EXPLOITING STRUCTURE OF SPATIO-TEMPORAL CORRELATION FOR DETECTION IN WIRELESS SENSOR NETWORKS Sadiq Ali, José A. López-Salcedo, Gonzalo Seco-Granados Signal Processing for Communications and Navigation (SPCOMNAV), Universitat Autònoma de Barcelona (UAB) Email:{sadiq.ali, jose.salcedo, gonzalo.seco}@uab.es ABSTRACT In dense Wireless Sensor Networks (WSN) consecutive mea- surements obtained by sensors are spatio-temporally corre- lated in applications that involve the observation of the vari- ation of a physical phenomenon. To exploit this spatio- temporal 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 pro- posed 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. Index Terms— Spatio-Temporal Correlation, Kronecker Structure, GLRT, Wireless Sensor Network. 1. INTRODUCTION In wireless senor networks (WSNs), dense deployment of sensor nodes makes the sensor observations highly correlated in the space domain. In other words, the existence of spatial correlation implies that the readings from sensor nodes which are geographically close to each other are expected to be largely correlated. In environment monitoring applications, sensor nodes periodically sample and communicate the data to the fusion center. The nature of the energy-radiating phys- ical phenomenon yields temporal correlation between each consecutive observation of a sensor node [1]. Existence of temporal correlation implies that the readings observed at one time instant are related to the readings observed at the previ- ous time instants. To sum it up this means that the physical phenomena often exhibit both spatial and temporal correla- This work was supported in part by the Spanish Ministry of Science and Innovation project TEC 2011-28219, by the Catalan Government under the grant FI-DGR-2011-FIB00711/ 2009 SGR 298 and the Chair of Knowledge and Technology Transfer "Parc de Recerca UAB - Santander". tion. By noticing the fact that sensor readings are both spa- tially and temporally correlated, the detection of an event can be performed by capturing the spatio-temporal correlation in the sensor readings. While considering large scale WSN, we assume that a sub- set of sensors (i.e. those located close to the event) receive the signal emitted by the event and send their measurements to the fusion center. Intuitively, spatial correlation present in observations of these sensors indicates that measurements are received from same neighborhood and it is most likely that some real event has happend. Similarly, if there is strong cor- relation between the consecutive time measurements then it further confirms the actual presence of an event. There have been some attempts to consider the correlated measurements into formulation of the signal detection. However, many of these studies consider the presence of correlation as a delete- rious effect [2]. On the contrary, there are some contributions that focus on the discrimination between only spatially cor- related and spatially independent observations by exploiting the structure of covariance matrix [3, Ch. 9-10][4]. However, these works consider observations received as temporally in- dependent and do not capture spatio-temporal characteristics of the physical phenomenon. The GLRT approach in [5] detects spatial correlation in time series based on the decision whether the spatio-temporal sample covariance matrix is block diagonal or not. This ap- proach typically ends up with a simple quotient between the determinant of the spatio-temporal sample covariance matrix and the determinant of its diagonal version. As the GLRT involves estimation of unknown parameters (i.e. covariance matrix), therefore, it depends on the sample size and the di- mensionality. In practice, GLRT is used based on the assump- tion that the sample size is large while the sample dimension is small. In the case of large WSN when the sample support available for estimating the covariance matrix is limited, the GLRT degenerates due to singular and ill-conditioned covari- ance matrix [6]. To cope with this problem we propose novel detectors that are robust against the high dimensionality of spatio-temporal data. Consequently, the proposed detectors are based on splitting the spatio-temporal covariance matrix 20th European Signal Processing Conference (EUSIPCO 2012) Bucharest, Romania, August 27 - 31, 2012 © EURASIP, 2012 - ISSN 2076-1465 774