The Generation of Correlated Weibull Clutter for Signal Detection Problems

A method is discussed for generating Weibull vectors with a desired correlation matrix and specified parameters. Such vectors may represent samples of a correlated clutter signal. The presented method makes use of a suitable nonlinear transformation of random Gaussian vectors with correlated components. Computational aspects of the method are also discussed.     

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     

Analysis of an adaptive CFAR detector in non-Gaussian interference

Coherent signal detection in non-Gaussian interference is presently of interest in adaptive array applications. Conventional array detection algorithms inherently model the interference with a multivariate Gaussian random vector. However, non-Gaussian interference models are also under investigation for applications where the Gaussian assumption may not be appropriate. We analyze the performance of an adaptive array receiver for signal detection in interference modeled with a non-Gaussian distribution referred to as a spherically invariant random vector (SIRV). We first motivate this interference model with results from radar clutter measurements collected in the Mountain Top Program. Then we develop analytical expressions for the probability of false alarm and the probability of detection for the adaptive array receiver. Our analysis shows that the receiver has constant false alarm rate (CFAR) performance with respect to all the interference parameters. Some illustrative examples are included that compare the detection performance of this CFAR receiver with a receiver that has prior knowledge of the interference parameters     

Data quantization effects in CFAR signal detection

In this paper, we investigate data quantization effects in constant false alarm rate (CFAR) signal detection. Exponential distribution for the input data and uniform quantization are assumed for the CFAR detector analysis. Such assumptions are valid in the case of radar for a Swerling I target in Gaussian clutter plus noise and a receiver with analog square-law detection followed by analog-to-digital (A/D) conversion. False alarm and detection probabilities of the cell averaging (CA) and order statistic (OS) CFAR detectors operating on quantized observations are analytically determined. In homogeneous backgrounds with 15 dB clutter power fluctuations, we show analytically that a 12-bit uniform quantizer is sufficient to achieve false alarm rate invariance. Detector performance characteristics in nonhomogeneous backgrounds, due to regions of clutter power transitions and multiple interfering targets, are also presented and detailed comparisons are given     

Probability of Detecting a Fluctuating Target Immersed in Both Noise and Clutter

The probability of detecting either a Swerling 1 or Swerling 2 target immersed in both Rayleigh-distributed noise and log-normally distributed clutter is calculated. Results are presented which demonstrate the effect of noise-to-clutter ratio, signal-to-noise ratio, and number of pulses integrated on the detection statistics.     

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     

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.     

Adaptive detection schemes in compound-Gaussian clutter

Radar detection of coherent pulse trains embedded in compound-Gaussian disturbance with partially known statistics is discussed. We first give a thorough derivation of two recently proposed adaptive detection structures. Next, we derive a different detection scheme exploiting the assumption that the clutter is wide-sense stationary. Resorting to the theory of circulant matrices, in fact, we demonstrate that the estimation of the structure of the clutter covariance matrix can be reduced to the estimation of its eigenvalues, which in turn can be (efficiently) done via fast Fourier transform codes. After a thorough performance assessment, mostly carried on via computer simulations, the results show that the newly proposed detector achieves better performance than the two previously introduced adaptive detectors. Moreover, a sensitivity analysis shows that, even though this detector does not strictly guarantee the constant false alarm rate property with respect to the clutter covariance matrix, it is robust, in the sense that its performance is only slightly affected by variations in the clutter temporal correlation     

CFAR detection of distributed targets in non-Gaussian disturbance

The subject of detection of spatially distributed targets in non-Gaussian noise with unknown statistics is addressed. At the design stage, in order to cope with the a priori uncertainty, we model noise returns as Gaussian vectors with the same structure of the covariance matrix, but possibly different power levels (heterogeneous environment). We also assume that a set of secondary data, free of signal components, is available to estimate the correlation properties of the disturbance The proposed detector assumes no a priori knowledge about the spatial distribution of the target scatterers and ensures the constant false alarm rate (CFAR) property with respect to both the structure of the covariance matrix and the power levels. Finally, the performance assessment, conducted modeling the disturbance as a spherically invariant random process (SIRP), confirms its validity to operate in real radar scenarios     

非高斯杂波下自适应雷达目标检测新方法

在球不变随机向量(SIRV)非高斯杂波背景下,研究了多脉冲相参雷达目标的自适应检测问题。假设杂波具有相同的协方差矩阵结构和可能相关的纹理分量,提出了新的协方差矩阵估计器,并获得了相应的自适应归一化匹配滤波器(ANMF)。理论分析表明,在估计杂波分组大小与实际情况匹配时,所获得的ANMF对杂波功率水平和协方差矩阵结构均具有恒虚警率(CFAR)特性。仿真结果表明:当估计的杂波分组大小失配时,所获得的ANMF具有近似CFAR特性,并进一步分析了不同参数变化对所提检测器性能的影响。与已有的ANMF相比,所获得的ANMF具有更好的检测性能,且迭代次数更小,其相对于已知杂波协方差矩阵的最优归一化匹配滤波器(NMF)的检测损失也更小,具有很好的实际应用前景。     

