Abstract
In this work, a distributed estimation problem for wireless sensor networks is considered. A wireless sensor network involves numbers of sensors and a fusion center. We design the compression functions in the sensor nodes and apply a certain estimator in the fusion center. Let each sensor transmit only one bit to the fusion center. We consider the sensing noise distribution is uniform or Gaussian. And both the noise-free communication channels and binary symmetric channels are also considered. First, we evaluate the mean square error (MSE) function of the system. Then the optimal binary quantization thresholds for sensors can be found by using the Newton’s Method based on minimizing the MSE. Finally, we find that when the sensing noise is getting large, the optimal thresholds will approach to each other. When the communication noise is getting large, the optimal thresholds will converge to the conventional method (the same threshold for each sensor setting in the middle of the sensing range). In conclusion, when the sensing noise or the communication noise variance are not too large, the proposed method has better performance, or we say less MSE, than the conventional one.