Non-Gaussian random vector identification using sphericallyinvariant random processes

With the modeling of non-Gaussian radar clutter in mind, elegant and tractable techniques are presented for characterizing the probability density function (PDF) of a correlated non-Gaussian radar vector. The need for a library of multivariable correlated non-Gaussian PDFs in order to characterize various clutter scenarios is discussed. Specifically,. the theory of spherically invariant random processes (SIRPs) is examined in detail. Approaches based on the marginal envelope PDF and the marginal characteristic function have been used to obtain several multivariate non-Gaussian PDFs. An important result providing the PDF of the quadratic form of a spherically invariant random vector (SIRV) is presented. This result enables the problem of distributed identification of a SIRV to be addressed     

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     

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     

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...     

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     

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.     

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.     

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     

Performance analysis of radar antenna systems

If modern airborne radar systems are to function properly, the radar antenna radiation patterns must meet certain specifications. Until recently, most radar antennas were designed and tested in a clean antenna environment, i.e., there is no near field scattering from host structures or radome effects. However, these higher order effects are the matter of increasing concern with added performance demands in the ever-increasing jammer and clutter interference environments. We investigated the capabilities and limitations of currently available analysis techniques and computer codes for installed performance of airborne radar antenna systems. Then we developed an extended ray-optical technique that could predict total installed performance of airborne radar antenna systems, i.e., the near field scattering from aircraft structures and radome effects. The new analysis technique utilized a ray-tracing method in both airframe and radome simulation. Thus, it can efficiently predict the total installed performance of large radar antenna systems on an aircraft structure     

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     

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。     

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     

A Model for Generating Synthetic VHF SAR Forest Clutter Images

We propose a model for generating low-frequency synthetic aperture radar (SAR) clutter that relates model parameters to physical characteristics of the scene. The model includes both distributed scattering and large-amplitude discrete clutter responses. The model also incorporates the SAR imaging process, which introduces correlation among image pixels. The model may be used to generate synthetic clutter for a range of environmental operating conditions for use in target detection performance evaluation of the radar and automatic target detection/recognition algorithms. We derive a statistical representation of the proposed clutter model's pixel amplitudes and compare with measured data from the CARABAS-II SAR. Simulated clutter images capture the structure and amplitude responses seen in the measured data. A statistical analysis shows an order of magnitude improvement in model fit error compared with standard maximum-likelihood (ML) density fitting methods.     

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     

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     

Track-While-Scan Algorithm in a Clutter Environment

A track-while scan (TWS) algorithm is developed for targets in a clutter environment. The problem has been studied using only the position measurements [1, 5-8], but the simulation results have not been satisfactory. Modern processing techniques (FFT processor) ) in air traffic control and surveillance radar receivers provide both position and radial velocity. The radial velocity measurement may be conveniently used in the target-track correlation process, which will reduce the association ambiguity in the clutter environment. t. In the clear environment the algorithm using the position and radial velocity measurements has been treated in [3, 4]. A TWS algorithm, using both position and radial velocity measurements for targets in a clutter environment, is presented here. The algorithm obtained is nonlinear and adaptive. In order to evaluate the improvement due to radial velocity measurement a simulation has been performed on a digital computer. The algorithm was run with and without radial velocity measurements to compare its performances. An improvement was noted especially when the target path included an accelerated portion.     

HRR Detector for Slow-Moving Targets in Sea Clutter

The radar detection of targets in the presence of sea clutter has historically relied upon the radial velocity of targets with respect to the radar platform either by exploiting the relative target Dopplers (for targets with sufficient radial velocity) or by discerning the paths targets traverse from scan to scan. For targets with little to no radial velocity component, though, it can become quite difficult to differentiate targets from the surrounding sea clutter. This paper addresses the detection of slow-moving targets in sea clutter using a high resolution radar (HRR) such that the target has perceptible extent in range. Under the assumption of completely random sea clutter spikes based on an epsiv-contaminated mixture model with the signal and clutter powers known, optimal detection performance results from using the likelihood ratio test (LRT). However, for realistic sea clutter, the clutter spikes tend to be a localized phenomenon. Based upon observations from real radar data measurements, a heuristic approach exploiting a salient aspect of the idealized LRT is developed which is shown to perform well when applied to real measured sea clutter.     

Angle/Doppler estimation in heavy-tailed clutter backgrounds

This work describes new methods on the modeling of the amplitude statistics of airborne radar clutter by means of alpha-stable distributions. We develop joint target angle and Doppler, maximum likelihood-based estimation techniques from radar measurements retrieved in the presence of impulsive uncorrelated noise modeled as an alpha-stable random process. We derive the Cramer-Rao bounds (CRBs) for the additive Cauchy interference scenario to assess the best case estimation accuracy which can be achieved. In addition, we introduce a new joint spatial- and Doppler-frequency high-resolution estimation technique based on the fractional lower order statistics of the measurements of a radar array. Simulation results demonstrate that the proposed methods can be of interest in the study of space-time adaptive processing (STAP) for airborne pulse Doppler radar arrays operating in impulsive interference environments