机载雷达空时自适应检测方法研究进展

王永良 刘维建 谢文冲 段克清 高 飞 王泽涛

①(空军预警学院 武汉 430019)

②(国防科学技术大学电子科学与工程学院 长沙 410073)

1 引言

针对机载雷达空时2维滤波问题，Brennan等人[1]于 1973年首次提出了空时自适应处理(Space-Time Adaptive Processing, STAP)理论。在此基础上，各种背景下的STAP技术被不断提出。经过40年的不断发展，STAP技术不断完善，并形成理论体系[2－4]。更重要的是，该技术已经面向工程实用。根据有关报道，STAP技术已在美国生产的E-2D预警机上得到应用。

需要指出的是，STAP技术是机载雷达杂波抑制的有效途径，但是杂波抑制仅是目标检测的一个步骤，而不是机载雷达的最终目标。雷达最重要的作用是目标检测与参数估计，任何信号处理方法都应以此为目的[5]。现有的机载雷达目标检测方法通常是先利用脉冲多普勒技术或STAP技术进行杂波抑制，然后再利用诸如单元平均等恒虚警率(Constant False Alarm Rate, CFAR)处理进行目标检测。文献[6,7]把以空时联合为框架、以机载雷达目标检测为目的的自适应处理技术称为空时自适应检测(Space-Time Adaptive Detection, STAD)。STAD方法根据待检测单元的数据及训练样本形成检测统计量，直接判定有无目标。可以看出，STAP属于滤波的范畴，而STAD属于检测的范畴。

STAD实现了杂波抑制与检测的一体化，结构简单，仅需要设计合理的检测器即可，而不必设计滤波器。从本质上讲，杂波抑制是数据白化的过程，对于STAD技术，这一过程隐含在检测器中，而不需要额外的杂波抑制步骤。与先杂波抑制后检测的方法相比，STAD具有3个主要的优点：

(1) STAD往往具CFAR特性，不需要额外的CFAR技术。这大大地简化了检测的流程和成本。例如，从滤波角度，根据最优输出信杂噪比(SCNR)准则得到的采用协方差矩阵求逆(Sample Matrix Inversion, SMI)[8]算法可看做检测器，但是 SMI不具有 CFAR特性。而根据两步广义似然比(Two-Step Generalized Likelihood Ratio Test, 2S-GLRT)准则得到的自适应匹配滤波器(Adaptive Matched Filter, AMF)[9,10]，从滤波角度看，其滤波性能与SMI相同，但却具有CFAR特性。

(2) STAD技术往往比先杂波抑制后检测方法具有更高的检测概率。例如，在信噪比(Signal-to-Noise Ratio, SNR)不是特别高时，基于GLRT准则得到的KGLRT (Kelly’s GLRT)[11]检测器比从滤波角度得到SMI或AMF检测器的检测概率要高。

(3) STAD设计灵活，可根据不同的准则，基于不同的度量进行设计。常用的检测器设计准则有 3种[12－14]：GLRT准则，Rao准则和Wald准则。对检测器的度量指标包括：检测概率的高低、对失配信号的稳健性和对失配信号的抑制能力，等等。

针对色噪声下多通道信号的自适应检测问题，国内外的学者展开了多方面的研究，并取得了大量成果，这些方法均可应用到STAD中。但很少有文献针对STAD进行单独研究，没有深入地分析机载雷达STAD与常规色噪声下多通道自适应检测方法的区别。此外，值得指出的是，Klemm在其著作[15]中曾指出，STAP下一步的一个研究热点为自适应检测。

本文旨在对STAD这一技术进行简要介绍，阐述STAD技术与现有STAP杂波抑制后检测方法相比具有的优势，并综述可用到STAD中的现有自适应检测方法，探讨下一步的研究方向，起到抛砖引玉的作用。