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。     

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     

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     

Correlated K-distributed clutter generation for radar detection andtrack

The generation of correlated vectors for non-Gaussian clutter is considered for log normal, Weibull, and K-probability distributions. Previous results for log normal and Weibull distributions are summarized. Expressions for the probability distributions and moments of K-distributed clutter of any correlation are derived. Procedures for forming samples of each type of clutter are shown to be equivalent to passing white Gaussian noise through a linear filter followed by a nonlinear operation. Curves of correlation coefficients necessary for the simulation of these vectors are presented for each distribution     

Computer generation of correlated non-Gaussian radar clutter

We develop computer simulation procedures which enable us to generate any correlated non-Gaussian radar clutter that can be modeled as a spherically invariant random process (SIRP). In most cases, when the clutter is a correlated non-Gaussian random process, performance of the optimal radar signal processor cannot be evaluated analytically. Therefore, in order to evaluate such processors, there is a need for efficient computer simulation of the clutter. We present two canonical simulation procedures for the generation of correlated non-Gaussian clutter. A new approach for the goodness-of-fit test is proposed in order to assess the performance of the simulation procedure     

Statistical tests for higher order analysis of radar clutter: their application to L-band measured data

We design three statistical tests to ascertain whether radar data comply with the hypotheses of multivariate Gaussianity, spatial homogeneity, and covariance persymmetry, respectively. For the first issue we develop a statistical procedure based on quadratic distributional distances, which exploits the representation of Gaussian vectors in generalized spherical coordinates. As to the spatial homogeneity we propose a technique, based on the Kolmogorov-Smirnov (KS) test, relying on the properties of quadratic forms constructed from Gaussian vectors and Wishart distributed matrices. Finally, in order to analyze the persymmetry property of the disturbance covariance matrix, we design a testing procedure based on the generalized likelihood ratio test (GLRT). We thus apply the new tests to L-band experimentally measured clutter data, collected by the MIT Lincoln Laboratory Phase One radar, at the Katahdin Hill site. The results show that the multivariate Gaussian hypothesis for the considered data file is reasonable. On the contrary the assumption of spatial homogeneity can be done only within small clutter regions which, in general, exhibit also a persymmetric covariance matrix.     

GLRT subspace detection for range and Doppler distributed targets

A generalized likelihood ratio test (GLRT) is derived for adaptive detection of range and Doppler-distributed targets. The clutter is modeled as a spherically invariant random process (SIRP) and its texture component is range dependent (heterogeneous clutter). We suppose here that the speckle component covariance matrix is known or estimated thanks to a secondary data set. Thus, unknown parameters to be estimated are local texture values, the complex amplitudes and Doppler frequencies of all scattering centers. To do so, we use superresolution methods. The proposed detector assumes a priori knowledge on the spatial distribution of the target and has the precious property of having a constant false alarm rate (CFAR) with the assumption of a known speckle covariance matrix or by the use of frequency agility.     

Detection performance in K-distributed and correlatedRayleigh clutters

Performance prediction for a detection system employing noncoherent integration is carried out for a chi-square family of fluctuating targets in K-distributed clutter plus noise. The detection performance for Swerling 11 targets in the K-distributed clutter plus noise is compared with that in exponentially correlated Rayleigh clutter. The results show that the performance prediction based on N pulses integrated in clutter plus noise using the K-distributed clutter model may be approximately equivalent to that using the exponentially correlated Rayleigh-distributed clutter model     

Detection Performance of Logarithmic Receivers Employing Video Integrators

The detection performance of logarithmic receivers in Rayleigh and non-Gaussian clutter is investigated. In Rayleigh clutter the performance is determined for steady, Swerling case 1, and Swerling case 2 targets. The detection loss of logarithmic receivers is generally less than the ? log n loss conjectured by Green, but consistent with the 1.08-dB asymptotic loss established by Hansen. The Swerling case 2 loss, important in frequency- agility applications, canbe severe for a small number of integrated pulses and high Pd, and apparently approaches the 1.08-dB asymptotic loss as a lower bound. Graphs of GramCharlier series cumulants are provided to allow determination of logarithmic-receiver performance. Curves are presented to allow the detection performance of logarithmic receivers in log-normal and Weibull clutter to be determineds.     

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