Distributed Maximum Likelihood Estimation for Bandwidth-Constrained Wireless Sensor Networks

In this paper, distributed maximum likelihood estimation for bandwidth constrained wireless sensor networks is investigated. We consider an estimation system that involves temporal and spatial domain observations. In particular, we consider the case where there are a total of K sensors, each making N temporal observations. We choose different K and N, but fix KN = M, which means that the total number of temporal and spatial observations is fixed, to examine the trade-off of having a larger K with a smaller N versus having a smaller K with a larger N. The temporal signals observed at each local sensor node are quantized before transmission to a fusion center and estimation at the fusion center is made based on these quantized data. For fair comparison and to bring out the effect of different choices of K and N, we fix the total number of bits used by the K sensors to be gammaM. That is, each sensor sends gammaN bits of the quantized data. We derive the maximum likelihood estimator and examine its estimation accuracy in term of mean-squared error (MSE), as well as the Cramer Rao lower bound (CRLB) for the above distributed estimation problem