The CFAR adaptive subspace detector is a scale-invariant GLRT

The constant false alarm rate (CFAR) matched subspace detector (CFAR MSD) is the uniformly most-powerful-invariant test and the generalized likelihood ratio test (GLRT) for detecting a target signal in noise whose covariance structure is known but whose level is unknown. Previously, the CFAR adaptive subspace detector (CFAR ASD), or adaptive coherence estimator (ACE), was proposed for detecting a target signal in noise whose covariance structure and level are both unknown and whose covariance structure is estimated with a sample covariance matrix based on training data. We show here that the CFAR ASD is GLRT when the test measurement is not constrained to have the same noise level as the training data, As a consequence, this GLRT is invariant to a more general scaling condition on the test and training data than the well-known GLRT of Kelly (1986)     

Polarimetric adaptive detection of range-distributed targets

We address the problem of polarimetric adaptive detection of range-spread targets in Gaussian noise with unknown covariance matrix. At the design stage, we model the target echo from each polarimetric channel as a deterministic signal known up to a scaling factor (possibly varying from cell to cell), which accounts for the polarimetric scattering properties of the target. We first show the failure of the generalized likelihood ratio test (GLRT) procedure to deal with this kind of problem, and thus, we propose a fully adaptive detector based on the method of sieves. We also derive the analytical expression for the probability of false alarm and show that the newly introduced receiver can be made bounded constant false alarm rate (CFAR). Finally, we present simulation results highlighting the performance gain that can be achieved by resorting to polarization diversity in conjunction with high resolution.     

Detection of broadband planewaves in the presence of Gaussian noiseof unknown covariance: asymptotically optimum tests using the 2-Dautoregressive noise model

This paper addresses the problem of detecting a broadband planewave in noise of unknown spatial and temporal covariance at a linear array of sensors. Results of asymptotic detection theory are applied to derive detectors that approach optimal performance for large data records. A parametric approach is used to model the statistics of the data. A 2-D autoregressive (2DAR) model is chosen to model the noise process. Two broadband planewave signal models are considered. Both models represent the signal as a sum of monochromatic planewaves. In the Gaussian model, the amplitudes are assumed to be Gaussian with a single variance parameter, whereas in the deterministic assumption, they are individual unknown parameters. Detectors based on asymptotic theory are derived for both models. As part of the development of the asymptotically (AS) optimum detector, the Fisher information matrix (FIM) is derived. A proof of the locally asymptotic normal (LAN) property is provided for the Gaussian model probability density function (PDF). Both detectors, however, are AS equivalent to the generalized likelihood ratio test (GLRT), are AS of constant false alarm rate (CFAR), and perform AS as well as the GLRT constructed with full knowledge of the noise statistics. The performance of both detectors are compared with each other and to a standard spatially normalized beamformer in a computer simulation     

Adaptive Detection and Interference Rejection of Multiple Point-Like Radar Targets

We present an adaptive algorithm aimed at detecting multiple point-like radar targets embedded in correlated Gaussian noise. The proposed detector modifies and improves the adaptive beamformer orthogonal rejection test (ABORT) idea to address detection of multiple targets. More precisely, it relies on the so-called two-step generalized likelihood ratio test (GLRT) design procedure implemented without assignment of a distinct set of secondary data. The newly proposed detector can guarantee the constant false alarm rate (CFAR) property and the performance assessment, conducted resorting to simulated data, has shown that it exhibits better rejection capabilities of mismatched signals than previously proposed detectors, at the price of an acceptable performance loss for matched signals     

One- and Two-Stage Tunable Receivers

In this paper, we propose and assess a CFAR detector that can adjust its “directivity” through a real scalar parameter. It relies on the usual assumption that a set of homogeneous training data is available and encompasses as special cases the well-known Kelly's GLRT and the recently introduced W-ABORT detector. More important, it can be tuned in order to control the level to which sidelobe signals are rejected. Such functionality is particularly important to contain the number of false alarms in presence of mismatched signals. We also consider a parametric detector which resorts to a diagonally loaded sample covariance matrix commonly adopted to take advantage of the presence of strong interferers. The performance assessment of such detector has shown that it can significantly outperform Kelly's GLRT in terms of prediction probabilities for matched signals and in terms of selectivity, but it is not strictly CFAR. We also propose to use the CFAR parametric detector as second stage of a two-stage tunable detector and show that such a two-stage detector can outperform already proposed tunable receivers in terms of selectivity. The analysis of the detectors is conducted assuming a homogeneous Gaussian environment; with reference to this scenario and to the CFAR detectors we derive analytical expressions for the probability of false alarm and the probability of detection for both matched and mismatched signals.      

