Robust Detection of Random Events with Spatially Correlated Data in Wireless Sensor Networks via Distributed Compressive Sensing

摘要

In this paper, we exploit the theory of compressive sensing to performdetection of a random source in a dense sensor network. When the sensors aredensely deployed, observations at adjacent sensors are highly correlated whilethose corresponding to distant sensors are less correlated. Thus, thecovariance matrix of the concatenated observation vector of all the sensors atany given time can be sparse where the sparse structure depends on the networktopology and the correlation model. Exploiting the sparsity structure of thecovariance matrix, we develop a robust nonparametric detector to detect thepresence of the random event using a compressed version of the data collectedat the distributed nodes. We employ the multiple access channel (MAC) modelwith distributed random projections for sensors to transmit observations sothat a compressed version of the observations is available at the fusioncenter. Detection is performed by constructing a decision statistic based onthe covariance information of uncompressed data which is estimated usingcompressed data. The proposed approach does not require any knowledge of thenoise parameter to set the threshold, and is also robust when the distributedrandom projection matrices become sparse.