On the performance of serial networks in distributed detection

Distributed detection on the serial (or tandem) topology is considered with the probability of error performance criterion. Previously published efforts, while presenting probability of detection versus false alarm results, limited the number of array elements to two or three. For the detection of known, equally likely signals in additive, symmetric noise, the author presents simple recursive expressions for the threshold values and the performance of the system. Examples for known signals in Gaussian and Laplacian noise show the degradation in performance due to the array structure     

Radar detection in clutter

Clutter is defined as any unwanted radar return. The presence of clutter in a range/Doppler cell complicates the detection of a target return signal in that cell. In order to quantify the effect of clutter on the probability of detection, we must first specify sets of models suitable for representing the clutter and target. The simplest and most common model for clutter is based on the gamma density. We include two additional models, the NCG and NCGG clutter models for low grazing angles. They are motivated by physical arguments, the latter of which can accommodate the well-known phenomenon of speckle. Using one of these models for clutter together with one of several models for targets, we determine, in a range/Doppler cell, expressions for probabilities of detection of a target in the presence of clutter. It is important to control the probability of false alarms. The presence of clutter in a cell necessitates an increase in the detection threshold setting in order to control false alarms, thus lowering the probability of detection. If the clutter level is unknown, then we need to take measurements of the clutter and use it to adjust the threshold. The more clutter samples we take, the better the estimate of the clutter level and the less is the resulting detection loss. Using the expressions for the probability of detection in clutter, we can quantify the detection loss for a pair of commonly used constant false-alarm rate (CFAR) techniques and investigate how the loss varies with different parameter values, especially with regard to the number of clutter samples taken to estimate the clutter level.     

Mean-Level Detection of Nonfluctuating Signals

Analysis of the performance of a mean-level threshold in the detection of nonfluctuating signals is performed. Formulas for the probability of detection are derived and a simple recursive method that can be used for computations is described. Binary integration is discussed, and it is shown that the loss in sensitivity due to the use of an adaptive threshold followed by binary integration is only a fraction of a decibel when compared with optimum binary integration. Binary integration results are given for both fluctuating and nonfluctuating signals.     

Weak Signal Detection in Non-Gaussian Noise of Unknown Level

An adaptive threshold detector to test for the presence of a weak signal in additive non-Gaussian noise of unknown level is discussed. The detector consists of a locally optimum detector, a noise level estimator, and a decision device. The detection threshold is made adaptive according to the information provided by the noise level estimator in order to keep a fixed false-alarm probability. Asymptotic performance characteristics are obtained indicating relationships among the basic system parameters such as the reference noise sample size and the underlying noise statistics. It is shown that, as the reference noise sample size is made sufficiently large, the adaptive threshold detector attains the performance of a corresponding locally optimum detector for detecting the weak signal were the noise level known.     

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     

Detection Performance of a Mean-Level Threshold

The problem of detecting signals in nonstationary clutter is met by presenting a mean-level or adaptive threshold which adjusts to the changing background level. Such a threshold performs better than a fixed threshold that must be set for the highest amplitude clutter. However, the mean-level threshold does not perform as well for stationary noise as a fixed threshold set at the proper value. One measure of effectiveness of an adaptive threshold is its performance in stationary noise (compared to the optimum fixed threshold) for a specified speed of response. For the mean-level threshold, a simple mathematical solution is found for the detection probability when the noise is stationary and the signal scintillates rapidly. The performance is evaluated for a wide range of mean-level-threshold time constants and for several false-alarm probabilities. The results are presented graphically. As an example, the mean-level threshold suffers 3 dB in detectability (equivalent signal-to-noise ratio) in the presence of stationary noise as compared to the optimum fixed threshold for 50-percent probability of detection, false-alarm probability of 10-8, and an adjustment time of 15 times the signal duration.     