2 STAD方法研究现状

上文指出，STAD属于检测范畴。进一步讲，STAD属于色噪声背景下的多通道信号自适应检测。因此，现有的色噪声背景下多通道信号检测方法都可以应用到STAD中。自适应的含义指的是杂波加噪声的协方差矩阵未知，这就需要利用训练样本来自适应地估计该协方差矩阵。训练样本必须与待检测单元中杂波加噪声的统计特性具有一定的相关性，否则训练样本不提供任何有价值的信息。

美国林肯实验室的Kelly于1986年基于GLRT准则，提出了著名的KGLRT，这成为色噪声中的多通道信号自适应检测的奠基之作。上文指出，常用的检测器设计准则有3种，即GLRT准则，Rao准则和 Wald准则1)需要注意的是，GLRT, Rao和 Wald并不是某一种特定的检测器，而是通用的检测器设计准则。在不同的环境下GLRT往往是不同的，Rao和Wald也是一样。此外，当我们说“提出了一种GLRT检测器、Rao检测器或 Wald检测器”时，指的是根据 GLRT准则、Rao准则或Wald准则，提出了相应的检测器。这一用法在现有文献中被普遍采用[24－27]。。此外，在实际中，三者对应的两步检测器设计准则也经常被应用。两步检测器设计准则的设计流程为：先假设协方差矩阵已知，然后根据相应的设计准则得到检测器，最后用采样协方差矩阵代替已得到检测器中的未知协方差矩阵[9,16]。

2.1 均匀环境中的目标检测

均匀环境指的是待检测单元中杂波加噪声的统计特性与训练样本中的统计特性完全相同[11]。在KGLRT的基础上，Chen等人[10]与Robey等人[9]利用两步GLRT设计准则在均匀环境下分别独立提出了自适应匹配滤波器(Adaptive Matched Filter,AMF)。De Maio分别在文献[17]和文献[18]中根据Rao检测器和Wald检测器提出了相应的检测器，并且证明了Wald检测器与AMF等价。为叙述方便，记文献[17]中的 Rao检测器为 DMRao(De Maio’s Rao)。

2.2 非均匀环境中的目标检测

由于载机飞行姿态的变化以及阵列结构摆放(共形阵、双基地)的影响，在实际中机载雷达所面临的环境往往是非均匀的。部分均匀环境是非均匀的一种，是指待检测单元的协方差矩阵和训练样本的协方差矩阵具有相同的结构，但具有不同的功率。文献[16]通过实测数据验证了部分均匀环境模型适用于机载雷达所面临的实际环境。基于2S-GLRT设计准则，Scharf于1996年提出了自适应相关估计器(Adaptive Coherence Estimator, ACE)[19]，该检测器被证明是部分均匀环境中的 GLRT[19]，相应的Rao和Wald检测器在文献[20]中提出，并且均等价于ACE。

文献[21,22]提出了一种广义特征关系(Generalized Eigen-Relation, GER)非均匀环境，并指出 GER非均匀模型在实际中往往可以很好地近似满足。该非均匀环境中的GLRT被证明与KGLRT具有相同的形式[23]，相应的Rao检测器即为双归一化自适应匹配滤波器(Double-Normailized AMF,DN-AMF)，而Wald检测器被证明与AMF等价[24]。

其它非均匀模型包括复合高斯模型[25,26]、球不变随机过程(Spherically Invariant Random Process,SIRP)模型[27]、及贝叶斯非均匀[28]、复椭圆等高线分布(Elliptically Contoured Distribution, ECD)非均匀[29,30]等。

2.3 信号失配下的目标检测

上述检测器都是在目标导向矢量确知情况下得到的，在实际中，由于存在阵元校正误差、指向误差和多径效应等影响，往往存在导向矢量失配的情况。文献[31]从滤波的角度研究了导向矢量失配对输出 SCNR的影响，并推广了 RMB(Reed-Mallet-Brennan)准则[8]。通过理论分析，文献[31]指出，当存在导向矢量失配时，只有通过增加训练样本数才能减小SCNR损失。信号失配下的检测最早由Kelly开始研究，在文献[32]中，Kelly指出信号失配对滤波和检测的影响不同，通过合理的设计检测器，可以降低信号失配对自适应检测的影响。这一功能由检测器的CFAR特性实现。