CFAR detection of multidimensional signals: an invariant approach

The paper deals with constant false alarm rate (CFAR) detection of multidimensional signals embedded in Gaussian noise with unknown covariance. We attack the problem by resorting to the principle of invariance,which proves a valuable statistical tool for ensuring a priori, namely at the design stage, the CFAR property. In this context, we determine a maximal invariant statistic with respect to a proper group of transformations that leave unaltered the hypothesis-testing problem under study, devise the optimum invariant detector, and show that no uniformly most powerful invariant (UMPI) test exists. Thus, we establish the conditions an invariant detector must fulfill in order to ensure the CFAR property. Finally, we discuss several suboptimal (implementable) invariant receivers and, remarkably, show that the generalized likelihood ratio test (GLRT) detector is a member of this class. The performance analysis, which has been carried out in the presence of a Gaussian signal array, shows that the proposed detectors exhibit a quite acceptable loss with respect to the optimum Neyman-Pearson detector.     

GLRT-based adaptive detection algorithms for range-spread targets

We address adaptive detection of a range-spread target or targets embedded in Gaussian noise with unknown covariance matrix. To this end, we assume that cells (referred to in the following as secondary data) that are free of signal components are available. Those secondary data are supposed to possess either the same covariance matrix or the same structure of the covariance matrix of the cells under test. In this context, we design detectors relying on the generalized likelihood ratio test (GLRT) and on a two-step GLRT-based design procedure. Remarkably, both criteria lead to receivers ensuring the constant false alarm rate (CFAR) property with respect to the unknown quantities. A thorough performance assessment of the proposed detection strategies, together with the evaluation of their processing cost, highlights that the two-step design procedure is to be preferred with respect to the plain GLRT. In fact, the former leads to detectors that achieve satisfactory performance under several situations of practical interest and are simpler to implement than those designed resorting to the latter     

复合高斯杂波中距离扩展目标的参数化Wald检测

本文研究复合高斯杂波环境中的距离扩展目标的自适应检测问题。有色杂波采用参数未知的自回归（AR）过程描述。结合Wald检测准则,仅需对H1假设条件下的未知参数进行最大似然估计,给出了一种新的基于参数化模型的扩展目标检测器——参数化Wald检测器。该检测器的检验统计量可解释为首先针对各个待测单元分别计算检验统计量,然后将所有待测单元的输出进行非相参累加,其对杂波的随机功率起伏具有恒虚警率(CFAR)特性。相比于常规的基于协方差矩阵的检测方法,参数化检测算法的执行过程不需要依赖辅助数据,仅利用待测扩展目标数据即可实现自适应处理,有效缓解了训练压力并降低了计算量。仿真实验表明,所提出的参数化Wald检测器的检测性能优于之前提出的参数化广义似然比检测器的性能。      

恒虚警极化自适应子空间检测器

本文研究了在未知统计特性的局部均匀高斯杂波环境中的相干雷达极化自适应目标检测问题.基于广义似然比检验提出极化自适应子空间检测器,并推导出虚警概率和检测概率的理论表达式.研究结果证明该算法在均匀杂波环境和局部均匀杂波环境都有恒虚警的性质.比较了均匀杂波环境下极化自适应子空间检测器、极化广义似然比检验和极化自适应匹配滤波器算法的检测性能,仿真分析了不同极化状态局部均匀杂波环境下极化自适应子空间检测器算法在的检测性能.     

