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This book provides an introductory treatment of the fundamentals of decision-making in a distributed framework. Classical detection theory assumes that complete observations are available at a central processor for decision-making. More recently, many applications have been identified in which observations are processed in a distributed manner and decisions are made at the distributed processors, or processed data (compressed observations) are conveyed to a fusion center that makes the global decision. Conventional detection theory has been extended so that it can deal with such distributed detection problems. A unified treatment of recent advances in this new branch of statistical decision theory is presented. Distributed detection under different formulations and for a variety of detection network topologies is discussed. This material is not available in any other book and has appeared relatively recently in technical journals. The level of presentation is such that the hook can be used as a graduate-level textbook. Numerous examples are presented throughout the book. It is assumed that the reader has been exposed to detection theory. The book will also serve as a useful reference for practicing engineers and researchers. I have actively pursued research on distributed detection and data fusion over the last decade, which ultimately interested me in writing this book. Many individuals have played a key role in the completion of this book.

Inhaltsverzeichnis

Frontmatter

1. Introduction

Abstract
All of us frequently encounter decision-making problems in every day life. Based on our observations regarding a certain phenomenon, we need to select a particular course of action from a set of possible options. This problem involving a single decision maker is typically a difficult one. Decision making in large-scale systems consisting of multiple decision makers is an even more challenging problem. Group decision-making structures are found in many real world situations. Application areas include financial institutions, air-traffic control, oil exploration, medical diagnosis, military command and control, electric power networks, weather prediction, and industrial organizations. For example, a medical doctor may order multiple diagnostic tests and seek additional peer opinions before a major surgical procedure is carried out, or a military commander may use data from radar and IR sensors along with intelligence information while deciding whether or not to launch an offensive. In many applications, multiple decision makers arise naturally, e.g., managers in an industrial organization. In many other applications, additional decision makers are employed to improve system performance. For example, deployment of multiple sensors for signal detection in a military surveillance application improves system survivability, results in improved detection performance or in a shorter decision time to attain a prespecified performance level, and may provide increased coverage in terms of surveillance region and number of targets.
Pramod K. Varshney

2. Elements of Detection Theory

Abstract
There are many practical situations in which one is faced with a decision-making problem, i.e., the problem of choosing a course of action from several possibilities. For example, in a radar detection context, a decision is to be made regarding the presence or absence of a target based on the radar return. In a digital communication system, one of several possible waveforms is transmitted over a channel. Based on the received noisy observation, we need to determine the symbol that was transmitted. In a biomedical application, based on a smear of human tissue, one needs to determine if it is cancerous. In a pattern recognition problem, one needs to determine the type of aircraft being observed based on some aircraft features. In all of the above applications, the common underlying problem is to make a decision among several possible choices. This is carried out based on available noisy observations. The branch of statistics dealing with these types of problems is known as statistical decision theory or hypothesis testing. In the context of radar and communication theory, it is known as detection theory.
Pramod K. Varshney

3. Distributed Bayesian Detection: Parallel Fusion Network

Abstract
As indicated earlier, detection networks can be organized in a number of topological structures. Among the topologies considered in the literature, the parallel fusion topology has received the most attention. In this chapter, we develop the theory of Bayesian detection for parallel fusion structures. In Section 3.2, we consider a parallel structure consisting of a number of detectors whose decisions are available locally and are not transmitted to a fusion center for decision combining. Costs of decision making are assumed to be coupled and a system wide optimization is carried out for binary and ternary hypothesis testing problems. Section 3.3 considers the design of fusion rules given the statistics of incoming decisions. Design of the parallel fusion network, consisting of a number of local detectors and a fusion center, is the subject of Section 3.4. Person-by-person optimal decision rules are derived. A number of special cases including conditionally independent local observations and identical detectors are considered. Efficient computational approaches are presented. Design of optimal parallel structures with dependent local observations is an NP-complete problem. This and other computational complexity issues are briefly considered. Finally, robust detection and nonparametric detection are discussed at the end of the chapter.
Pramod K. Varshney