在Kelly的研究[32]基础上不断有新方法被提出，按照对失配信号的敏感程度可把检测器分为两类，一类为稳健检测器，另一类为失配敏感检测器。前者在导向矢量失配量相对较大的情况下，仍然能以较高的检测概率检测出目标。而对于后者，即使导向矢量失配较小，检测器的检测概率也会大为下降，即不把失配信号作为感兴趣的目标。实际中究竟需要稳健检测器还是失配敏感检测器，要视具体情况而定。一般来说，当雷达工作在搜索模式时，需要选择稳健检测器，当雷达工作在跟踪模式时，需要选择失配敏感检测器。

针对导向矢量失配下的检测，通常有4种检测器设计方法：直接建模法[33－37]、增加虚拟信号/干扰法[38－42]、检测器级联法[17,22,43－49]和可调检测器法[49－52]。直接建模法指的是确定失配角的范围，假设目标实际导向矢量位于以阵列指向为轴心的真锥中，通过(凸)优化技术设计检测器。增加虚拟信号/干扰法指的是在 H0假设检验下，假设存在确定(非随机)信号或者虚拟随机干扰。检测器级联法指的是检测器由两个子检测器级联组成，并且这两个子检测器分别为稳健检测器和失配敏感检测器。可调检测器法指的是通过控制可调参数来控制检测器对失配信号的敏感程度。

值得指出的是直接建模法往往得不到闭合解；增加虚拟信号/干扰法得到的检测器对失配信号具有很好的抑制作用，但缺乏稳健性。检测器级联法和可调检测器法的一个共同特点是，针对匹配信号，通过实际合理的选择门限对或者可调参数，二者均可以达到比子检测器(对于检测器级联法)或特例检测器(对于可调检测器法)更高的检测概率。另外，检测器级联法对失配信号的稳健性和失配敏感性受制于子检测器的稳健性和敏感性，而可调检测器往往不受特例检测器对失配信号敏感程度的影响，具有更高的灵活性。

2.4 小训练样本数下的目标检测

机载雷达的自由度为阵元数与脉冲数的乘积。该自由度往往很大，导致杂波加噪声的协方差矩阵维数很高。根据RMB准则[8]，要获得满意的协方差矩阵估计，至少需要两倍于系统自由度维数的训练样本，然而这在实际中很难满足。因此，有必要研究小训练样本数下的自适应检测。

文献[53]分析了级联 STAD的性能，并与常规STAD进行了比较。文献[54]把联合域局域处理(Joint Domain Localised, JDL)与KGLRT结合，形成了JDL-GLRT检测器。文献[55]把对角加载[56]技术与 KGLRT结合，提出了对角加载 GLRT(Diagonally Loaded GLRT, DL-GLRT)。文献[6,7]把对角加载技术与AMF和ACE结合，提出了对角加载AMF(Diagonally Loaded AMF, DL-AMF)和对角加载 ACE(Diagonally Loaded ACE, DLACE)。文献[57]把主分量法[58]应用 KGLRT, AMF和 ACE中，形成了降秩 GLRT(Reduced-Rank GLRT, RR-GLRT)，降秩 AMF(Reduced-Rank AMF, RR-AMF)和降秩ACE(Reduced-Rank ACE,RR-ACE)。文献[59, 60]根据正交投影变换的思想，提出相应的降秩检测器，文献[61]把这一思想与ACE结合，提出了新的降秩检测器。

共轭梯度(Conjugate Gradient, CG)[62]、多级维纳滤波器(Multistage Wiener Filter, MWF)[63]和自适应辅助向量滤波器(Auxiliary-Vector Filtering,AVF)[64]属于Krylov子空间技术(数值计算中的一类方法)。近年来，Krylov子空间技术被成功应用到自适应检测中。文献[65]把CG法应用到最优检测器(即匹配滤波器，或称为匹配检测器，该检测器在协方差矩阵已知的前提下得到)中。文献[66]把MWF与AVF应用到自适应检测中，提出了相应的检测器。

