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.     

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     

Multiframe detector/tracker: optimal performance

We develop the optimal Bayes multiframe detector/tracker for rigid extended targets that move randomly in clutter. The performance of this optimal algorithm provides a bound on the performance of any other suboptimal detector/tracker. We determine by Monte Carlo simulations the optimal performance under a variety of scenarios including spatially correlated Gaussian clutter and non-Gaussian (K and Weibull) clutter. We show that, for similar tracking performance, the optimal Bayes tracker can achieve peak signal-to-noise ratio gains possibly larger than 10 dB over the commonly used combination of a spatial matched filter (spatial correlator) and a linearized Kalman-Bucy tracker. Simulations using real clutter data with a simulated target suggest similar performance gains when the clutter model parameters are unknown and estimated from the measurements     

Importance sampling for characterizing STAP detectors

This paper describes the development of adaptive importance sampling (IS) techniques for estimating false alarm probabilities of detectors that use space-time adaptive processing (STAP) algorithms. Fast simulation using IS methods has been notably successful in the study of conventional constant false alarm rate (CFAR) radar detectors, and in several other applications. The principal objectives here are to examine the viability of using these methods for STAP detectors, develop them into powerful analysis and design algorithms and, in the long term, use them for synthesizing novel detection structures. The adaptive matched filter (AMF) detector has been analyzed successfully using fast simulation. Of two biasing methods considered, one is implemented and shown to yield good results. The important problem of detector threshold determination is also addressed, with matching outcome. As an illustration of the power of these methods, two variants of the square-law AMF detector that are thought to be robust under heterogeneous clutter conditions have also been successfully investigated. These are the envelope-law and geometric-mean STAP detectors. Their CFAR property is established and performance evaluated. It turns out the variants have detection performances better than those of the AMF detector for training data contaminated by interferers. In summary, the work reported here paves the way for development of advanced estimation techniques that can facilitate design of powerful and robust detection algorithms     

Studies of target detection algorithms that use polarimetric radardata

Algorithms are described which make use of polarimetric radar information in the detection and discrimination of targets in a ground clutter background. The optimal polarimetric detector (OPD) is derived. This algorithm processes the complete polarization scattering matrix (PSM) and provides the best possible detection performance from polarimetric radar data. Also derived is the best linear polarimetric detector, the polarimetric matched filter (PMF), and the structure of this detector is related to simple polarimetric target types. New polarimetric target and clutter models are described and used to predict the performance of the OPD and the PME. The performance of these algorithms is compared with that of simpler detectors that use only amplitude information to detect targets. The ability to discriminate between target types by exploring differences in polarimetric properties is discussed     

Vector subspace detection in compound-Gaussian clutter. Part II: performance analysis

For pt. I see ibid., vol. 38, no. 4, p. 1295 (2002). In this second part we deal with the problem of detecting subspace random signals against correlated non-Gaussian clutter modeled by the compound-Gaussian distribution. In the first part of the paper, we derived the optimum Neyman-Pearson (NP) detector, the generalized likelihood ratio test (GLRT), and a constant false-alarm rate (CFAR) detector; we also provided some interesting interpretations of them. In this second part, these 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. Numerical examples concern a space-time adaptive processing (STAP) scenario and a ground-based surveillance radar system scenario.     

Optimal CFAR detection in Weibull clutter

Optimal, in the maximum likelihood sense, constant false-alarm rate (CFAR) detection for Weibull clutter statistics, is investigated. The proposed OW (optimal Weibull) estimator is proved to be an asymptotically efficient estimator of the mean power of the Weibull clutter. Theoretical analysis of the OW-CFAR detector is provided, while detection performance analysis is carried out using the Monte Carlo simulation method. The operation of the median and morphological (MEMO)-CFAR detector in Weibull clutter statistics is also explained. It performs almost optimally in uniform clutter and, simultaneously, it is robust in multitarget situations. The performance of the proposed OW-CFAR detector in uniformal Weibull clutter is used as a yardstick in the analysis of the MEMO cell-averager (CA) and ordered statistic (OS) CFAR detectors. Nonfluctuating and fluctuating (Swerling II) targets are considered in detection analysis. The performance of the detectors is also examined at clutter edges     

