王永良 劉維建 謝文沖 段克清 高 飛 王澤濤

①(空軍預(yù)警學(xué)院 武漢 430019)

②(國(guó)防科學(xué)技術(shù)大學(xué)電子科學(xué)與工程學(xué)院 長(zhǎng)沙 410073)

1 引言

針對(duì)機(jī)載雷達(dá)空時(shí)2維濾波問(wèn)題，Brennan等人[1]于 1973年首次提出了空時(shí)自適應(yīng)處理(Space-Time Adaptive Processing, STAP)理論。在此基礎(chǔ)上，各種背景下的STAP技術(shù)被不斷提出。經(jīng)過(guò)40年的不斷發(fā)展，STAP技術(shù)不斷完善，并形成理論體系[2－4]。更重要的是，該技術(shù)已經(jīng)面向工程實(shí)用。根據(jù)有關(guān)報(bào)道，STAP技術(shù)已在美國(guó)生產(chǎn)的E-2D預(yù)警機(jī)上得到應(yīng)用。

需要指出的是，STAP技術(shù)是機(jī)載雷達(dá)雜波抑制的有效途徑，但是雜波抑制僅是目標(biāo)檢測(cè)的一個(gè)步驟，而不是機(jī)載雷達(dá)的最終目標(biāo)。雷達(dá)最重要的作用是目標(biāo)檢測(cè)與參數(shù)估計(jì)，任何信號(hào)處理方法都應(yīng)以此為目的[5]?，F(xiàn)有的機(jī)載雷達(dá)目標(biāo)檢測(cè)方法通常是先利用脈沖多普勒技術(shù)或STAP技術(shù)進(jìn)行雜波抑制，然后再利用諸如單元平均等恒虛警率(Constant False Alarm Rate, CFAR)處理進(jìn)行目標(biāo)檢測(cè)。文獻(xiàn)[6,7]把以空時(shí)聯(lián)合為框架、以機(jī)載雷達(dá)目標(biāo)檢測(cè)為目的的自適應(yīng)處理技術(shù)稱(chēng)為空時(shí)自適應(yīng)檢測(cè)(Space-Time Adaptive Detection, STAD)。STAD方法根據(jù)待檢測(cè)單元的數(shù)據(jù)及訓(xùn)練樣本形成檢測(cè)統(tǒng)計(jì)量，直接判定有無(wú)目標(biāo)。可以看出，STAP屬于濾波的范疇，而STAD屬于檢測(cè)的范疇。

STAD實(shí)現(xiàn)了雜波抑制與檢測(cè)的一體化，結(jié)構(gòu)簡(jiǎn)單，僅需要設(shè)計(jì)合理的檢測(cè)器即可，而不必設(shè)計(jì)濾波器。從本質(zhì)上講，雜波抑制是數(shù)據(jù)白化的過(guò)程，對(duì)于STAD技術(shù)，這一過(guò)程隱含在檢測(cè)器中，而不需要額外的雜波抑制步驟。與先雜波抑制后檢測(cè)的方法相比，STAD具有3個(gè)主要的優(yōu)點(diǎn)：

(1) STAD往往具CFAR特性，不需要額外的CFAR技術(shù)。這大大地簡(jiǎn)化了檢測(cè)的流程和成本。例如，從濾波角度，根據(jù)最優(yōu)輸出信雜噪比(SCNR)準(zhǔn)則得到的采用協(xié)方差矩陣求逆(Sample Matrix Inversion, SMI)[8]算法可看做檢測(cè)器，但是 SMI不具有 CFAR特性。而根據(jù)兩步廣義似然比(Two-Step Generalized Likelihood Ratio Test, 2S-GLRT)準(zhǔn)則得到的自適應(yīng)匹配濾波器(Adaptive Matched Filter, AMF)[9,10]，從濾波角度看，其濾波性能與SMI相同，但卻具有CFAR特性。

(2) STAD技術(shù)往往比先雜波抑制后檢測(cè)方法具有更高的檢測(cè)概率。例如，在信噪比(Signal-to-Noise Ratio, SNR)不是特別高時(shí)，基于GLRT準(zhǔn)則得到的KGLRT (Kelly’s GLRT)[11]檢測(cè)器比從濾波角度得到SMI或AMF檢測(cè)器的檢測(cè)概率要高。