上述新的检测方法比常规的KGLRT, AMF和ACE等方法具有更高的检测概率，尤其是在训练样本数小的情况下，这一优势更为明显。

3 结论与展望

通过上文的分析可以看出，STAP以杂波抑制为目标，而STAD以检测目标的有无为目标。杂波抑制体现在STAD的中间过程中，而非作为一个独立的步骤。下面列出自适应检测的几个亟待解决的问题或新的研究方向：

(1) 严重非均匀及非高斯环境下的检测[67－69]；

(2) 结构化协方差矩阵下的检测[70－74]；

(3) 扩展目标的检测[14,16,75－79]；

(4) 机载MIMO或多基地检测[80－84]；

(5) 压缩感知检测[85]；

(6) 认知雷达检测[86]；

(7) 基于先验知识的检测[82,87－94]。

[1]Brennan L E and Reed L S.Theory of adaptive radar[J].IEEE Transactions on Aerospace and Electronic Systems,1973, 9(2): 237-252.

[2]王永良, 彭应宁.空时自适应信号处理[M].北京: 清华大学出版社, 2000.Wang Yong-liang and Peng Ying-ning.Space-Time Adaptive Processing[M].Beijing: Tsinghua University Press, 2000.

[3]Klemm R.Principles of Space-Time Adaptive Processing[M].3rd Edition, London: The Institution of Electrical Engineers,2006.

[4]Guerci J R.Space-Time Adaptive Processing for Radar[M].Boston: Artech House, 2003.

[5]Nickel U.Design of generalised 2D adaptive sidelobe blanking detectors using the detection margin[J].Signal Processing,2010, 90(5): 1357-1372.

[6]Liu W, Xie W, and Wang Y.Diagonally loaded space-time adaptive detection[C].IEEE International Conference on Radar, Chengdu, 2011.

[7]刘维建, 谢文冲, 王永良.基于对角加载的自适应匹配滤波器和自适应相干估计器[J].系统工程与电子技术, 2013, 35(3):463-468.Liu Wei-jian, Xie Wen-chong, and Wang Yong-liang.AMF and ACE detectors based on diagonal loading[J].Systems Engineering and Electronics, 2013, 35(3): 463-468.

[8]Reed I S, Mallett J D, and Brennan L E.Rapid convergence rate in adaptive arrays[J].IEE E Transactions on Aerospace and Electronic Systems, 1974, 10(6): 853-863.

[9]Robey F C, Fuhrmann D R, Kelly E J, et al..A CFAR adaptive matched filter detector[J].IEEE Transactions on Aerospace and Electronic Systems, 1992, 28(1): 208-216.

[10]Chen W-S and Reed I S.A new CFAR detection test for radar[J].Digital Signal Processing, 1991, 1(4): 198-214.

[11]Kelly E J.An adaptive detection algorithm[J].IEEE Transactions on Aerospace and Electronic Systems, 1986,22(1): 115-127.

[12]Kay S M.Fundamentals of Statistical Signal Processing:Detection Theory[M].Englewood Cliffs, NJ: Prentice-Hall,1998.

[13]De Maio A, Kay S M, and Farina A.On the invariance,coincidence, and statistical equivalence of the GLRT, Rao test, and wald test[J].IEEE Transactions on Signal Processing, 2010, 58(4): 1967-1979.

[14]Liu W, Wang Y, and Xie W.Fisher information matrix, Rao test, and Wald test for complex-valued signals and their applications[J].Signal Processing, 2014,DOI:10.1016/j.sigpro.2013.06.032.

[15]Klemm R.Applications of Space-Time Adaptive Processing[M].London: The Institution of Electrical Engineers, 2004: 415.

[16]Conte E, Maio A D, and Ricci G.GLRT-based adaptive detection algorithms for range-spread targets[J].IEEE Transactions on Signal Processing, 2001, 49(7): 1336-1348.

