Inner Source Identification for Field Estimation in Wireless Sensor Networks

In previous work, we presented a method for constructing dynamic input-output models for real-time state estimation in correlated dynamic fields using wireless sensor networks (WSNs). The input signals correspond to the sensors on the boundary of the physical space under study, reflecting the assumption there are no independent sources in the interior of the region. In this paper, we present a method to identify sensors not on the boundary that should be used as inputs in the dynamic models when there are inner sources, i.e., sources inside the physical space. We extend concepts from the behavioral model theory of Jan Willems to handle noisy time series. We construct a block-Hankel structured matrix based on the sensor data, and then calculate as an independence indicator the angle between each row of the matrix and the subspace determined by the span of the preceding rows. The inner sources are identified based on these angle values. Experimental results with real temperature data collected with a WSN, and including heat sources as inner sources, illustrate the proposed method