Exploiting structure of spatio-temporal correlation for detection in Wireless Sensor Networks

Abstract

In dense Wireless Sensor Networks (WSN) consecutive measurements obtained by sensors are spatio-temporally correlated in applications that involve the observation of the variation of a physical phenomenon. To exploit this spatiotemporal structure for event detection, the the traditional GLRT test degenerates in the case where dimensionality of data is equal to the sample size or larger. It is because the spatio-temporal sample covariance matrix becomes ill-conditioned or near singular. To circumvent this problem, we modify the traditional GLRT detector by splitting the large spatio-temporal covariance matrix into spatial and temporal covariance matrices. In addition, several detectors are proposed that are robust in the case of high dimensionality and small sample size. Numerical results are drawn, which show that the proposed detection schemes indeed out perform the traditional approaches when the dimension of data is larger than the sample size.