[17]De Maio A.Rao test for adaptive detection in Gaussian interference with unknown covariance matrix[J].IEEE Transactions on Signal Processing, 2007, 55(7): 3577-3584.

[18]De Maio A.A new derivation of the adaptive matched filter[J].IEEE Signal Processing Letters, 2004, 11(10):792-793.

[19]Kraut S and Scharf L L.The CFAR adaptive subspace detector is a scale-invariant GLRT[J].IEEE Transactions on Signal Processing, 1999, 47(9): 2538-2541.

[20]De Maio A and Iommelli S.Coincidence of the Rao test, Wald test, and GLRT in partially homogeneous environment[J].IEEE Signal Processing Letters, 2008, 15: 385-388.

[21]Richmond C D.Statistics of adaptive nulling and use of the generalized eigenrelation (GER) for modeling inhomogeneities in adaptive processing[J]. IEEE Transactions on Signal Processing, 2000, 48(5): 1263-1273.

[22]Richmond C D.Performance of a class of adaptive detection algorithms in nonhomogeneous environments[J].IEEE Transactions on Signal Processing, 2000, 48(5): 1248-1262.

[23]Besson O and Orlando D.Adaptive detection in nonhomogeneous environments using the generalized eigenrelation[J].IEEE Signal Processing Letters, 2007, 14(10):731-734.

[24]Hao C, Orlando D, and Hou C.Rao and Wald tests for nonhomogeneous scenarios[J].Sensors, 2012, 12(4): 4730-4736.

[25]Conte E, Lops M, and Ricci G.Asymptotically optimum radar detection in compound-Gaussian clutter[J].IEEE Transactions on Aerospace and Electronic Systems, 1995,31(2): 617-625.

[26]Gini F and Farina A.Vector subspace detection in compound-Gaussian clutter part I: Survey and new results[J].IEEE Transactions on Aerospace and Electronic Systems,2002, 38(4): 1295-1311.

[27]Conte E, Lops M, and Ricci G.Adaptive matched filter detection in spherically invariant noise[J].IEEE Signal Processing Letters, 1996, 3(8): 248-250.

[28]Bidon S, Besson O, and Tourneret J-Y.A Bayesian approach to adaptive detection in nonhomogeneous environments[J].IEEE Transactions on Signal Processing, 2008, 56(1):205-217.

[29]Richmond C D.A note on non-Gaussian adaptive array detection and signal parameter estimation[J].IE EE Signal Processing Letters, 1996, 3(8): 251-252.

[30]Besson O and Abramovich Y I.Invariance properties of the likelihood ratio for covariance matrix estimation in some complex elliptically contoured distributions[J].Journal of Multivariate Analysis, 2014, 124: 237-246.

[31]Boroson D M.Sample size considerations for adaptive arrays[J].IEEE Transactions on Aerospace and Electronic Systems, 1980, 16(4): 446-451.

[32]Kelly E J.Performance of an adaptive detection algorithm:rejection of unwanted signals[J].IEEE Transactions on Aerospace and Electronic Systems, 1989, 25(2): 122-133.

[33]De Maio A.Robust adaptive radar detection in the presence of steering vector mismatches[J].IEEE Transactions on Aerospace and Electronic Systems, 2005, 41(4): 1322-1337.

[34]Bandiera F, De Maio A, and Ricci G.Adaptive CFAR radar detection with conic rejection[J].IEEE Transactions on Signal Processing, 2007, 55(6): 2533-2541.

[35]De Maio A, De Nicola S, and Farina A.GLRT versus mflrt for adaptive CFAR radar detection with conic uncertainty[J].IEEE Signal Processing Letters, 2009, 16(8): 707-710.

[36]Bandiera F, Orlando D, and Ricci G.CFAR detection strategies for distributed targets under conic constraints[J].IEEE Transactions on Signal Processing, 2009, 57(9):3305-3316.

[37]Maio A D, Nicola S D, Farina A, et al..Adaptive detection of a signal with angle uncertainty[J].IET Radar, Sonar &Navigation, 2010, 4(4): 537-547.