Performance analysis of linearly combined order statistic CFARdetectors

Linearly combined order statistic (LCOS) constant false-alarm rate (CFAR) detectors are examined for efficient and robust threshold estimation applied to exponentially distributed background observations for improved detection. Two optimization philosophies have been employed to determine the weighting coefficients of the order statistics. The first method optimizes the coefficients to obtain efficient estimates of clutter referred to the censored maximum likelihood (CML) and best linear unbiased (BLU) CFAR detectors. The second optimization involves maximizing the probability of detection under Swerling II targets and is referred to as the most powerful linear (MPL) CFAR detector. The BLU-CFAR detector assumes no knowledge of the target distribution in contrast to the MPL-CFAR detector which requires partial knowledge of the target distribution. The design of these CFAR detectors and the probability of detection performance are mathematically analyzed for background observations having homogeneous and heterogeneous distributions wherein the trade-offs between robustness and detection performance are illustrated     

Radar Detection of Correlated Targets in Clutter

This paper provides general models of radar echoes from a target. The rationale of the approach is to consider the echoes as the output of a linear dynamic system driven by white Gaussian noise (WGN). Two models can be conceived to generate N target returns: samples generated as a batch, or sequentially generated one by one. The models allow the accommodation of any correlation between pulses and nonstationary behavior of the target. The problem of deriving the optimum receiver structure is next considered. The theory of "estimator-correlator" receiver is applied to the case of a Gaussian-distributed time-correlated target embedded in clutter and thermal noise. Two equivalent detection schemes are obtained (i. e., the batch detector and the recursive detector) which are related to the above mentioned procedures of generating radar echoes. A combined analytic-numeric method has been conceived to obtain a set of original detection curves related to operational cases of interest. Finally, an adaptive implementation of the proposed processor is suggested, especially with reference to the problem of on-line estimation of the clutter covariance matrix and of the CFAR threshold. In both cases detection loss due to adaptation has been evaluated by means of a Monte Carlo simulation approach. In summary, the original contributions of the paper lie in the mathematical formulation of a powerful model for radar echoes and in the derivation of a large set of detection curves.     

无需辅助数据的分布式目标自适应检测器

在非高斯背景和没有辅助数据的条件下,研究了高分辨率雷达分布式目标的自适应检测问题.首先采用有序检测理论和协方差矩阵的迭代估计方法粗略估计散射点集合,进一步利用迭代估计方法获得协方差矩阵的近似最大似然估计,提出了无需辅助数据的自适应检测器(ADWSD).ADWSD在非高斯背景下具有近似恒虚警率特性,且检测性能远好于修正的...     

A Nonadaptive Processing of Radar Pulse Trains for Clutter Rejection

The problem of detecting coherent pulse trains with uniform amplitude in a clutter-plus-noise environment is considered. A radar processor for detecting targets moving radially with respect to the clutter is proposed. The minimum interpulse spacing of the transmitted signal is assumed long enough that returns are not received simultaneously from different ranges within a region of extended clutter, and the central frequency of the clutter power spectrum is postulated to be known. The processor is singled out as the linear filter, orthogonal to the clutter central frequency component, which yields the maximum ratio of peak signal power to average noise power. The filter can be implemented by slightly modifying the structure of the conventional matched filter. The performance of such a filter is compared with that achievable if full a priori knowledge of the input interference were available and with that of the conventional matched filter. This comparison is made on a signal-to-interference power ratio basis after assuming a transmitted signal consisting of equally spaced pulses and an interference characterized by an exponential covariance matrix.     

Optimal speckle reduction in polarimetric SAR imagery

Speckle is a major cause of degradation in synthetic aperture radar (SAR) imagery. With the availability of fully polarimetric SAR data, it is possible to use the three complex elements (HH, HV, VV) of the polarimetric scattering matrix to reduce speckle. The optimal method for combining the elements of the scattering matrix to minimize image speckle is derived, and the solution is shown to be a polarimetric whitening filter (PWF). A simulation of spatially correlated, K-distributed, fully polarimetric clutter is then used to compare the PWF with other, suboptimal speckle-reduction methods. Target detection performance of the PWF, span, and single-channel |HH|² detectors is compared with that of the optimal polarimetric detector (OPD). A novel, constant-false-alarm-rate (CFAR) detector (the adaptive PWF) is as a simple alternative to the OPD for detecting targets in clutter. This algorithm estimates the polarization covariance of the clutter, uses the covariance to construct the minimum-speckle image, and then tests for the presence of a target. An exact theoretical analysis of the adaptive PWF is presented; the algorithm is shown to have detection performance comparable with that of the OPD     

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.     

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.     

