Asynchronous distributed detection

Binary parallel distributed-detection architectures employ a bank of local detectors to observe a common volume of surveillance, and form binary local decisions about the existence or nonexistence of a target in that volume. The local decisions are transmitted to a central detector, the data fusion center (DEC), which integrates them to a global target or no target decision. Most studies of distributed-detection systems assume that the local detectors are synchronized. In practice local decisions are made asynchronously and the DFC has to update its global decision continually. In this study the number of local decisions observed by the central detector within any observation period is Poisson distributed. An optimal fusion rule is developed and the sufficient statistic is shown to be a weighted sum of the local decisions collected by the DFC within the observation interval. The weights are functions of the individual local detector performance probabilities (i.e., probabilities of false alarm and detection). In this respect the decision rule is similar to the one developed by Chair and Varshney for the synchronized system. Unlike the Chair-Varshney rule, however, the DFC's decision threshold in the asynchronous system is time varying. Exact expressions and asymptotic approximations are developed for the detection performance with the optimal rule. These expressions allow performance prediction and assessment of tradeoffs in realistic decision fusion architectures which operate over modern communication networks     

Optimum multisensor fusion of correlated local decisions

A distributed detection system consisting of a number of local detectors and a fusion center is considered. Each detector makes a decision for the underlying binary hypothesis testing problem based on its own observation and transmits its decision to the fusion center where the global decision is derived. The local decision rules are assumed to be given, but the local decisions are correlated. The correlation is generally characterized by a finite number of conditional probabilities. The optimum decision fusion rule in the Neyman-Pearson sense is derived and analyzed. The performance of the distributed detection system versus the degree of correlation between the local decisions is analyzed for a correlation structure that can be indexed by a single parameter. System performance as well as the performance advantage of using a larger number of local detectors degrade as the degree of correlation between local decisions increases     

Optimum local decision space partitioning for distributed detection

A distributed detection system is considered that consists of a number of independent local detectors and a fusion center. The decision statistics and performance characteristics (i.e. the false alarm probabilities and detection probabilities) of the local detectors are assumed as given. Communication is assumed only between each local detector and the fusion center and is one-way from the former to the latter. The fusion center receives decisions from the local detectors and combines them for a global decision. Instead of a one-bit hard decision, the authors propose that each local detector provides the fusion center with multiple-bit decision value which represents its decision and, conceptually, its degree of confidence on that decision. Generating a multiple-bit local decision entails a subpartitioning of the local decision space the optimization of which is studied. It is shown that the proposed system significantly outperforms one in which each local detector provides only a hard decision. Based on optimum subpartitioning of local decision space, the detection performance is shown to increase monotonically with the number of partitions     

Fault Detection in Dynamic Systems via Decision Fusion

Due to the growing demands for system reliability and availability of large amounts of data, efficient fault detection techniques for dynamic systems are desired. In this paper, we consider fault detection in dynamic systems monitored by multiple sensors. Normal and faulty behaviors can be modeled as two hypotheses. Due to communication constraints, it is assumed that sensors can only send binary data to the fusion center. Under the assumption of independent and identically distributed (1ID) observations, we propose a distributed fault detection algorithm, including local detector design and decision fusion rule design, based on state estimation via particle filtering. Illustrative examples are presented to demonstrate the effectiveness of our approach.     

Decentralized CFAR signal detection

The authors develop the theory of CA-CFAR (cell-averaging constant false-alarm rate) detection using multiple sensors and data fusion, where detection decisions are transmitted from each CA-CFAR detector to the data fusion center. The overall decision is obtained at the data fusion center based on some k out of n fusion rule. For a Swerling target model I embedded in white Gaussian noise of unknown level, the authors obtain the optimum threshold multipliers of the individual detectors. At the data fusion center, they derive an expression for the overall probability of detection while the overall probability of false alarm is maintained at the desired value for the given fusion rules. An example is presented showing numerical results     

Blind adaptive decision fusion for distributed detection

We consider the problem of decision fusion in a distributed detection system. In this system, each detector makes a binary decision based on its own observation, and then communicates its binary decision to a fusion center. The objective of the fusion center is to optimally fuse the local decisions in order to minimize the final error probability. To implement such an optimal fusion center, the performance parameters of each detector (i.e., its probabilities of false alarm and missed detection) as well as the a priori probabilities of the hypotheses must be known. However, in practical applications these statistics may be unknown or may vary with time. We develop a recursive algorithm that approximates these unknown values on-line. We then use these approximations to adapt the fusion center. Our algorithm is based on an explicit analytic relation between the unknown probabilities and the joint probabilities of the local decisions. Under the assumption that the local observations are conditionally independent, the estimates given by our algorithm are shown to be asymptotically unbiased and converge to their true values at the rate of O(1/k/sup 1/2/) in the rms error sense, where k is the number of iterations. Simulation results indicate that our algorithm is substantially more reliable than two existing (asymptotically biased) algorithms, and performs at least as well as those algorithms when they work.     