[38]Pulsone N B and Rader C M.Adaptive beamformer orthogonal rejection test[J].IEEE Transactions on Signal Processing, 2001, 49(3): 521-529.

[39]Bandiera F, Besson O, and Ricci G.An abort-like detector with improved mismatched signals rejection capabilities[J].IEEE Transactions on Signal Processin g, 2008, 56(1): 14-25.

[40]Besson O.Detection in the presence of surprise or undernulled interference[J].IEEE Signal Processing Letters,2007, 14(5): 352-354.

[41]Orlando D and Ricci G.A Rao test with enhanced selectivity properties in homogeneous scenarios[J].IEE E Transactions on Signal Processing, 2010, 58(10): 5385-5390.

[42]Liu W, Xie W, and Wang Y.A Wald test with enhanced selectivity properties in homogeneous environments[J].E URASIP Journal on Ad vances in Signal Processing, 2013,DOI:10.1186/1687-6180-2013-14.

[43]Richmond C D.Performance of the adaptive sidelobe blanker detection algorithm in homogeneous environments[J].IEEE Transactions on Signal Processing, 2000, 48(5): 1235-1247.

[44]Pulsone N B and Zatman M A.A computationally efficient two-step implementation of the GLRT[J].IEEE Transactions on Signal Processing, 2000, 48(3): 609-616.

[45]Bandiera F, Orlando D, and Ricci G.A subspace-based adaptive sidelobe blanker[J].IEEE Transactions on Signal Processing, 2008, 56(9): 4141-4151.

[46]Raghavan R S, Pulsone N, and McLaughlin D J.Performance of the GLRT for adaptive vector subspace detection[J].IEEE Transactions on Aerospace and Electronic Systems, 1996,32(4): 1473-1487.

[47]Bandiera F, Besson O, Orlando D, et al..An improved adaptive sidelobe blanker[J].IEEE Transactions on Signal Processing, 2008, 56(9): 4152-4161.

[48]Hao C, Liu B, and Cai L.Performance analysis of a two-stage Rao detector[J].Signal Processing, 2011, 91(8): 2141-2146.

[49]Bandiera F, Orlando D, and Ricci G.One- and two-stage tunable receivers[J].IEEE Transactions on Signal Processing,2009, 57(8): 3264-3273.

[50]Kalson S Z.An adaptive array detector with mismatched signal rejection[J].IEEE Transactions on Aerospace and Electronic Systems, 1992, 28(1): 195-207.

[51]Hao C, Liu B, Yan S, et al..Parametric adaptive radar detector with enhanced mismatched signals rejection capabilities[J].EUR ASIP Journal on Advances in Signal Processing, 2010, DOI: 10.1155/2010/375136.

[52]Liu W, Xie W, and Wang Y.Parametric detector in the situation of mismatched signals[J].IET Radar, Sonar &Navigation, 2014, 8(1): 48-53.

[53]Reed I S, Gau Y L, and Truong T K.CFAR detection and estimation for STAP radar[J].IEEE Transactions on Aerospace and Electronic Systems, 1998, 34(3): 722-735.

[54]Wang H and Cai L.On adaptive spatial-temporal processing for airborne surveillance radar systems[J].IEEE Transactions on Aerospace and Electronic Systems, 1994, 30(3): 660-670.

[55]Ayoub T F and Haimovich A M.Modified GLRT signal detection algorithm[J].IEEE Transactions on Aerospace and Electronic Systems, 2000, 36(3): 810-818.

[56]Carlson B D.Covariance matrix estimation errors and diagonal loading in adaptive arrays[J].IEEE Transactions on Aerospace and Electronic Systems, 1988, 24(4): 397-401.

[57]Wang Y, Liu W, Xie W, et al..Reduced-rank space-time adaptive detection for airborne radar[J].S CIENCE CHINA Information Sciences, 2014,DOI:10.1007/s11432-013-4984-5.

