Adaptive Detection of a Signal Known Only to Lie on a Line in a Known Subspace, When Primary and Secondary Data are Partially Homogeneous

This paper deals with the problem of detecting a signal, known only to lie on a line in a subspace, in the presence of unknown noise, using multiple snapshots in the primary data. To account for uncertainties about a signal's signature, we assume that the steering vector belongs to a known linear subspace. Furthermore, we consider the partially homogeneous case, for which the covariance matrix of the primary and the secondary data have the same structure but possibly different levels. This provides an extension to the framework considered by Bose and Steinhardt. The natural invariances of the detection problem are studied, which leads to the derivation of the maximal invariant. Then, a detector is proposed that proceeds in two steps. First, assuming that the noise covariance matrix is known, the generalized-likelihood ratio test (GLRT) is formulated. Then, the noise covariance matrix is replaced by its sample estimate based on the secondary data to yield the final detector. The latter is compared with a similar detector that assumes the steering vector to be known     

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     

均匀和部分均匀杂波中子空间目标的斜对称自适应检测方法

在雷达目标的自适应检测领域, 当参考单元数不足时, 充分挖掘协方差矩阵的结构信息是有效提高检测性能的途径之一。为此, 针对多维子空间目标的检测问题, 该文在协方差矩阵关于次对角线具有斜对称结构的约束下, 分别基于一步和两步广义似然比(GLRT), 推导了均匀和部分均匀杂波中的斜对称自适应检测器。由于检测器在设计阶段利用了协方差矩阵的结构信息, 仿真结果表明, 与已有检测器相比, 在参考单元数不足时, 斜对称自适应检测器可明显改善检测性能。此外, 分别从协方差估计方法的影响、目标子空间维数的影响、目标子空间失配性能以及目标起伏的影响4个方面对检测性能进行了仿真分析。      

无参考数据的分布目标知识辅助检测

该文利用待检测单元杂波协方差矩阵的先验信息,基于贝叶斯方法,研究无参考数据条件下的分布目标的知识辅助检测问题。首先针对非均匀场景,假定各个距离单元杂波协方差矩阵依概率1不相等,给出了广义似然比检验和最大后验-广义似然比检验两种检测器。然后针对均匀杂波场景,给出了单步和双步广义似然比检验两种检测器。进一步利用计算机仿真分析了先验模型失配条件下的检测器性能。分析结果表明,先验模型参数u较小时,检测器性能与先验模型匹配程度密切相关。当u趋于无穷大时,该文给出的几种检测算法性能趋于相同。     

非高斯杂波下基于子空间的距离扩展目标检测器

在辅助数据缺失的非高斯杂波背景下,采用两步法设计策略研究了距离扩展目标检测方法.首先,在杂波纹理分量已知的条件下,对待检测数据进行高斯化,利用高斯背景下杂波协方差矩阵和目标散射点幅度的合适估计,建立检验统计量.其次,利用待检测数据在信号子空间正交补上的正交投影,估计杂波纹理分量,提出了基于子空间的距离扩展目标自适应检测器,并证明了其对杂波纹理分量的恒虚警率（CFAR,Constant False Alarm Rate）特性.仿真结果表明,在典型非高斯背景下,所提检测器的CFAR特性和检测性能均优于对比检测器;另外,阵元数、目标距离单元数或杂波尖峰的增加,能不同程度改善检测性能.     

一种高分辨率雷达海上目标自适应检测器

针对海上目标因波浪起伏和转向等导致的姿态变化引起的散射点起伏问题,在未知协方差矩阵的复高斯噪声背景下,研究了高距离分辨率雷达的距离扩展目标自适应检测问题.利用与待检测单元具有相同协方差矩阵结构的辅助教据估计未知噪声协方差矩阵,基于两步法检测策略获得了自适应检测器.恒虚警率特性分析表明,该检测器对不同噪声背景均具有很好的自适应特性.检测性能分析表明,该检测器对不同的目标模型具有很好的鲁棒性,且能有效避免“坍塌损失”.另外,通过增加传感器个数,可有效提高检测器性能.     

部分均匀环境下适用于空间对称线阵的修正广义似然比检测方法

针对部分均匀高斯干扰环境下的点目标检测问题,该文基于广义似然比准则(GLRT)提出一种适用于空间对称线阵的修正GLRT检测方法.考虑到采样时存在的目标能量泄漏,在接收信号建模时采用目标能量泄漏采样模型弥补泄漏损失,并基于干扰协方差矩阵的斜对称结构降低对辅助数据的需求,最终联合待检测数据和辅助数据实现未知参数的估计,得到...     

