Linear decentralized estimation of correlated data for wireless sensor networks

In this paper, we consider distributed estimation of an unknown random vector by using wireless sensors and a fusion center (FC). We adopt a linear model for distributed estimation of a vector source where both observation models and sensor operations are linear and the multiple access channel (MAC) is coherent. The sensors are designed to minimize the mean square error (MSE) at the fusion center without considering the noise at the fusion center. Subsequently, a filter is designed to cancel out the effect of the noise at the fusion center. We present a closed form solution. When the number of unknown parameters increases, an approximate closed form solution is provided that can be implemented distributively. Since there is no power constraint imposed on transmit power of each sensor, we investigate the average transmit power of each sensor. We show that as the number of unknown parameters increases, the sensor power is inversely proportional to the number of unknown parameters of interest. Finally, simulations are provided to verify the analysis and present the performance of the proposed scheme.