its scaled local observation. The scaling factor is properly chosen to exploit the tradeoff between the probability that a sensor transmits and the quality of the received signal at the fusion center. However, even when a sensor does not transmit, the fact that it remains silent still contains information regarding the magnitude of the observation. The maximum-likelihood estimator (MLE) is adopted at the fusion center to exploit this knowledge and is derived based on the statistics of the energy arrivals. Two cases are considered: the case with no batteries at the sensors and the case with finite-capacity batteries at the sensors. Since the sensors' available energy is unknown at the fusion center, the computation of the MLE will require averaging over the energy arrival at all sensors and in all time slots, which can be intractable in the case with batteries. A particle-filtering based expectation-maximization (EM) algorithm is proposed to address this issue. The effectiveness of our proposed schemes is demonstrated through Monte Carlo simulations.