先验失配条件下的知识辅助检测器稳健性分析

充分利用探测环境的先验信息是提高雷达探测能力的有效途径之一。先验信息必须在雷达检测算法设计阶段确定下来,因此先验信息与当前探测环境之间可能存在不一致性。以复合高斯杂波中的、利用纹理分量先验信息的知识辅助(KA)检测器作为研究对象,首先建立了该检测器检测性能与先验分布参数失配之间的量化关系,然后根据给定的杂波探测环境模型参数,分析了先验模型失配对检测性能的影响。分析结果表明:知识辅助检测器的稳健性与当前探测环境模型参数有关。进一步给出了先验模型失配的容许区间,当先验模型参数在这个区间内,知识辅助检测器性能优于不使用先验信息的检测器性能。     

Detection of Target Maneuver Onset

A classical maneuvering target tracking (MTT) problem (detection of the onset of a target maneuver) is presented in two parts. The first part reviews most traditional maneuver onset detectors and presents results from a comprehensive simulation study and comparison of their performance. Six algorithms for maneuver onset detection are examined: measurement residual chi-square, input estimate chi-square, input estimate significance test, generalized likelihood ratio (GLR), cumulative sum, and marginalized likelihood ratio (MLR) detectors. The second part proposes two novel maneuver onset detectors based on sequential statistical tests. Cumulative sums (CUSUM) type and Shiryayev sequential probability ratio (SSPRT) maneuver onset detectors are developed by using a likelihood marginalization technique to cope with the difficulty that the target maneuver accelerations are unknown. The proposed technique gives explicit solutions for Gaussian-mixture prior distributions, and can be applied to arbitrary prior distributions through Gaussian-mixture approximations. The approach essentially utilizes a~priori information about the maneuver accelerations in typical tracking engagements and thus allows to improve detection performance as compared with traditional maneuver detectors. Simulation results demonstrating the improved capabilities of the proposed onset maneuver detectors are presented.     

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     

Adaptive polarimetric target detection with coherent radar. I.Detection against Gaussian background

The derivation of a completely adaptive polarimetric coherent scheme to detect a radar target against a Gaussian background is presented. A previously proposed Generalized Likelihood Ratio Test (GLRT) polarimetric detector is extended to the case of a general number of channels; this exploits the polarimetric characteristics of the received radar echoes to improve the detection performance. Together with the fully adaptive scheme, a model-based detector is derived that has a lower estimation loss. A complete theoretical expression is derived for the detection performance of both proposed polarimetric detectors. They are shown to have Constant False Alarm Rate (CFAR) when operating against Gaussian clutter, but to be sensitive to deviations from the Gaussian statistic. The application to recorded radar data demonstrates the performance improvement achievable in practice     

Optimum and mismatched detection against K-distributed plusGaussian clutter

We derive the optimum radar receiver to detect fluctuating and non-fluctuating targets against a disturbance which is modeled as a mixture of coherent K-distributed and Gaussian-distributed clutter. In addition, thermal noise, which is always present in the radar receiver, is considered. We discuss the implementation of the optimum coherent detector, which derives from the likelihood ratio test under the assumption of perfectly known disturbance statistics, and evaluate its performance via a numerical procedure, when possible, and via Monte Carlo simulation otherwise. Moreover, we compare the performance of the optimum detector with those of two detectors which are optimum for totally Gaussian and totally K-distributed clutter respectively, when they are fed with such a mixed disturbance. We conclude that, though the optimum detector has a larger computational cost, it provides sensibly better detection performance than the mismatched detectors in a number of operational situations. Thus, there is a need to derive suboptimum target detectors against the mixture of disturbances which trade-off the detection performance and the implementation complexity     

Correlation between horizontal and vertical monopulse measurements

Many radar systems use the monopulse ratio to extract angle of arrival (AOA) measurements in both azimuth and elevation angles. The accuracies of each such measurement are reasonably well known: each measurement is, conditioned on the sum-signal return, Gaussian-distributed with calculable bias (relative to the true AOA), and variance. However, we note that the two monopulse ratios are functions of basic radar measurements that are not entirely independent, specifically in that the sum signal is common to both. The effect of this is that the monopulse ratios are dependent, and a simple explicit expression is given for their correlation; this is of considerable interest when the measurements are supplied to a tracking algorithm that requires a measurement covariance matrix. The system performance improvement when this is taken into account is quantified: while it makes little difference for a tracking radar with small pointing errors, there are more substantial gains when a target is allowed to stray within the beam, as with a rotating (track-while-scan) radar or when a single radar dwell interrogates two or more targets at different ranges. But in any case, the correct covariance expression is so simple that there is little reason not to use it. We additionally derive the Cramer-Rao lower bound (CRLB) on joint azimuth/elevation angle estimation and discover that it differs only slightly from the covariance matrix corresponding to the individual monopulse ratios. Hence, using the individual monopulse ratios and their simple joint accuracy expression is an adequate and quick approximation of the optimal maximum likelihood procedure for single resolved targets.     