A Bayesian Approach to Adaptive Detection in Nonhomogeneous Environments

We consider the adaptive detection of a signal of interest embedded in colored noise, when the environment is nonhomogeneous, i.e., when the training samples used for adaptation do not share the same covariance matrix as the vector under test. A Bayesian framework is proposed where the covariance matrices of the primary and the secondary data are assumed to be random, with some appropriate joint distribution. The prior distributions of these matrices require a rough knowledge about the environment. This provides a flexible, yet simple, knowledge-aided model where the degree of nonhomogeneity can be tuned through some scalar variables. Within this framework, an approximate generalized likelihood ratio test is formulated. Accordingly, two Bayesian versions of the adaptive matched filter are presented, where the conventional maximum likelihood estimate of the primary data covariance matrix is replaced either by its minimum mean-square error estimate or by its maximum a posteriori estimate. Two detectors require generating samples distributed according to the joint posterior distribution of primary and secondary data covariance matrices. This is achieved through the use of a Gibbs sampling strategy. Numerical simulations illustrate the performances of these detectors, and compare them with those of the conventional adaptive matched filter.     

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.     

Range dependent clutter rejection using range-recursive space-time adaptive processing (STAP) algorithms

We here address the issue of ground clutter rejection for the detection of slowly moving targets in a non-side looking (NSL) array configuration airborne radar. The optimum space-time adaptive processing (STAP) filter needs the knowledge of the inverse of the space-time covariance matrix. In practice, it is unknown and has to be estimated. The most popular approximated method is the sample matrix inversion (SMI) method which consists in inverting the covariance matrix estimated by an average of the sample matrix over the secondary range cells. This estimator is unbiased in case of i.i.d. data. In an NSL configuration, the clutter power spectrum is range dependent and the data are consequently not i.i.d. We here present a solution to mitigate this range dependency of the data: the range recursive subspace-based algorithms. They are used in two architectures: a fully and a partially adaptive ones. Then a new range-recursive algorithm using Taylor series expansion is investigated. The performance of these algorithms are compared with that of the conventional STAP algorithms in term of SINR loss.     

Interference mitigation in STAP using the two-dimensional Wold decomposition model

We propose a novel parametric approach for modeling, estimation, and detection in space-time adaptive processing (STAP) radar systems. The proposed parametric interference mitigation procedures can be applied even when information in only a single range gate is available, thus achieving high performance gain when the data in the different range gates cannot be assumed stationary. The model is based on the Wold-like decomposition of two-dimensional (2D) random fields. It is first shown that the same parametric model that results from the 2D Wold-like orthogonal decomposition naturally arises as the physical model in the problem of space-time processing of airborne radar data. We exploit this correspondence to derive computationally efficient fully adaptive and partially adaptive detection algorithms. Having estimated the models of the noise and interference components of the field, the estimated parameters are substituted into the parametric expression of the interference-plus-noise covariance matrix. Hence, an estimate of the fully adaptive weight vector is obtained, and a corresponding test is derived. Moreover, we prove that it is sufficient to estimate only the spectral support parameters of each interference component in order to obtain a projection matrix onto the subspace orthogonal to the interference subspace. The resulting partially adaptive detector is simple to implement, as only a very small number of unknown parameters need to be estimated, rather than the field covariance matrix. The performance of the proposed methods is illustrated using numerical examples.     

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.      

A hybrid STAP approach to target detection for heterogeneous scenarios in radar seekers

Adaptive detection of moving targets on the sea is important for radar seekers. Recently, more attention has been paid to the deleterious effect of clutter heterogeneity on space-time adaptive processing (STAP) for pulse Doppler radar. Since secondary samples are no longer statistically independent and identically distributed (IID) in heterogeneous environments, this is subjected to a great challenge to target detection for radar seekers. Due to the fact that chaff jamming severely affects the performance degradation of target detection, the hybrid detection algorithm is proposed to suppress the sea clutter and chaff jamming. Firstly, the range cells can be classified into two regions according to the power, namely clutter region and hybrid region. Then we propose different algorithms to process two regions. The fixed point (FP) estimator is used to estimate the clutter covariance matrix in clutter region. While the power selected training (PST) algorithm is used to select the homogeneous secondary samples, and an algorithm based on two-step subspace projection for hybrid interference suppression is presented in hybrid region. Finally, the proposed Pareto-based generalized likelihood ratio test (PBGLRT) detector can detect the slowly moving targets in heterogeneous interference. Simulation results show that the PBGLRT detector outperforms both the low rank normalized adaptive match filter (LRNAMF) and normalized adaptive match filter (NAMF) detectors against interference heterogeneity.     

