Compressed distributed detection and estimation

Detection and estimation are two fundamental tasks that are performed by distributed sensor networks. It is a challenging problem to design efficient protocols and algorithms to perform these tasks taking the inherent scarce network resources, such as limited node power and the limited communication bandwidth, into account. Despite there being quite a rich literature related to energy efficiency in distributed sensor networks, there is still much ongoing research on investigating how to optimize power and communication bandwidth in processing high-dimensional (multimodal) data generated at emerging sensors with high fidelity and resolution. Recent advances in compressive sensing (CS) have led to novel ways of thinking about energy efficient signal processing in sensor networks. CS is well motivated for distributed sensor network applications since data compression at the sensors prior to transmission to the fusion center (FC) is vital to minimize the energy and communication requirements. The universal and agnostic nature of the CS measurement scheme is promising in acquiring compressed data for a variety of inference tasks. In many distributed sensor network applications, sparsity is a common characteristic that can be observed in various forms. While the CS theory widely focuses on sparse signal reconstruction, further research beyond the standard CS framework is needed to understand its applicability in solving a variety of inference problems. In this book chapter, our goal is to provide an up-to-date review on CS-based detection and estimation as applicable to sensor networks. After an introduction, we provide a brief overview of the theory of CS. Then, we discuss CS-based detection and parameter estimation problems considering different signal and noise models. The impact of compression via CS on detection and estimation is quantified in terms of different performance metrics.