OS-CFAR thresholding in decentralized radar systems

In a decentralized detection scheme, several sensors perform a binary (hard) decision and send the resulting data to a fusion center for the final decision. If each local decision has a constant false alarm rate (CFAR), the final decision is ensured to be CFAR. We consider the case that each local decision is a threshold decision, and the threshold is proportional, through a suitable multiplier, to a linear combination of order statistics (OS) from a reference set (a generalization of the concept of OS thresholding). We address the following problem: given the fusion rule and the relevant system parameters, select each threshold multiplier and the coefficients of each linear combination so as to maximize the overall probability of detection for constrained probability of false alarm. By a Lagrangian maximization approach, we obtain a general solution to this problem and closed-form solutions for the AND and OR fusion logics. A performance assessment is carried on, showing a global superiority of the OR fusion rule in terms of detection probability (for operating conditions matching the design assumptions) and of robustness (when these do not match). We also investigate the effect of the hard quantization performed at the local sensors, by comparing the said performance to those achievable by the same fusion rule in the limiting case of no quantization     

多传感器决策融合系统中的决策空间优化划分研究

在假定各局部检测器的决策规则已经给定以及在Ｂｈａｔａｃｈａｒｙｙａ距离最大的意义下,对多传感器融合系统中的决策空间优化划分设计进行了研究。首先基于Ｂｈａｔａｃｈａｒｙｙａ距离准则,把对整个系统决策空间的优化划分解耦为分别对各局部检测器决策空间的优化划分;然后从理论上证明了这种划分设计在最大Ｂｈａｔａｃｈａｒｙｙａ距离意义下的最优性,以及这种基于最大Ｂｈａｔａｃｈａｒｙｙａ距离准则进行优化划分设计的合理性;最后,通过对瑞利起伏环境下信号检测融合问题的数值计算表明,本文方法的性能优于基于Ｊ－散度方法的性能。     

Optimal Detection and Performance of Distributed Sensor Systems

Global optimization of a distributed sensor detection system withfusion is considered, where the fusion rule and local detectors aresolved to obtain overall optimal performance. This yields coupledequations for the local detectors and the fusion center.The detection performance of the distributed system with fusionis developed. The globally optimal system performance is comparedwith two suboptimal systems. Receiver operating characteristics(ROCs) are computed numerically for the problem of detecting aknown signal embedded in non-Gaussian noise.     

Distributed binary integration

A distributed radar detection system that employs binary integration at each local detector is studied. Local decisions are transmitted to the fusion center where they are combined to yield a global decision. The optimum values of the two thresholds at each local processor are determined so as to maximize the detection probability under a given probability of false alarm constraint. Using an important channel model, performance comparisons are made to determine the integration loss     

Local SNR considerations in decentralized CFAR detection

We consider the decentralized detection problem, involving N sensors and a central processor, in which the sensors transmit unquantized data to the fusion center. Assuming a homogeneous background for constant false-alarm rate (CFAR) analysis, we obtain the performances of the system for the Swerling I and Swerling III target models. We demonstrate that a simple nonparametric fusion rule at the central processor is sufficient for nearly optimum performance. The effect of the local signal-to-noise ratios (SNRs) on the performances of the optimum detector and two suboptimum detectors is also examined. Finally, we obtain a set of conditions, related to the SNRs, under which better performance may be obtained by using decentralized detection as compared with centralized detection     

基于均匀性判定规则的统计MIMO雷达多通道融合检测技术

针对统计MIMO雷达各观测通道统计特性不一致的情况,提出了一种多通道融合检测技术。该技术利用均匀性判定规则,选择一组均匀的、"被认为是具有较高信杂噪比"的局部检验统计量来构建全局检验统计量,即新的检测器。给出了新检测器的设计步骤和均匀性判定规则,并利用全概率公式证明了新检测器的虚警概率与每一操作步骤中过门限概率的关系,从而为仿真得出检测门限提供了理论基础。仿真结果表明,在不同通道间信噪比分布类型条件下,新检测器的检测性能具有较强的稳健性,且与不同条件下性能最优的检测器相比,其性能损失很小。     

Decentralized detection over multiple-access channels

We study the decentralized detection problem in a general framework where arbitrary number of quantization levels at the local sensors are allowed, and transmission from the sensors to the fusion center is subject to both noise and interchannel interference. We treat both Bayesian and Neyman-Pearson approaches to the problem, and develop an iterative descent algorithm to design the optimal quantizers and fusion rule. Some numerical examples for both approaches are also presented     

Nonstochastic adaptive decision fusion in distributed-detection systems

Implementing the optimal Neyman-Pearson (NP) fusion rule in distributed detection systems requires the sensor error probabilities to be a priori known and constant during the system operation. Such a requirement is practically impossible to fulfil for every resolution cell in a multiflying target multisensor environment. The true performance of the fusion center is often worse than expected due to fluctuations of the observed environment and instabilities of sensor thresholds. This work considers a nonparametric data fusion situation in which the fusion center knows only the number of the sensors, but ignores their error probabilities and cannot control their thresholds. A data adaptive approach to the problem is adopted, and combining P reports from Q independent distributed sensors through a least squares (LS) formulation to make a global decision is investigated. Such a fusion scheme does not entail strict stationarity of the noise environment nor strict invariance of the sensor error probabilities as is required in the NP formulation. The LS fusion scheme is analyzed in detail to simplify its form and determine its asymptotic behavior. Conditions of performance improvement as P increases and of quickness of such improvement are found. These conditions are usually valid in netted radar surveillance systems.     