Performance Analysis of a Target Detection System Using Infrared Imagery

The automatic detection of targets in cluttered infrared imagery is considered. The environment for the problem is that of a "fire-and-forget" weapon, and the mission philosophy for such a weapon dictates that the weapon has to find one and only one target in the automatic detection phase. A detection system that meets this requirement is presented. The system uses techniques of image processing and pattern recognition, with the extension that ranking methods are used instead of thresholds to accommodate the requirement of finding one and only one target. A probability model of the system is developed to determine the system performance as a function of throughput and expressions derived for the probability that the object chosen by the system as the target is actually a target. In order to validate the theoretical results, the actual performance of the detection system on a database of 68 infrared images is determined and compared with the predicted performance of the system. It is shown that there is good correspondence between the empirical results and the theoretical performance.     

Evaluating the Detectability of Gaussian Stochastic Signals by Steepest Descent Integration

It is shown how to compute the detection probability of certain signals by numerical integration of the Laplace inversion integral involving the characteristic function or the moment-generating function of the detection statistic. The contour of integration is taken as the path of steepest descent of the integrand and is determined numerically as the integration proceeds. The method is applied to calculating the performance of the optimum detector of a Gaussian stochastic signal in white noise when the signals actually present have a different average s.n.r. from that assumed in the design. Results are presented for narrowband signals with Lorentz and rectangular spectral densities. The detectability of the former is shown to be more sensitive than that of the latter to the value of the design s.n.r. The relative disadvantage of the threshold detector, also assessed by this method, is smaller for signals with a rectangular than for those with a Lorentz spectral density.     

分布式接收宽带多目标信号盲检测迭代处理方法

随着软硬件技术的飞速发展和宽带接收机的广泛使用,频谱检测向着高瞬时带宽的方向发展,传统基于信道化处理的频谱检测方法存在搜索速度慢、处理效率低下的问题。文章提出了 1种新的分布式接收宽带多目标信号盲检测迭代处理方法,在无须预先知道信号数目及信号频谱位置的情况下,能够实现特定虚警概率多信号盲检测,具备较高的灵活性和稳健性。首先,在对信号特征进行分析的基础上,通过构造线性模型,将分布式接收多目标信号检测转化为线性模型求解问题进行处理;然后,基于贝叶斯多参数联合求解模型,在对未知参数先验分布进行合理假设的基础上,推导了各未知参数变分分布及信号检测门限的解析表达式,采用变分分布软信息迭代的方式实现多传感器信号、多参数联合估计,并利用每次迭代参数估计结果,对信号检测门限进行更新,通过置零操作实现预设虚警概率下的多信号盲检测;最后,通过仿真实验对所提方法性能进行了分析,并与相关方法进行了对比。仿真结果表明,所提方法能够有效利用多路接收信号信息,实现宽带未知多目标信号的盲检测,有效提升短数据下的算法处理效能,与现有方法相比,在接收单元数目较多以及信噪比较低时具有明显优势。     

False alarm analysis of the envelope detection GO-CFAR processor

The greatest of constant false alarm rate processor (GO CFAR) is a useful architecture for adaptively setting a radar detection threshold in the presence of clutter edges. The GO CFAR input is often the envelope detected in-phase (I) and quadrature (Q) channels of the baseband signal (x_e=√(I²+Q²)). This envelope detection can also be approximated using x=a max{|I|,|Q|}+b min{|I|,|Q|} which requires less complex hardware (a and b are simple multiplying coefficients). The envelope GO CFAR processor and several envelope approximation GO CFAR processors are compared in terms of the probability of false alarm (PFA) performance. Closed-form expressions which describe the PFA performance are given and their accuracy evaluated. It is shown that for all cases, the PFA is proportional to the number of reference cells n for small threshold multiplier T and inversely proportional to n for large T. A region of intersection occurs where the PFA is the same for two different values of n. For example, at T'=1.68 in the |I|+|Q| GO CFAR (a=1, b=1) the PFA for n=1 is equal to the optimal n=∞ fixed-threshold PFA (PFA=0.112)     

Simple Expressions for Determining Radar Detection Thresholds

The threshold value required to obtain a specified false-alarm probability, when postdetection integration follows a square-law or an envelope detector, is frequently needed in theoretical and practical studies of radar signal processor performance. The determination of such threshold values requires a substantial numerical computational effort. In this correspondence, simple expressions are presented with which these thresholds can be determined with excellent accuracy using only a scientific calculator.     