Fast converging adaptive detection of Doppler-shifted,range-distributed targets

A generalized likelihood ratio test (GLRT) for the adaptive detection of a target or targets that are Doppler-shifted and distributed in range is derived. The unknown parameters associated with the hypothesis test are the complex amplitudes in range of the desired target and the unknown covariance matrix of the additive interference, which is assumed to be characterized as complex zero-mean correlated Gaussian random variables. The target's or targets' complex amplitudes are assumed to be distributed across the entire input data block (sensor × range). The unknown covariance matrix is constrained to have the reasonable form of the identity matrix (the internal noise contribution) plus an unknown positive semidefinite (psdh) matrix (the external interference contribution). It is shown via simulation for a variety of interference scenarios that the new detector has the characteristic of having a bounded constant false alarm rate (CFAR), i.e., for our problem, the probability of false alarm P_F for a given detection threshold is bounded by the P_F that results when no external interference is present. It is also shown via simulation that the new detector converges relatively fast with respect to the number of sample vectors K necessary in order to achieve a given probability of detection P_D     

分布式目标的子空间双门限GLRT CFAR检测

 研究了分布式目标在球不变随机变量杂波中的检测问题,提出了一种具有恒虚警特性的双门限广义似然比检测器。分布式目标建模为子空间信号,在距离维和多普勒频率维同时扩展.第一门限的作用是筛选信杂比高的待检测距离单元.将选出的距离单元进行能量积累并与第二门限进行比较做出判决.假设杂波协方差矩阵已知,构造了双门限检测器,并通过推导检测器虚警概率说明其具有恒虚警特性.将基于辅助通道数据的杂波协方差矩阵的估计值替换假设已知的杂波协方差矩阵,得到一个自适应检测器.通过Monte Carlo仿真进行性能分析,说明检测器的有效性和鲁棒性.     

极化空时自适应匹配滤波检测器

针对极化空时自适应处理时目标极化状态和杂波协方差矩阵未知等实际瓶颈问题,提出了一种适应于机载极化阵列雷达的极化空时自适应匹配滤波(PST-AMF)检测算法.该检测算法先利用回波数据估计目标的极化状态,然后再将估值代入似然比得到了新的检验统计量,进一步推导了检测器虚警概率和检测概率的解析表达式,从理论上证明了该检测方法具备恒虚警(CFAR)特性.该检测器计算量比极化空时广义似然比检测器(PST-GLRT)少,易于工程实现.最后,仿真验证了在检测慢速运动目标时,其性能优于单个通道的空时自适应匹配滤波检测器(ST-AMF),具备较强的稳健性.     

A Subspace-Based Adaptive Sidelobe Blanker

We propose a modified version of the adaptive sidelobe blanker (ASB) consisting of a generalized likelihood ratio test (GLRT)-based subspace detector followed by the adaptive coherence estimator. The performance analysis shows that it possesses the constant false alarm rate property with respect to the unknown covariance matrix of the noise in homogeneous environment and that it guarantees a wider range of “directivity” values with respect to the plain ASB. The probability of false alarm and the probability of detection (the latter for matched signals only) have been evaluated in closed form in homogeneous environment and by resorting to Monte Carlo simulation for the other considered cases.      

Invariant Gauss-Gauss detection

The detection of information-bearing Gaussian processes immersed in additive white Gaussian noise (WGN) is an important problem that arises in many signal processing applications. When the level of the WGN is unknown, classical approaches to the problem fail. In this paper a principle of invariance is used to derive a detector with performance that is invariant (or insensitive) to system gain, or equivalently channel attenuation. The detector structure can be realized and detection thresholds set without prior knowledge of the WGN level. When the observation interval is large the detector has the structure of a spectral estimator-correlator, the output of which is compared to an adaptive threshold. The invariance feature of the detector makes it a constant false alarm rate (CFAR) receiver; an ad hoc structure for suboptimal CFAR Gauss-Gauss detection is discussed as well.     

ADAPTIVE NONPARAMETRIC DETECTOR ON CORRELATION GAUSSIAN NOISE

The problem of adaptive nonparametric detector in correlation Gaussian noise isconsidered.The nonparametric detectors are CFAR(Constant-False-Alarm-Rate)detectors,whenthe input received reference cells are IID(Identical Independent Distribution)variances.But the falsealarm probability(P_(fa))of the nonparametric detectors could not be constant if the samples of thereference range cells are not independent.A simple and easily implemented adaptive nonparametricdetection method is proposed in the paper.In orde to maintain CFAR the weight of the detection rangecell of the detector must be changed by different output values of the IIR filter for measurement of thecorrelation coefficient(p)of the input noise.In this paper the closed form expressions for detectionprobability(P_d)and P_(fa)of the weighted nonparametric detector are derived.The ARE(AsymptoticRelative Efficiency)of the weighted detectors is investigated.In the end the detection performance ofthe adaptive nonparametric detector is determined by Monte Carlo simulation on the digital computer.     