Adaptive detection of distributed targets in partially homogeneous environment with Rao and Wald tests

This paper deals with the problem of detecting distributed targets in the presence of partially homogeneous Gaussian disturbance with unknown covariance matrix. Since no uniformly most powerful test exists for the problem at hand, we devise and assess two detection strategies based on the Rao test, and the Wald test respectively. Remarkably both tests ensure the constant false alarm rate (CFAR) property with respect to both the structure of the covariance matrix as well as the power level. A preliminary performance assessment, conducted by resorting to simulated data, also in comparison to previously proposed detectors, has confirmed the effectiveness of the newly proposed detection algorithms.     

Analysis of the adaptive matched filter algorithm for cases withmismatched clutter statistics

In the majority of adaptive radar detection algorithms, the covariance matrix for the clutter plus noise is estimated using samples taken from range cells surrounding the test cell. In a nonhomogeneous environment, this can lead to a mismatch between the mean of the estimated covariance matrix and the true covariance matrix for the test cell. Closed-form expressions are provided, which give the performance for such cases when the popular adaptive matched filter algorithm is used. The expressions are exact in some cases and provide useful approximations in others. To simplify the analysis, the samples from the surrounding range cells are assumed to be independent and identically distributed (i.i.d.), and these samples are assumed to be independent from the sample taken from the test cell. The performance depends on a small number of important parameters. These parameters describe which types of mismatches are important and which are not. Numerical examples are provided to illustrate how performance varies with each of the important parameters. Monte Carlo simulations are included that closely match the predictions of our equations. An airborne radar example is provided that demonstrates that covariance matrix mismatch can have a significant effect on performance in some practical cases     

Exact performance of STAP algorithms with mismatched steering andclutter statistics

Adaptive algorithms for receivers employing antenna arrays have received significant attention for radar systems applications. In the majority of these algorithms, the covariance matrix for the clutter-plus-noise is characterized by using samples taken from range cells surrounding the test cell. If the underlying covariance matrix of the test cell is different from the average covariance matrix of the surrounding range cells, significant performance degradation may result. Exact expressions for performance are derived for such cases, when any of a set of popular space-time adaptive processing (STAP) algorithms are used. Numerical evaluation of these expressions illustrates how variations in the parameters of these equations affect probability of detection and probability of false alarm. The equations are utilized to determine an upper bound an the performance of this class of STAP algorithms     

空间非平稳噪声下的宽带DOA估计算法

投影子空间正交性测试(TOPS)法是利用子空间的正交性实现宽带信号DOA估计,而在空间非平稳噪声环境下子空间的正交性条件不再满足,尤其是在低信噪比或低快拍条件下子空间估计将出现较大误差,TOPS算法性能将急剧下降。针对该问题,提出了一种空间非平稳噪声下宽带DOA估计算法。该算法首先通过构造特殊对角矩阵将噪声从数据协方差矩阵中剔除,从而克服非平稳噪声对DOA估计的影响;然后利用平方TOPS法实现宽带信号DOA估计,消除了传统TOPS算法中的伪峰。该算法适用于空间非平稳噪声背景及低信噪比环境,提高了对角度相近目标的分辨性能;仿真实验表明了该算法的有效性。     

Knowledge-aided Bayesian radar adaptive detection in heterogeneous environment: GLRT, Rao and Wald tests

Adaptive filtering is an effective method for clutter suppression and radar detection. However, the performances degrade severely if the environment is heterogeneous. To solve this problem, we resort to a Bayesian framework and design knowledge-aided detectors under partially homogeneous model assumption, which outperform their conventional counterparts in heterogeneous environment. It is also proved that the proposed Bayesian generalized likelihood ratio test (GLRT) coincides with the Bayesian Rao and Wald tests, under the assumption that the covariance matrix of the cell under test is proportional to that of the training data.     

脉冲噪声环境下基于矩阵差分的远近场混合源定位

为了提高脉冲噪声环境下基于二阶协方差矩阵差分（COV-MD）的远近场混合源定位算法的估计性能,本文提出了基于分数低阶协方差矩阵差分（FLOC-MD）和基于压缩变换协方差矩阵差分（CTC-MD）的远近场混合源定位算法。所提出的算法首先利用一维MUSIC谱峰搜索获得远场源信号的方位角估计,然后利用矩阵差分法实现远近场信号源的分离得到扩展的近场源分数低阶协方差矩阵（或压缩变换协方差矩阵）,最后在利用类旋转不变方法（ESPRIT-Like）估计得到的近场源方位角的基础上,再次利用一维MUSIC谱峰搜索获得近场源距离的估计。计算机仿真结果表明:CTC-MD算法和FLOC-MD算法在强脉冲和低信噪比情况下的估计性能都要明显优于COV-MD算法和其他基于二阶统计量的远近场混合源定位算法,同时CTC-MD算法的性能要好于FLOC-MD算法并且不依赖于脉冲噪声的先验信息。      

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。