一种变信噪比条件下的恒虚警野值检测方法

野值检测又称异常值检测,是模式识别、机器智能和知识发现等领域经常面临的一个问题。当出现环境失配,数据信噪比（SNR）发生变化时,测试样本和训练样本所含噪声会有不同方差,以往的野值检测方法在虚警控制方面将会失效。针对这一问题,提出一种基于归一化残差（NR）的野值检测方法。该方法首先根据所需虚警概率和噪声方差变化情况确定野值检测门限,其次基于训练样本计算待考查模式的NR值,再比较NR值与检测门限的相对大小,从而判断待考查模式是否为野值。这一方法所依赖的检测门限对所需虚警率和噪声方差变化具有适应能力,因此可以在变信噪比条件下实现恒虚警（CFAR）野值检测。仿真实验验证了所提方法在虚警控制和野值检测方面的优越性能。     

Noncoherent Detection of Sinusoidal Signals in Sinusoidal Clutter

Probability density expressions associated with the noncoherent detection of a sinusoidal signal have been obtained. The signal is assumed to be imbedded in sinusoidal clutter at the same frequency and narrow-band Gaussian noise. The density expressions are shown to be a function of the signal-to-noise power ratio and the clutter-to-noise power ratio. The expressions have been numerically evaluated for a number of conditions, and the results under each reception hypothesis are presented graphically. Under large-sample conditions, the probability density for a multisample test statistic is shown to be Gaussian, and the probability of detection expression is written such that commonly available tabulated data can be utilized to determine the probabilities.     

PCM Frame Synchronization with a Self-Varying Threshold

An improved method for frame synchronization of PCM telemetered data is described and performance analyses are presented. This method is based on the utilization of a threshold detector whose level is selfvarying according to the characteristics of the received data. It is simple to implement and simpler from an operational point of view than the frame synchronizers currently in use in that a threshold control is altogether eliminated. Analyses show, furthermore, that a synchronizer using a self-varying threshold always has a higher probability of detecting the synchronization code no matter what the frame length, sync code length, or error level.     

Adaptive Radar Detection with Asymptotically Regulated False-Alarm Rate

An adaptive detection procedure is described by which the detection threshold is so adjusted as to provide an asymptotic false-alarm probability PFA that is approximately invariant with changes in radar clutter return amplitude probability density functions (pdf's) in a broad class. The class includes Rayleigh, chi, Weibull, and lognormal pdf's. The receiver noise is also taken into account. The clutter-plus-noise pdf is approximated by a truncated generalized Laguerre series, the coefficients of which are estimated from the radar returns using "cell averaging" techniques. This estimation is assumed to be perfect. The results obtained indicate that the "bias" error, defined as the normalized difference between the design PFA and the asymptotic PFA corresponding to the computed threshold, lies within a fraction of an order of magnitude for 10-3?PFA ? 10-6. For PFA ?10-6 the bias error is more than an order of magnitude. These results are for the case when a single independent radar return is processed at a time. The bias error decreases as the number of postdetection integrations of independent returns increases.     

Threshold Control for Automatic Detection in Radar Systems

In automatic detection in radar systems an estimate of background clutter power is used to set the detection threshold. Usually detection cells surrounding the cell under test for the presence of a target are used to estimate the clutter power. In the research reported herein, the target location is taken to be uncertain and thus returns from a target could corrupt this clutter power estimate. It is shown how the threshold should be varied to compensate for the resulting degradation in detection performance. The threshold control procedure is based on a priori information about target location that could be supplied by the radar's tracking system. In addition, a simple procedure for calculating detection and false alarm probabilities for Swerling II target models is presented.     