4. Distributed Bayesian Detection: Other Network Topologies

Abstract
Bayesian hypothesis testing for the parallel fusion network was discussed extensively in Chapter 3. This chapter considers the problem of Bayesian hypothesis testing for several other network topologies. In Section 4.2, we consider the serial or tandem network, a widely studied network topology. System design methodology is developed and its performance is compared with that of the parallel network. Interesting issues, such as sequencing and placement of detectors, are also discussed. A brief discussion on tree networks is presented in Section 4.3. In Section 4.4, distributed detection networks with feedback are treated. In this class of networks, information flows both downstream as well as upstream, i.e., toward the fusion center and away from it. Feedback is shown to improve system performance. An important issue for this configuration is its data transmission requirement. Two protocols are presented that reduce this requirement. Finally, a unified methodology is presented to represent any decentralized detection network structure. Decision rules are also obtained. This methodology is applicable to detection networks that include memory as well as feedback.
Pramod K. Varshney

5. Distributed Detection with False Alarm Rate Constraints

Abstract
In this chapter, we consider the distributed detection problem for situations where the probability of false alarm is to remain less than an acceptable value. This formulation is especially suitable for radar applications. First, we consider the Neyman—Pearson formulation of the problem. This formulation does not require the knowledge of a priori probabilities associated with different hypotheses or an assignment of costs to different courses of action. System probability of detection is maximized under a probability of false alarm constraint. Under this formulation, the parallel fusion network topology without a fusion center is not appropriate because systemwide probabilities of detection and false alarm can not be defined. Therefore, a fusion center is always assumed to be present. We consider only the parallel fusion network topology here. Other network topologies can be treated similarly. In Section 5.2, the distributed Neyman—Pearson detection problem is formulated and decision rules are derived. A number of interesting issues, such as randomization, arise. These and other related aspects are discussed. In practical radar signal detection scenarios, noise and clutter background are often nonstationary. In this case, the optimum Neyman—Pearson detector with a fixed threshold fails to maintain a constant false alarm rate (CFAR), and adaptive thresholding based on observations from the neighboring region is required. Distributed CFAR processing is discussed in Section 5.3. Issues, such as robustness in the presence of homogeneous and nonhomogeneous backgrounds, are also examined. In Section 5.4, distributed detection of weak signals is considered, and locally optimum decision rules are derived.
Pramod K. Varshney

6. Distributed Sequential Detection

Abstract
This chapter considers distributed sequential detection problems. In sequential detection, observations are assumed to arrive sequentially at the detectors. As observations continue to arrive, detectors include them in their decision making. Unlike fixed-sample-size detection problems where decisions are made after receiving the entire set of observations, sequential detectors may choose to stop at any time and make a final decision or continue to take additional observations. In this chapter, we will consider a Bayesian formulation of two distributed sequential detection problems for parallel fusion network topologies. In Section 6.2, we consider a parallel fusion network without a fusion center. For simplicity, we restrict our attention to a two-detector network. Sequential tests are implemented at individual detectors. The system is optimized based on a coupled cost assignment. These decisions can still be combined using a fixed fusion rule. In Section 6.3, we consider a parallel fusion network consisting of N peripheral detectors and a fusion center. The local detectors send a sequence of summary messages to the fusion center where a sequential test is implemented. The fusion center makes the decision whether to continue taking additional observations or to stop and make a final decision on the hypothesis present. In general, distributed sequential detection problems are quite complex as is evident from the discussion included in this chapter.
Pramod K. Varshney

7. Information Theory and Distributed Hypothesis Testing

Abstract
Information theory was developed to determine the fundamental limits on the performance of communication systems. Detection theory involves an application of statistical decision theory to the problem of determining the presence or absence of signals in noise. Both of these theories deal with the communication problem. The relationship between information theory and conventional (centralized) detection theory has been discussed in the literature. Kullback [Ku159] discussed the use of discrimination to study hypothesis testing problems. Middleton [Mid60] employed cost functions based on information theory for optimizing signal detection systems. Csiszar et al. [CsL71] and Blahut [Bla74] have formulated the detection problem as a coding problem and have carried out an asymptotic analysis of detection systems based on the error exponent function. In this chapter, we briefly present some extensions of the above work for the distributed detection problem. In Section 7.2, we discuss the design of distributed detection systems based on an information theoretic cost function. In Section 7.3, we present a brief summary of some asymptototic results on the performance of distributed detection systems.
Pramod K. Varshney

Backmatter

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