On the Interdependence of Sensing, Accuracy, and Complexity in Large-scale Detection Applications

This thesis presents fundamental limits and practical algorithms for multi-sensor systems in ‘large-scale detection’ applications. Multi-sensor systems combine multiple sensor observations to detect or estimate the state of an environment. We define ‘large-scale detection’ as a detection problem where sensors are used to detect the state of a discrete grid or vector. Such problems characterize many important applications, including detection and classification of targets in a geographical area using a sensor network, and detecting complex chemicals using a chemical sensor array. While multi-sensor systems have been deployed in large-scale detection applications, many basic theoretical questions regarding sensor allocation and sensor selection have not been addressed in earlier work. To understand the performance limits of such systems, recent work proposed the idea of a ‘sensing capacity.’ While a definition was provided, the existence of a strictly positive sensing capacity, and therefore the practical value of this idea, remained an open question. One of the main contributions of this thesis is to define a sensing capacity that allows for a tolerable detection error. For this definition, we prove the existence of a positive sensing capacity for a number of multi-sensor system models. The sensing capacity provides fundamental limits on the number of sensor measurements required to detect the state of an environment. We obtain our theoretical results by using the insight that large-scale detection problems bear a striking resemblance to the problem of communicating over a noisy channel. In communications, Shannon’s celebrated channel capacity results bound the maximum rate of transmission below which coding schemes with error probability arbitrarily close to zero are feasible. For a large-scale detection application, our results bound the minimum number of sensors required to achieve a desired detection accuracy with arbitrarily small probability of error.