CFAR data fusion center with inhomogeneous receivers

Detection systems with distributed sensors and data fusion are increasingly used by surveillance systems. A system formed by N inhomogeneous constant false alarm rate (CFAR) detectors (cell-averaging (CA) and ordered statistic (OS) CFAR detectors) is studied. A recursive formulation of an algorithm that permits a fixed level of false alarms in the data fusion center is presented, to set the optimum individual threshold levels in the CFAR receivers and the optimum `K out of N' decision rule in order to maximize the total probability of detection. The algorithm also considers receivers of different quality or with different communication channel qualities connecting them with the fusion center. This procedure has been applied to several hypothetical networks with distributed CA-CFAR and OS-CFAR receivers and for Rayleigh targets and interference, and it was seen that in general the fusion decision OR rule is not always the best     

Mutual and conditional mutual informations for optimizingdistributed Bayes detectors

This paper considers optimization of distributed detectors under the Bayes criterion. A distributed detector consists of multiple local detectors and a fusion center that combines the local decision results to obtain a final decision. Introduced first are distributional distance measures, the mutual information (MI) and the conditional mutual information (CMI), that are obtained by applying information theoretic concepts to detection problems. Error bound analyses show that these distance measures approximate the Bayesian probability of error better than the conventional ones regardless of the operational environments. Then, a new optimization technique is proposed for distributed Bayes detectors. The method uses the distributional distances instead of the original Bayes criterion to avoid the complexity barrier of the optimization problem. Numerical examples show that the proposed distance measures yield solutions far better than the existing ones     

Optimal distributed decision fusion

The problem of decision fusion in distributed sensor systems is considered. Distributed sensors pass their decisions about the same hypothesis to a fusion center that combines them into a final decision. Assuming that the sensor decisions are independent of each other for each hypothesis, the authors provide a general proof that the optimal decision scheme that maximizes the probability of detection at the fusion for fixed false alarm probability consists of a Neyman-Pearson test (or a randomized N-P test) at the fusion and likelihood-ratio tests at the sensors     

Detection with Distributed Sensors

The extension of classical detection theory to the case of distributed sensors is discussed, based on the theory of statistical hypothesis testing. The development is based on the formulation of a decentralized or team hypothesis testing problem. Theoretical results concerning the form of the optimal decision rule, examples, application to data fusion, and open problems are presented.     

Optimal Decision Fusion in Multiple Sensor Systems

The problem of optimal data fusion in the sense of the Neyman-pearson (N-P) test in a centralized fusion center is considered. The fusion center receives data from various distributed sensors. Each sensor implements a N-P test individually and independently of the other sensors. Due to limitations in channel capacity, the sensors transmit their decision instead of raw data. In addition to their decisions, the sensors may transmit one or more bits of quality information. The optimal, in the N-P sense, decision scheme at the fusion center is derived and it is seen that an improvement in the performance of the system beyond that of the most reliable sensor is feasible, even without quality information, for a system of three or more sensors. If quality information bits are also available at the fusion center, the performance of the distributed decision scheme is comparable to that of the centralized N-P test. Several examples are provided and an algorithm for adjusting the threshold level at the fusion center is provided.     

A new distributed constant false alarm rate detector

A new constant false alarm rate (CFAR) test termed signal-plus-order statistic CFAR (S+OS) using distributed sensors is developed. The sensor modeling assumes that the returns of the test cells of different sensors are all independent and identically distributed In the S+OS scheme, each sensor transmits its test sample and a designated order statistic of its surrounding observations to the fusion center. At the fusion center, the sum of the samples of the test cells is compared with a constant multiplied by a function of the order statistics. For a two-sensor network, the functions considered are the minimum of the order statistics (mOS) and the maximum of the order statistics (MOS). For detecting a Rayleigh fluctuating target in Gaussian noise, closed-form expressions for the false alarm and detection probabilities are obtained. The numerical results indicate that the performance of the MOS detector is very close to that of a centralized OS-CFAR and it performs considerably better than the OS-CFAR detector with the AND or the OR fusion rule. Extension to an N-sensor network is also considered, and general equations for the false alarm probabilities under homogeneous and nonhomogeneous background noise are presented.