A rapidly growing collection of modern systems rely on sensors to collect measurements from which inference is performed via suitably designed signal processing. These include autonomous vehicles, environmental monitoring systems, smart buildings, security and surveillance systems, air traffic control, and many others. Moreover,in many of these existing and emerging applications, there are often stringent energy, cost, bandwidth, or other constraints that must be taken into account in the system design. Problems of placement, scheduling, and functionality of sensors have traditionally been difficult optimization problems. This research develops the important role that submodular optimization techniques have to play in addressing such problems. Indeed, while there has been significant development in submodular optimization tools and applications in recent years, a wealth of applications involving sensing, signal processing and inference have yet to be explored.
The research investigates several instances and aspects of these problems, including: optimization of spatial arrays in passive and active sensing systems subject to diverse practical constraints; joint optimization of sensor placement and scheduling for efficient learning of environmental dynamics; optimization of spatial and temporal sensing subject to computational constraints on the associated signal processing for the inference task of interest; development of families of submodular information measures for target applications involving both high- and low-level inference; development of robust, adaptive, and universal designs for sensing that mitigate the effects of incomplete knowledge of aspects of the system and environment; and optimization of sensing system parameters beyond space and time via weighted selection formulations exploiting submodularity in the absence of convexity. Each of these investigations involves the development of the required analysis, algorithms, and architectures, guided by contemporary motivating applications.