[58]Guerci J R, Goldstein J S, and Reed I S.Optimal and adaptive reduced-rank STAP[J].IEEE Transactions on Aerospace and Electronic Systems, 2000, 36(2): 647-663.

[59]Reed I S and Gau Y-L.A fast CFAR detection space-time adaptive processing algorithm[J].IEEE Transactions on Signal Processing, 1999, 47(4): 1151-1154.

[60]Gau Y-L and Reed I S.An improved reduced-rank CFAR space-time adaptive radar detection algorithm[J].IE EE Transactions on Signal Processing, 1998, 46(8): 2139-2146.

[61]Liu W, Xie W, and Wang Y.Adaptive detection based on orthogonal partition of the primary and secondary data[J].Journal of Systems Engineerin g and Electronics, 2014, 25(1):34-42.

[62]Chang P S and Alan N W, Jr.Analysis of conjugate gradient algorithms for adaptive filtering[J].IEEE Transactions on Signal Processing, 2000, 48(2): 409-418.

[63]Goldstein J S, Reed I S, and Scharf L L.A multistage representation of the wiener filter based on orthogonal projections[J].IEEE Transactions on Information Th eory,1998, 44(7): 2943-2959.

[64]Pados D A and Batalama S N.Joint space-time auxiliary-vector filtering for ds/CDMA systems with antenna arrays[J].IEEE Transactions on Communications, 1999,47(9): 1406-1415.

[65]Jiang C, Li H, and Rangaswamy M.On the conjugate gradient matched filter[J].IEEE Transactions on Signal Processing, 2012, 60(5): 2660-2666.

[66]Liu W, Xie W, and Wang Y.Adaptive detectors in the Krylov subspace[J].S CIEN CE CHINA Information Sciences,2014,DOI:10.1360/SCIS-2012-0749.R4.

[67]Michels J H, Himed B, and Rangaswamy M.Robust STAP detection in a dense signal airborne radar environment[J].S ignal Processin g Special Section on New Trends and Find ings in Antenna Array Processing for Radar, 2004, 84(9):1625-1636.

[68]Maio A D.Generalized CFAR property and UMP invariance for adaptive signal detection[J].IEEE Transactions on Signal Processing, 2013, 61(8): 2104-2115.

[69]Guan J, Chen X-L, Huang Y, et al..Adaptive fractional fourier transform-based detection algorithm for moving target in heavy sea clutter[J].IET Radar, Sonar &Navigation, 2012, 6(5): 389-401.

[70]Fuhrmann D R.Application of Toeplitz covariance estimation to adaptive beamforming and detection[J].IE EE Transactions on Signal Processing, 1991, 39(10): 2194-2198.

[71]Kim H S, Alfred O, and Hero I.Comparison of GLR and invariant detectors under structured clutter covariance[J].IEEE Transactions on Image Processing, 2001, 10(10):1509-1520.

[72]Bose S and Steinhardt A O.A maximal invariant framework for adaptive detection with structured and unstructured covariance matrices[J].IE EE Transactions on Signal Processing, 1995, 43(9): 2164-2175.

[73]Wang P, Li H, and Himed B.A new parametric GLRT for multichannel adaptive signal detection[J].IEEE Transactions on Signal Processing, 2010, 58(1): 317-325.

[74]Gao Y, Liao G, Zhu S, et al..Persymmetric adaptive detectors in homogeneous and partially homogeneous environments[J].IEE E Transactions on Signal Processing,2014, 62(2): 331-342.

[75]Liu W, Xie W, and Wang Y.Rao and Wald tests for distributed targets detection with unknown signal steering[J].IEEE Signal Processin g Letters, 2013, 20(11): 1086-1089.

[76]Shuai X, Kong L, and Yang J.Adaptive detection for distributed targets in Gaussian noise with Rao and Wald tests[J].SCIEN CE CHINA Information Sciences, 2012, 55(6):1290-1300.