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     

Angle estimation for two unresolved targets with monopulse radar

Most present-day radar systems use monopulse techniques to extract angular measurements of sunbeam accuracy. The familiar "monopulse ratio" is a very effective means to derive the angle of a single target within a radar beam. For the simultaneous estimation of the angles of two closely-spaced targets, a modification on the monopulse ratio was derived in (Blair and Pearce, 2001), while (Sinha et al., 2002) presented a maximum likelihood (ML) technique via numerical search. In this paper it is shown that the ML solution can in fact be found explicitly, and the numerical search of ((Sinha et al., 2002) is unnecessary. However, the ML solution requires the signal to noise ratio (SNR) for each target to be known, and hence we generalize it so it requires only the relative SNR. Several versions of expectation maximization (EM) joint angle estimators are also derived, these differing in the degree to which prior information on SNR and on beam pattern are assumed. The performances of the different direction-of-arrival (DOA) estimators for unresolved targets are studied via Monte Carlo, and it is found that most have similar performance: this is remarkable since the use of prior information (SNR, relative SNR, beam pattern) varies widely between them. There is, however, considerable performance variability as a function of the two targets' off-boresight angles. A simple combined technique that fuses the results from different approaches is thus proposed, and it performs well uniformly.     

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     

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     

Calculating the performance of linear and square-law detectors

A method is presented for calculating the performance of linear and square-law detectors in detection schemes that employ noncoherent integration. The method consists of transforming the coherent characteristic function, which is usually easy to obtain to a noncoherent moment generating function describing the test statistic of a linear or square-law detector. The method provides a single mathematical framework for many signal models (both classical and new) and can be implemented using standard numerical routines. Although the method is not always optimum in terms of computing speed for specific classical models, its common approach for all signal models makes it very efficient in term of learning and implementation times. Classical results as well as results for an extended set of target models consisting of an arbitrary number of constant amplitude random phase returns are presented to demonstrate the technique. It is shown for the signal parameters considered that the performance difference between the linear and square-law detectors is relatively insignificant     

The Effect of Jamming on Monopulse Accuracy

An expression is applied for the probability density function (pdf) of the monopulse ratio when skin echoes from a passive target are contaminated by interference from a jammer. The analysis is valid for arbitrary signal-to-jam ratio and arbitrary locations of the target and jammer in the beam. For an on-axis skin target and a stand-off jammer at an off-axis location, the "pulling" effect of the jammer and the accuracy of the angle estimate are compared with the approximations currently employed in radar performance analysis. The pdf of the monopulse ratio for large and for small signal-to-jam ratios is presented, showing that the pdf is bimodal at small signal-to-jam ratio.     

Structures for radar detection in compound Gaussian clutter

The problem of coherent radar target detection in a background of non-Gaussian clutter modeled by a compound Gaussian distribution is studied here. We show how the likelihood ratio may be recast into an estimator-correlator form that shows that an essential feature of the optimal detector is to compute an optimum estimate of the reciprocal of the unknown random local power level. We then proceed to show that the optimal detector may be recast into yet another form, namely a matched filter compared with a data-dependent threshold. With these reformulations of the optimal detector, the problem of obtaining suboptimal detectors may be systematically studied by either approximating the likelihood ratio directly, utilizing a suboptimal estimate in the estimator-correlator structure or utilizing a suboptimal function to model the data-dependent threshold in the matched filter interpretation. Each of these approaches is studied to obtain suboptimal detectors. The results indicate that for processing small numbers of pulses, a suboptimal detector that utilizes information about the nature of the non-Gaussian clutter can be implemented to obtain quasi-optimal performance. As the number of pulses to be processed increases, a suboptimal detector that does not require information about the specific nature of the non-Gaussian clutter may be implemented to obtain quasi-optimal performance     

Performance of a Two-Sample Mann-Whitney Nonparametric Detector in a Radar Application

The detection of signals in an unknown, typically non-Gaussian noise environment, while attempting to maintain a constant false-alarm rate, is a common problem in radar and sonar. The raw receiver data is commonly processed initially by a bank of frequency filters. The further processing of the outputs from the filter bank by a two-sample Mann-Whitney detector is considered. When the noise statistics in all filters are identical, the Mann-Whitney detector is distribution free, i. e., the false-alarm probability may be prescribed in advance regardless of the precise form of the noise statistics. The primary purpose of this paper is to demonstrate the potential advantage of nonparametric detectors over conventional detectors. The signal detection performance of the Mann-Whitney detector is compared to that of an ordinary linear envelope detector plus integrator in the presence of Gaussian and several hypothetical forms of non-Gaussian noise. This comparison is made for both uniform and nonuniform distributions of noise power across the filter bank. Besides providing a much more constant false-alarm rate than the conventional detector, the Mann-Whitney detector's signal detection performance is found also to be much less sensitive to the form of the noise statistics. In one case, its detection sensitivity is found to be 11 dB better than that of the conventional detector. Even when the noise power density is made moderately nonuniform across the filter bank, the detection performance of the Mann-Whitney detector is found not to be significantly affected.     