The effect of the clutter-to-noise ratio on Doppler filterperformance

The effect of the clutter-to-noise ratio on the performance of a Doppler filter is considered. Clutter is assumed to have a power level which is unknown and varies in range. The assessment of the performance of a Doppler filter is based on the gain of the filter, which is the normalized output signal-to-interference ratio improvement at a given Doppler. The gain is generally a complex function of the statistics of the clutter. New upper and lower bounds on the gain differential between the expected design point clutter-to-noise ratio and the actual clutter-to-noise ratio are found. These bounds are independent of the clutter covariance matrix and are only a function of the unknown clutter-to-noise ratio. The bounds are valid for both Gaussian and non-Gaussian noise and for arbitrary linear filters. The upper and lower bounds differ by the theoretical coherent integration gain, 10 logN dB, where N is the number of pulses. A tighter lower bound is found for the case when the filters are matched filters. A simple exact expression is found for matched filters assuming a Gaussian Markov clutter model as the clutter spectral width approaches zero. An easily implementable adaptive procedure is given which improves performance due to the unknown clutter-to-noise ratio. This work extends a previous result, valid for the Emerson filter, that shows the effect of clutter-to-noise ratio on performance in terms of an average quantity, the improvement factor     

A mean level adaptive detector using nonconcurrent data

Convergence results for a mean level adaptive detector (MLAD) are presented. The MLAD consists of an adaptive matched filter (for spatially correlated inputs) followed by a mean level detector (MLD). The optimal weights of the adaptive matched filter are estimated from one batch of data and applied to a statistically independent batch of nonconcurrent data. The threshold of the MLD is determined from the resultant data. Thereafter a candidate cell is compared against this threshold. Probabilities of false alarm and detection are derived as a function of the threshold factor, the order of the matched filter, the number of independent samples per channel used to calculate the adaptive matched filter weights, the number of samples used to set the MLD threshold, and the output signal-to-noise power ratio of the optimal matched filter. A number of performance curves are shown and discussed     

非高斯杂波背景中距离扩展目标的盲积累检测器

在采用球不变随机向量(SIRV)建模的非高斯杂波背景下,研究了导向矢量失配或未知时距离扩展目标的检测问题。先假设导向矢量已知,采用广义似然比检验(GLRT)得到每个距离单元的归一化匹配滤波器(NMF)统计量,再将多个距离单元的统计量进行非相干积累得到扩展目标的NMF积累检测器(NMFI),然后通过最大化检测统计量的方法,结合特征值分解技术,对导向矢量进行估计,提出了距离扩展目标的盲NMFI(B-NMFI)。仿真分析表明:当导向矢量失配时,NMFI的检测性能优于GLRT;当导向矢量未知时,B-NMFI能有效地检测目标,并且对不同方位的目标具有很好的鲁棒性。     

Detection by incoherent recombination with partial information

Matched filter (MF) detection in spread environments is often seriously degraded by the mismatch between the waveform replica and the composite signal formed by the spreading environment. Typically the spreading is caused by multiple delayed reflections due to scatter extent or multipath especially in shallow water sonar applications. It is possible to recover some detector performance by incoherent summation of weighted MF realizations in a process called incoherent recombining (IR). Several IR strategies for Gaussian data that assume varying amounts of prior scattering function (SF) information are examined, their receiver operating characteristics (ROCs) computed, and compared with those of the unrealizable “prescient” receiver (PR). They include optimally weighted and unweighted versions of the maximum likelihood estimator-correlator (EC), and variations of the “at-least-one” (ALO) detector that examines sequences of MF realizations declaring a detection if at least one threshold is crossed. As might be expected, performance improves with the accuracy of the prior information incorporated in the detector formulation     

Matched subspace CFAR detection of hovering helicopters

A constant false alarm rate (CFAR) strategy for detecting a Gaussian distributed random signal against correlated non-Gaussian clutter is developed. The proposed algorithm is based on Scharf's matched subspace detector (MSD) and has the CFAR property with respect to the clutter amplitude probability density function (apdf), provided that the clutter distribution belongs to the compound-Gaussian family and the clutter covariance matrix is known to within a scale factor. Analytical expressions of false alarm and detection probabilities are derived. An application to the problem of detecting hovering helicopters against vegetated ground clutter is reported     

Locally optimal and suboptimal signal detection in transformationnoise

The efficacy of the optimal detector of a known vanishingly small signal in additive nonwhite transformation noise is compared with that of some eleven structurally simpler suboptimal detectors. Simulation is done under various signal choices, marginal densities, and correlation functions. The block g_lo and the block combination g followed by R_v^-1 in the optimal detector structure are found to be important for good performance in constant and oscillating signals, respectively. Two suboptimal detectors with these block structures, D₈ and D₁₀, are found to perform well consistently in all situations considered. A structurally simple suboptimal detector D₂ is found to be good in the cases with less correlated noise