[77]Hao C, Yang J, Ma X, et al..Adaptive detection of distributed targets with orthogonal rejection[J].IET Radar,Sonar & Navigation, 2012, 6(6): 483-493.

[78]Liu W, Xie W, Liu J, et al..Adaptive double subspace signal detection in Gaussian background—Part I: Homogeneous environments[J].IEE E Transactions on Signal Processing,2014, 62(9): 2345-2357.

[79]Liu W, Xie W, Liu J, et al..Adaptive double subspace signal detection in Gaussian background—Part II: Partially homogeneous environments[J].IEEE Transactions on Signal Processing, 2014, 62(9): 2358-2369.

[80]Wang J, Jiang S, He J, et al..Adaptive detectors with diagonal loading for airborne multi-input multi-output radar[J].IET Radar, Sonar & Navigation, 2009, 3(5): 493-501.

[81]王鞠庭, 江胜利, 何劲, 等.基于对角加载的机载MIMO雷达GLRT检测器[J].电子学报, 2009, 37(12): 2614-2619.Wang Ju-ting, Jiang Sheng-li, He Jin, et al..GLRT detector with diagonal loading for MIMO radars[J].Acta Electronica Sinica, 2009, 37(12): 2614-2619.

[82]Zhang T, Cui G, Kong L, et al..Adaptive Bayesian detection using MIMO radar in spatially heterogeneous clutter[J].IEEE Signal Processin g Letters, 2013, 20(6): 547-550.

[83]Goodman N A and Bruyere D.Optimum and decentralized detection for multistatic airborne radar[J]. IEEE Transactions on Aerospace and Electronic Systems, 2007,43(2): 806-813.

[84]江胜利, 王鞠庭, 何劲, 等.基于对角加载的机载MIMO雷达自适应匹配滤波检测器[J].宇航学报, 2009, 30(5): 1979-1984.

[85]Anitori L, Maleki A, Otten M, et al..Design and analysisof compressed sensing radar detectors[J].IE EE Transactions on Signal Processing, 2013, 61(4): 813-827.

[86]Zhang J, Zhu D, and Zhang G.Adaptive compressed sensing radar oriented toward cognitive detection in dynamic sparse target scene[J].IEEE Transactions on Signal Processing,2012, 60(4): 1718-1729.

[87]De Maio A, Farina A, and Wicks M.KB-GLRT: exploiting knowledge of the clutter ridge in airborne radar[J].IEE Proceedings-Radar, Sonar and Navigation, 2005, 152(6):421-428.

[88]Bandiera F, Besson O, and Ricci G.Knowledge-aided covariance matrix estimation and adaptive detection in compound-Gaussian noise[J].IEEE Transactions on Signal Processing, 2011, 58(10): 5390-5396.

[89]Besson O, Tourneret J-Y, and Bidon S.Knowledge-aided Bayesian detection in heterogeneous environments[J].IEEE Signal Processing Letters, 2007, 14(5): 355-358.

[90]Maio A D, Farina A, and Foglia G.Knowledge-aided Bayesian radar detectors & their application to live data[J].IEEE Transactions on Aerospace and Electronic Systems,2010, 46(1): 170-183.

[91]Zhou Y and Zhang L-R.Knowledge-aided Bayesian radar adaptive detection in heterogeneous environment: GLRT,Rao and Wald test[J].AEU-International Journal of Electronics and Communications, 2012, 66(3): 239-243.

[92]Aubry A, Maio A D, Pallotta L, et al..Radar detection of distributed targets in homogeneous interference whose inverse covariance structure is defined via unitary invariant functions[J].IEEE Transactions on Signal Processing, 2013,61(20): 4949-4961.

[93]Bidon S, Besson O, and Tourneret J-Y.Knowledge-aided STAP in heterogeneous clutter using a hierarchical Bayesian algorithm[J].IEEE Transactions on Aerospace and Electronic Systems, 2011, 47(3): 1863-1879.

[94]Hao C, Shang X, Bandiera F, et al..Bayesian radar detection with orthogonal rejection[J].IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2012, E95-A(2): 596-599.