Sequential track extraction

Sensors like radar or sonar usually produce data on the basis of a single frame of observation: target detections. The detection performance is described by quantities like detection probability Pd and false alarm density f. A different task of detection is formation of tracks of targets unknown in number from data of multiple consecutive frames of observation. This leads to quantities which are of a higher level of abstraction: extracted tracks. This again is a detection process. Under benign conditions (high Pd, low f and well separated targets) conventional methods of track initiation are recommended to solve a simple task. However, under hard conditions the process of track extraction is known to be difficult. We here concentrate on the case of well separated targets and derive an optimal combinatorial method which can be used under hard operating conditions. The method relates to MHT (multiple hypothesis tracking), uses a sequential likelihood ratio test and derives benefit from processing signal strength information. The performance of the track extraction method is described by parameters such as detection probability and false detection rate on track level, while Pd and f are input parameters which relate to the signal-to-noise interference ratio (SNIR), the clutter density, and the threshold set for target detection. In particular the average test lengths are analyzed parametrically as they are relevant for a user to estimate the time delay for track formation under hard conditions     

Optimum detection and location estimation of target lines in the range-time space of a search radar

The average likelihood ratio detector is derived as the optimum detector for detecting a target line with unknown normal parameters in the range-time data space of a search radar, which is corrupted by Gaussian noise. The receiver operation characteristics of this optimum detector is derived to evaluate its performance improvement in comparison with the Hough detector, which uses the return signal of several successive scans to achieve a non-coherent integration improvement and get a better performance than the conventional detector. This comparison, which is done through analytic derivations and also through simulation results, shows that the average likelihood ratio detector has a better performance for different SNR values. This result is justified by showing the disadvantages of the Hough method, which are eliminated by the optimum detector. To have an estimate for the location of the detected target line in the optimum detection method as the Hough method, which detects and localizes the target lines simultaneously, we present the maximum a posteriori probability estimator. The estimation performance of the two methods is then compared and it is shown that the maximum a posteriori probability estimator localizes the detected target lines with a better performance in comparison with the Hough method.     

Optimal polarimetric detection of radar target in a slowlyfluctuating environment of clutter

It is shown that in a situation where a radar target is distant enough from the radar and is included in a natural or artificial clutter environment in such a manner that the conventional detection methods fail, it is possible to improve the radar detection performance by using appropriate signal processing on two orthogonal polarization states. A CFAR (constant false alarm rate) polarimetric detection system based on the study of the polarization difference between clutter and target is proposed. Since the polarization state of the clutter echoes fluctuates slowly from cell to cell, an autoregressive model can be applied to the components of the polarization vector to predict the detection thresholds needed to follow the polarization state variation. The detection thresholds are determined to maintain a false alarm probability equal to 10^-6. The presence of a target registers as a significant variation of the estimation error of the polarization vector. Results obtained from measurements of simple and canonical targets with artificial clutter are presented, and these results validate the principle of polarimetric detection     

M-correlated sweeps performance analysis of mean-level CFARprocessors in multiple target environments

This paper is devoted to the detection performance evaluation of the mean-level (ML) constant false-alarm rate (CFAR) detectors processing M-correlated sweeps in the presence of interfering targets. The consecutive pulses are assumed to be fluctuating according to the Swerling I model. Exact expressions are derived for the detection probability of the conventional mean-level detector (MLD) and its modified versions under Rayleigh fluctuating target model. Performance for independent sweeps can be easily obtained by setting the sweep-to-sweep correlation coefficient equal to zero. Results are obtained for both homogeneous and nonhomogeneous background environments. It is shown that for fixed M, the relative improvement over the single sweep case increases as the correlation between sweeps decreases. For the same parameter values, the minimum MLD has the best performance in the presence of extraneous target returns among the reference noise samples