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     

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     

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。     

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     

Statistical analysis of real clutter at different range resolutions

A statistical analysis is presented of real radar clutter data collected using the McMaster I FIX radar in 1998 and stored in the Grimsby database. We first show the deviations of the amplitude statistics from the Rayleigh model and the suitability of the K- and Weibull-distribution for the first-order amplitude statistical characterization. Thus we focus on the I and Q components of the available data and study their statistical compatibility with the compound Gaussian model. Towards this goal it has been necessary devising appropriate testing procedures; in particular, with reference to the higher order statistics agreement, we have designed a validation procedure involving the clutter representation into generalized spherical coordinates. Remarkably the results have confirmed the suitability of the spherically invariant random processes (SIRPs) for the correct modeling of the radar clutter. Finally we have performed a spectral analysis highlighting the close matching between the estimated clutter spectral density and the exponential model.     

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     

Fitting a statistical model to SIR-C SAR images of the sea surface

A suite of statistical procedures aimed at assessing to what extent polarimetric and/or multifrequency synthetic aperture radar (SAR) images of the sea surface can be modeled in terms of spherically invariant random vectors and matrices (SIRVs and SIRMs) is presented. The proposed tests assume that images can be described by resorting to the compound-Gaussian model, but do not require any a priori knowledge about the actual first-order probability density function (pdf) of the texture. The tests have also been used to analyze three data sets from STR-C/X-SAR missions.     

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.     

Coherent detection of radar targets in a non-gaussian background

The problem of detecting radar targets against a background of coherent, correlated, non-Gaussian clutter is studied with a two-step procedure. In the first step, the structure of the amplitude and the multivariate probability density functions (pdfs) describing the statistical properties of the clutter is derived. The starting point for this derivation is the basic scattering problem, and the statistics are obtained from an extension of the central limit theorem (CLT). This extension leads to modeling the clutter amplitude statistics by a mixture of Rayleigh distributions. The end product of the first step is a multidimensional pdf in the form of a Gaussian mixture, which is then used in step 2. The aim of step 2 is to derive both the optimal and a suboptimal detection structure for detecting radar targets in this type of clutter. Some performance results for the new detection processor are also given     

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     

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     

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.     

Coverage area analysis for decentralized detection in Weibullclutter

The performance of a decentralized constant false-alarm rate (CFAR) detection system with data fusion in homogeneous non-Gaussian background is analyzed in terms of ground area covered. The advantages of using a distributed radar system and the differences between the system behavior in Rayleigh clutter and in Weibull clutter are stressed. Notably, the increasing benefit of cooperative decision making when clutter becomes spikier is pointed out     

Polish radar technology

Polish radar research and development since 1953 is reviewed, covering the development and production of surveillance radars, height finders, tracking radars, air traffic control (ATC) radars and systems, and marine and Doppler radars. Some current work, including an L-band ATC radar for enroute control, a weather channel for primary surveillance radar, signal detection in non-Gaussian clutter, adaptive MTI filters and postdetection filtering, and a basic approach to radar polarimetry, is examined.<>     

Adaptive polarimetric target detection with coherent radar. II.Detection against non-Gaussian background

For pt. I see ibid., vol. 37, no. 4, pp. 1194-1206 (2001).This paper presents the derivation of a polarimetric coherent adaptive scheme to detect a radar target against a non-Gaussian background. This completes the results presented in Part I for the Gaussian background. A Texture Free-Generalized Likelihood Ratio Test (TF-GLRT) detector is derived that exploits the polarimetric characteristics of the received radar echoes to improve the detection performance. The proposed polarimetric detector is shown to have Constant False Alarm Rate (CFAR) when operating against compound-Gaussian clutter with unknown parameters. Its performance is fully characterized by both theoretical analysis and simulation. Moreover, the application to recorded radar data demonstrates the performance improvement achievable in practice     

基于3DT的空时自适应单脉冲参数估计算法

空时自适应处理(STAP)是机载预警雷达抑制杂波和干扰的一项关键技术,而多普勒三通道联合自适应处理(3DT)是适合工程实现的降维(RD)STAP方法。STAP目标检测后还需进一步估计目标的角度参数,因此将自适应单脉冲(AM)技术引入3DT,提出了一种高精度联合估计目标速度与方位空间角的空时自适应单脉冲算法。理论分析与仿真实验结果表明,当目标多普勒频率偏离检测多普勒单元中心频率时,该算法能同时减少目标多普勒跨越损失和空时导引矢量失配损失,进而提高输出信杂噪比(SCNR),改善目标测角精度。     

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.     

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     

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