Distributed non-parametric estimation in a bandwidth-constrained sensor network

Non-parametric estimation of an unknown position parameter in a bandwidth-constrained wireless sensor network (WSN) is considered in this paper. Due to bandwidth constraint, each sensor is restricted to send only one bit of information to a fusion center. We propose a non-parametric estimator that employs a recently introduced adaptive quantization (AQ) scheme. Specifically, the position parameter is estimated as the sample mean of the quantization thresholds used in AQ. The proposed non-parametric estimator is based on the fact that the AQ thresholds asymptotically converge (in mean) to the unknown position parameter, under the condition that the position parameter is an integer multiple of the stepsize used in AQ. When the condition is not met, there is a bias which can, however, be made negligible by choosing the stepsize to be small (compared with the position parameter). Numerical results are provided to demonstrate the effectiveness of the proposed non-parametric estimator.