(3) STAD設(shè)計(jì)靈活，可根據(jù)不同的準(zhǔn)則，基于不同的度量進(jìn)行設(shè)計(jì)。常用的檢測(cè)器設(shè)計(jì)準(zhǔn)則有 3種[12－14]：GLRT準(zhǔn)則，Rao準(zhǔn)則和Wald準(zhǔn)則。對(duì)檢測(cè)器的度量指標(biāo)包括：檢測(cè)概率的高低、對(duì)失配信號(hào)的穩(wěn)健性和對(duì)失配信號(hào)的抑制能力，等等。

針對(duì)色噪聲下多通道信號(hào)的自適應(yīng)檢測(cè)問(wèn)題，國(guó)內(nèi)外的學(xué)者展開(kāi)了多方面的研究，并取得了大量成果，這些方法均可應(yīng)用到STAD中。但很少有文獻(xiàn)針對(duì)STAD進(jìn)行單獨(dú)研究，沒(méi)有深入地分析機(jī)載雷達(dá)STAD與常規(guī)色噪聲下多通道自適應(yīng)檢測(cè)方法的區(qū)別。此外，值得指出的是，Klemm在其著作[15]中曾指出，STAP下一步的一個(gè)研究熱點(diǎn)為自適應(yīng)檢測(cè)。

本文旨在對(duì)STAD這一技術(shù)進(jìn)行簡(jiǎn)要介紹，闡述STAD技術(shù)與現(xiàn)有STAP雜波抑制后檢測(cè)方法相比具有的優(yōu)勢(shì)，并綜述可用到STAD中的現(xiàn)有自適應(yīng)檢測(cè)方法，探討下一步的研究方向，起到拋磚引玉的作用。

2 STAD方法研究現(xiàn)狀

上文指出，STAD屬于檢測(cè)范疇。進(jìn)一步講，STAD屬于色噪聲背景下的多通道信號(hào)自適應(yīng)檢測(cè)。因此，現(xiàn)有的色噪聲背景下多通道信號(hào)檢測(cè)方法都可以應(yīng)用到STAD中。自適應(yīng)的含義指的是雜波加噪聲的協(xié)方差矩陣未知，這就需要利用訓(xùn)練樣本來(lái)自適應(yīng)地估計(jì)該協(xié)方差矩陣。訓(xùn)練樣本必須與待檢測(cè)單元中雜波加噪聲的統(tǒng)計(jì)特性具有一定的相關(guān)性，否則訓(xùn)練樣本不提供任何有價(jià)值的信息。

美國(guó)林肯實(shí)驗(yàn)室的Kelly于1986年基于GLRT準(zhǔn)則，提出了著名的KGLRT，這成為色噪聲中的多通道信號(hào)自適應(yīng)檢測(cè)的奠基之作。上文指出，常用的檢測(cè)器設(shè)計(jì)準(zhǔn)則有3種，即GLRT準(zhǔn)則，Rao準(zhǔn)則和 Wald準(zhǔn)則1)需要注意的是，GLRT, Rao和 Wald并不是某一種特定的檢測(cè)器，而是通用的檢測(cè)器設(shè)計(jì)準(zhǔn)則。在不同的環(huán)境下GLRT往往是不同的，Rao和Wald也是一樣。此外，當(dāng)我們說(shuō)“提出了一種GLRT檢測(cè)器、Rao檢測(cè)器或 Wald檢測(cè)器”時(shí)，指的是根據(jù) GLRT準(zhǔn)則、Rao準(zhǔn)則或Wald準(zhǔn)則，提出了相應(yīng)的檢測(cè)器。這一用法在現(xiàn)有文獻(xiàn)中被普遍采用[24－27]。。此外，在實(shí)際中，三者對(duì)應(yīng)的兩步檢測(cè)器設(shè)計(jì)準(zhǔn)則也經(jīng)常被應(yīng)用。兩步檢測(cè)器設(shè)計(jì)準(zhǔn)則的設(shè)計(jì)流程為：先假設(shè)協(xié)方差矩陣已知，然后根據(jù)相應(yīng)的設(shè)計(jì)準(zhǔn)則得到檢測(cè)器，最后用采樣協(xié)方差矩陣代替已得到檢測(cè)器中的未知協(xié)方差矩陣[9,16]。