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     

Maximum-Likelihood Detection of Unresolved Radar Targets and Multipath

Interference in the form of multipath or uncooperative targets can seriously degrade the angle-of-arrival estimation accuracy of mutiplebeam processors. In this paper, the generalized likelihood ratio test is used to derive a test to detect the presence of interference for multiple beam processors. The detector performance is then analyzed in detail with respect to its dependence on signal-to-noise ratio (SNR), signal-to-interference ration (SIR), and on the relative phase between the target and interfering signals. It is shown that good detection performance can be obtained unless the phase difference between the target and interference signals is either in or out of phase.     

Vector subspace detection in compound-Gaussian clutter. Part I: survey and new results

Deals with the problem of detecting subspace random signals against correlated non-Gaussian clutter exploiting different degrees of knowledge on target and clutter statistical characteristics. The clutter process is modeled by the compound-Gaussian distribution. In the first part of the paper, the optimum Neyman-Pearson (NP) detector, the generalized likelihood ratio test (GLRT), and a constant false-alarm rate (CFAR) detector are sequentially derived both for the Gaussian and the compound-Gaussian scenarios. Different interpretations of the various detectors are provided to highlight the relationships and the differences among them. In particular, we show how the GLRT detector may be recast into an estimator-correlator form and into another form, namely a generalized whitening-matched filter (GWMF), which is the GLRT detector against Gaussian disturbance, compared with a data-dependent threshold. In the second part of this paper, the proposed detectors are tested against both simulated data and measured high resolution sea clutter data to investigate the dependence of their performance on the various clutter and signal parameters.     

Performance Analysis of the Censored Mean-Level Detector

The censored mean-level detector (CMLD) is an alternative to the mean-level detector that achieves robust detection performance in a multiple-target environment by censoring several of the largest samples of the maximum likelihood estimate of the background noise level. Here we derive exact expressions for the probability of detection of the CMLD in a multiple-target environment when a fixed number of Swerling II targets are present. The primary target is modeled by Swerling case II, and only single-pulse processing is analyzed. Optimization of the CMLD parameters is considered, and a comparison to other detectors is presented.     

单脉冲成像算法性能分析

单脉冲技术通过比较单个脉冲多路回波信号的信息实现对目标角度位置的精确测量,广泛运用于跟踪雷达中。在雷达成像中引入单脉冲技术可以显著提高前视这一合成孔径雷达(SAR)与多普勒波束锐化(DBS)成像盲区雷达图像的清晰度。本文着重对单脉冲成像算法的成像效果分析方法进行研究。从单脉冲和差比的概率密度函数出发,提出了目标图像位置失真、分辨率以及图像信噪比3个对图像质量进行衡量的指标。分析了决定这3个指标的系统及外部环境参数,并给出了相应的计算方法。最终通过数值积分以及Monte-Carlo仿真实验对理论分析结果进行了验证。     

Spatially distributed target detection in non-Gaussian clutter

Two detection schemes for the detection of a spatially distributed, Doppler-shifted target in non-Gaussian clutter are developed. The non-Gaussian clutter is modeled as a spherically invariant random vector (SIRV) distribution. For the first detector, called the non-scatterer density dependent generalized likelihood ratio test (NSDD-GLRT), the detector takes the form of a sum of logarithms of identical functions of data from each individual range cell. It is shown under the clutter only hypothesis, that the detection statistic has the chi-square distribution so that the detector threshold is easily calculated for a given probability of false alarm P_F. The detection probability P_D is shown to be only a function of the signal-to-clutter power ratio (S/C)_opt of the matched filter, the number of pulses N, the number of target range resolution cells J, the spikiness of the clutter determined by a parameter of an assumed underlying mixing distribution, and P_F. For representative examples, it is shown that as N, J, or the clutter spikiness increases, detection performance improves. A second detector is developed which incorporates a priori knowledge of the spatial scatterer density. This detector is called the scatterer density dependent GLRT (SDD-GLRT) and is shown for a representative case to improve significantly the detection performance of a sparsely distributed target relative to the performance of the NSDD-GLRT and to be robust for a moderate mismatch of the expected number of scatterers. For both the NSDD-GLRT and SDD-GLRT, the detectors have the constant false-alarm rate (CFAR) property that P_F is independent of the underlying mixing distribution of the clutter, the clutter covariance matrix, and the steering vector of the desired signal