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     

Optimal m-ary data fusion with distributed sensors

An optimal data fusion rule is derived for an m-ary detection problem. Each detector determines a local decision using a local decision rule and transmits the local decision to the fusion center. Considering the reliability of local detectors, local decisions are combined to produce the final decision. In this study, based upon the maximum posterior probability concept, optimal decision rules for m-ary detection problems are proposed for the local detector and the data fusion center     

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.     

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     

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.     

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     

Optimal Data Fusion in Multiple Sensor Detection Systems

There is an increasing interest in employing multiple sensors for surveillance and communications. Some of the motivating factors are reliability, survivability, increase in the number of targets under consideration, and increase in required coverage. Tenney and Sandell have recently treated the Bayesian detection problem with distributed sensors. They did not consider the design of data fusion algorithms. We present an optimum data fusion structure given the detectors. Individual decisions are weighted according to the reliability of the detector and then a threshold comparison is performed to obtain the global decision.     

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.     

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.     

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。     

Distributed CFAR detection in homogeneous and nonhomogeneousbackgrounds

The performance of distributed constant false alarm rate (CFAR) detection with data fusion both in homogeneous and nonhomogeneous Gaussian backgrounds is analyzed. The ordered statistics (OS) CFAR detectors are employed as local detectors. With a Swerling type I target model, in the homogeneous background, the global probability of detection for a given fixed global probability of false alarm is maximized by optimizing both the threshold multipliers and the order numbers of the local OS-CFAR detectors. In the nonhomogeneous background with multiple targets or clutter edges, the performance of the detection system is analyzed and its performance is compared with the performance of the distributed cell-averaging (CA) CFAR detection system     

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。     

Multistatic-Radar Binomial Detection

The performance of multistatic-radar binomial detectors is investigated. Although conceptually similar to the well-knwn "M-out-of-N" detector frequently considered for monostatic systems, the multistatic detector must cope with false alarms generated by target et ghosting as well as by noise threshold crossings. A procedure for deriving the detection statistics of multistatic binomial detectors ors is presented. The procedure is applied to derive the detection probabilities for a spectrum of false alarm probabilities, target densities, and numbers of radar receivers.     

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     

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     

Coherent detection in Laplace noise

The discrete-time detection of a time-varying, additive signal in independent Laplace noise is considered. Previous efforts in this area have been restricted to the constant signal, and identically distributed noise case. Theoretical (closed form) expressions for the false alarm and detection probabilities are developed for both the Neyman-Pearson optimal detector and the classical matched filter detector. Comparisons between the two detectors are made which illustrate the effects of signal-to-noise power ratio and sample size for certain false alarm and detection probability constraints. In view of the fact that the optimal Laplace detector is not UMP, we also investigate the effect of signal amplitude mismatch     

Decision fusion rules in multi-hop wireless sensor networks

The decision fusion problem for a wireless sensor network (WSN) operating in a fading environment is considered. In particular, we develop channel-aware decision fusion rules for resource-constrained WSNs where binary decisions from local sensors may need to be relayed through multi-hop transmission in order to reach a fusion center. Each relay node employs a binary relay scheme whereby the relay output is inferred from the channel impaired observation received from its source node. This estimated binary decision is subsequently transmitted to the next node until it reaches the fusion center. Under a flat fading channel model, we derive the optimum fusion rules at the fusion center for two cases. In the first case, we assume that the fusion center has knowledge of the fading channel gains at all hops. In the second case, we assume a Rayleigh fading model, and derive fusion rules utilizing only the fading channel statistics. We show that likelihood ratio (LR) based optimum decision fusion statistics for both cases reduce to respective simple linear test statistics in the low channel signal-to-noise ratio (SNR) regime. These suboptimum detectors are easy to implement and require little a priori information. Performance evaluation, including a study of the robustness of the fusion statistics with respect to unknown system parameters, is conducted through simulations.