Asymptotic design of quantization and bit allocation for distributed estimation in wireless sensor networks

摘要

This paper investigates the schemes of asymptotically optimal quantization and bit allocation for distributed estimation in wireless sensor networks in which a total bit rate constraint is imposed. Because there is no communication among all sensors, quantizers for observations need to be designed separately. The Lloyd-Max quantizer is shown to be asymptotically optimal for each sensor. Moreover, it is shown that the level number of asymptotically optimal quantization for sensors is proportional to the signal-to-noise ratio, which is determined by the variances of observation and noise. Because the original quantized minimum mean-square error estimator often corresponds to a high computational cost when a large number of sensors are active, in our work, an asymptotically equivalent algorithm of iterative quantized estimator (IQE), which enjoys a low computational cost, is proposed. In addition, an IQE algorithm can be applied to wireless sensor networks with delay or packet loss. Simulation results of this work indicate that the effectiveness of our IQE algorithm is obvious; that is, a significant improvement of estimation performance is achieved by using the optimal bit allocation when comparing with the uniform bit allocation. Copyright © 2016 John Wiley & Sons, Ltd.