This paper demonstrates fundamental limits of sensor networks for detection problems where the number of hypotheses is exponentially large. Such problems characterize many important applications including detection and classification of targets in a geographical area using a network of seismic sensors, and detecting complex substances with a chemical sensor array. We refer to such applications as large-scale detection problems. Using the insight that these problems share fundamental similarities with the problem of communicating over a noisy channel, we define the “sensing capacity” and lower bound it for a number of sensor network models. The sensing capacity expression differs significantly from the channel capacity due to the fact that for a fixed sensor configuration, codewords are dependent and nonidentically distributed. The sensing capacity provides a bound on the minimal number of sensors required to detect the state of an environment to within a desired accuracy. The results differ significantly from classical detection theory, and provide an intriguing connection between sensor networks and communications. In addition, we discuss the insight that sensing capacity provides for the problem of sensor selection.
From the Publisher: This timely book presents such a consistent framework for addressing data fusion and sensor management. While the framework and the methods presented are applicable to a wide variety of multi-sensor systems, the book focuses on decentralized systems. The book also describes an actual to robot navigation and presents real data and results. The vehicle makes use of sonar sensors with focus of attention capability.