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     

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     

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     

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     

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.     

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     

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.     

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     

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.     

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     

Explicit solutions for some simple decentralized detection problems

A decentralized detection problem is considered in which a number of identical sensors transmit a finite-valued function of their observations to a fusion center which makes a final decision on one of M alternative hypotheses. The authors consider the case in which the number of sensors is large, and they derive (asymptotically) optimal rules for determining the messages of the sensors when the observations are generated from a simple and symmetrical set of discrete distributions. They also consider the tradeoff between the number of sensors and the communication rate of each sensor when there is a constraint on the total communication rate from the sensors to the fusion center. The results suggest that it is preferable to have several independent sensors transmitting low-rate (coarse) information instead of a few sensors transmitting high-rate (very detailed) information. They also suggest that an M-ary hypothesis testing problem can be viewed as a collection of M(M-1)/2 binary hypothesis testing problems. From this point of view the most useful messages (decision rules) are those that provide information to the fusion center that is relevant to the largest possible numbers of these binary hypothesis testing problems     

Parallel Distributed CFAR Detection Optimization Based on Genetic Algorithm with Interval Encoding

Aiming at parallel distributed constant false alarm rate (CFAR) detection employing K/N fusion rule, an optimization algorithm based on the genetic algorithm with interval encoding is proposed. N-1 local probabilities of false alarm are selected as optimization variables. And the encoding intervals for local false alarm probabilities are sequentially designed by the person-by-person optimization technique according to the constraints. By turning constrained optimization to unconstrained optimization, the problem of increasing iteration times due to the punishment technique frequently adopted in the genetic algorithm is thus overcome. Then this optimization scheme is applied to spacebased synthetic aperture radar (SAR) multi-angle collaborative detection, in which the nominal factor for each local detector is determined. The scheme is verified with simulations of cases including two, three and four independent SAR systems. Besides, detection performances with varying K and N are compared and analyzed.     

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.     

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     

Quickest detection for sequential decentralized decision systems

Quickest detection procedures are techniques used to detect sudden or abrupt changes (also called disorders) in the statistics of a random process. The goal is to determine as soon as possible that the change occurred, while at the same time minimizing the chance of falsely signaling the occurrence of a disorder before the change. In this work the distributed quickest detection problem when the disorder occurs at an unknown time is considered. The distributed local detectors utilize a simple summing device and threshold comparator, with a binary decision at the output. At the fusion center, the optimal maximum likelihood (ML) procedure is analyzed and compared with the more practical Page procedure for quickest detection. It is shown that the two procedures have practically equivalent performance. For the important case of unknown disorder magnitudes, a version of the Hinkley procedure is also examined. Next, a simple method for choosing the thresholds of the local detectors based on an asymptotic performance measure is presented. The problem of selecting the local thresholds usually requires optimizing a constrained set of nonlinear equations; our method admits a separable problem, leading to straightforward calculations. A sensitivity analysis reveals that the resulting threshold settings are optimal for practical purposes. The issue of which sample size to use for the local detectors is investigated, and the tradeoff between decision delay and communication cost is evaluated. For strong signals, it is shown that the relative performance deteriorates as the sample size increases, that is, as the system cost decreases. Surprisingly, for the weak signal case, lowering the system cost (increasing the sample size) does not necessarily result in a degradation of performance     

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。     

Distributed detection by a large team of sensors in tandem

The problem of decentralized binary hypothesis testing by a team consisting of N decision makers (DMs) in tandem is considered. Each DM receives an observation and transmits a binary message to its successor; the last DM has to decide which hypothesis is true. The necessary and sufficient condition for the probability of error to go asymptotically to zero as N→∞ is that the log-likelihood ratio of the observation of each DM be unbounded. The result is generalized for multiple hypotheses and multiple messages. An easily implementable suboptimal decision scheme is also considered; in this case, the necessary and sufficient condition for the probability of error to asymptotically go to zero is that the log-likelihood ratio of the observation of each DM be unbounded from both above and below. The tradeoff between the complexity of the decision rules and their performance is examined, and numerical results are presented, in order to demonstrate that the performance of both decision schemes is comparable     

非线性系统中多传感器目标跟踪融合算法研究

 研究了在非线性系统中 ,基于转换坐标卡尔曼滤波器的多传感器目标跟踪融合算法。通过分析得出 :在非线性系统的多传感器目标跟踪中 ,基于转换坐标卡尔曼滤波器 ( CMKF)的分布融合估计基本可以重构中心融合估计。仿真实验也证明了此结论。由此可见分布的 CMKFA是非线性系统中较优的分布融合算法