复合高斯杂波环境中分布性目标相干雷达恒虚警检测算法研究

本文研究了在未知统计特性的复合高斯杂波环境中对分布性目标检测的问题。利用Toeplitz矩阵的次对称性提出了一种新的杂波协方差矩阵结构的估计方法,并用此估计方法来实现基于广义似然比检验的恒虚警检测算法。该算法能够在不需要杂波功率谱密度对称的情况下作到对杂波的结构分量和协方差矩阵都有恒虚警的性质,而且该实现方法的检测性能优于先前提出的实现方法。     

相关高斯噪声自适应非参量检测器

本文讨论了相关高斯噪声自适应非参量检测器。当输入噪声的采样满足独立、同分布(IID)条件时,不管分布是什么形式,非参量检测器均能保持虚警概率恒定(CFAR)。但是,许多类噪声并不能保持IID条件,检测器也就无法保持CFAR。本文提出一种简单、可行的自适应非参量检测器,能自动调节门限,使虚警概率(Pfa)趋于恒定。这种方法的关键在于用递归滤波器的输出值来测量噪声的相关系数(Pd),并由此改变秩值检测器的检测单元的权,使其Pfa趋于恒定。从而使在一定信噪比条件下发现概率(Pd)也趋于恒定。本文给出检测单元加权的非参量检测器的检测性能和渐近性能,然后还给出自适应非参量检测器的近似计算方法和计算机模拟结果。     

Adaptive subspace detection of extended target in white Gaussian noise using sinc basis

For the high resolution radar (HRR), the problem of detecting the extended target is considered in this paper. Based on a single observation, a new two-step detection based on sparse representation (TSDSR) method is proposed to detect the extended target in the presence of Gaussian noise with unknown covariance. In the new method, the Sinc dictionary is introduced to sparsely represent the high resolution range profile (HRRP). Meanwhile, adaptive subspace pursuit (ASP) is presented to recover the HRRP embedded in the Gaussian noise and estimate the noise covariance matrix. Based on the Sinc dictionary and the estimated noise covariance matrix, one step subspace detector (OSSD) for the first-order Gaussian (FOG) model without secondary data is adopted to realise the extended target detection. Finally, the proposed TSDSR method is applied to raw HRR data. Experimental results demonstrate that HRRPs of different targets can be sparsely represented very well with the Sinc dictionary. Moreover, the new method can estimate the noise power with tiny errors and have a good detection performance.     

Subspace-based adaptive generalized likelihood ratio detection

Subspace-based adaptive detection performance is examined for the generalized likelihood ratio detector based on Wilks' Λ statistic. The problem considered here is detecting the presence of one or more signals of known shape embedded in Gaussian distributed noise with unknown covariance structure. The data is mapped into a subspace prior to detection. The probability of false alarm is independent of the subspace transformation and depends only on subspace dimension. The probability of detection depends on the subspace transformation through a nonadaptive signal-to-noise ratio (SNR) parameter. Subspace processing results in an SNR loss that tends to decrease performance and a gain in statistical stability that tends to increase performance. It is shown that the statistical stability effect dominates the SNR loss for short data records, and subspace detectors can require substantially less SNR than full space detectors for equivalent performance. A method for designing the subspace transformation to minimize the SNR loss is proposed and illustrated through simulations     

集中式O FDM-MIMO雷达自适应检测算法

针对频率分集条件下，集中式OFDM-MIMO雷达在未知杂波环境中的目标检测问题，首先分析了OFDM-MIMO雷达回波数据模型，由于OFDM-MIMO雷达的频率分集特性，不同频率通道回波数据相互独立，在此基础上，分别基于一步和两步广义最大似然比准则，给出了集中式OFDM-MIMO雷达GLRT和OFDM-MIMO雷达AMF两种检测器，并分析了这两种检测器的恒虚警特性。两种检测器有效利用集中式OFDM-MIMO雷达频率分集特性，提升目标检测性能，同时降低了矩阵求逆维数，以及参考单元数目的要求，并且具有恒虚警性能。计算机仿真验证了算法的有效性。