2.1 均勻環(huán)境中的目標(biāo)檢測(cè)

均勻環(huán)境指的是待檢測(cè)單元中雜波加噪聲的統(tǒng)計(jì)特性與訓(xùn)練樣本中的統(tǒng)計(jì)特性完全相同[11]。在KGLRT的基礎(chǔ)上，Chen等人[10]與Robey等人[9]利用兩步GLRT設(shè)計(jì)準(zhǔn)則在均勻環(huán)境下分別獨(dú)立提出了自適應(yīng)匹配濾波器(Adaptive Matched Filter,AMF)。De Maio分別在文獻(xiàn)[17]和文獻(xiàn)[18]中根據(jù)Rao檢測(cè)器和Wald檢測(cè)器提出了相應(yīng)的檢測(cè)器，并且證明了Wald檢測(cè)器與AMF等價(jià)。為敘述方便，記文獻(xiàn)[17]中的 Rao檢測(cè)器為 DMRao(De Maio’s Rao)。

2.2 非均勻環(huán)境中的目標(biāo)檢測(cè)

由于載機(jī)飛行姿態(tài)的變化以及陣列結(jié)構(gòu)擺放(共形陣、雙基地)的影響，在實(shí)際中機(jī)載雷達(dá)所面臨的環(huán)境往往是非均勻的。部分均勻環(huán)境是非均勻的一種，是指待檢測(cè)單元的協(xié)方差矩陣和訓(xùn)練樣本的協(xié)方差矩陣具有相同的結(jié)構(gòu)，但具有不同的功率。文獻(xiàn)[16]通過(guò)實(shí)測(cè)數(shù)據(jù)驗(yàn)證了部分均勻環(huán)境模型適用于機(jī)載雷達(dá)所面臨的實(shí)際環(huán)境?；?S-GLRT設(shè)計(jì)準(zhǔn)則，Scharf于1996年提出了自適應(yīng)相關(guān)估計(jì)器(Adaptive Coherence Estimator, ACE)[19]，該檢測(cè)器被證明是部分均勻環(huán)境中的 GLRT[19]，相應(yīng)的Rao和Wald檢測(cè)器在文獻(xiàn)[20]中提出，并且均等價(jià)于ACE。

文獻(xiàn)[21,22]提出了一種廣義特征關(guān)系(Generalized Eigen-Relation, GER)非均勻環(huán)境，并指出 GER非均勻模型在實(shí)際中往往可以很好地近似滿足。該非均勻環(huán)境中的GLRT被證明與KGLRT具有相同的形式[23]，相應(yīng)的Rao檢測(cè)器即為雙歸一化自適應(yīng)匹配濾波器(Double-Normailized AMF,DN-AMF)，而Wald檢測(cè)器被證明與AMF等價(jià)[24]。

其它非均勻模型包括復(fù)合高斯模型[25,26]、球不變隨機(jī)過(guò)程(Spherically Invariant Random Process,SIRP)模型[27]、及貝葉斯非均勻[28]、復(fù)橢圓等高線分布(Elliptically Contoured Distribution, ECD)非均勻[29,30]等。

2.3 信號(hào)失配下的目標(biāo)檢測(cè)

上述檢測(cè)器都是在目標(biāo)導(dǎo)向矢量確知情況下得到的，在實(shí)際中，由于存在陣元校正誤差、指向誤差和多徑效應(yīng)等影響，往往存在導(dǎo)向矢量失配的情況。文獻(xiàn)[31]從濾波的角度研究了導(dǎo)向矢量失配對(duì)輸出 SCNR的影響，并推廣了 RMB(Reed-Mallet-Brennan)準(zhǔn)則[8]。通過(guò)理論分析，文獻(xiàn)[31]指出，當(dāng)存在導(dǎo)向矢量失配時(shí)，只有通過(guò)增加訓(xùn)練樣本數(shù)才能減小SCNR損失。信號(hào)失配下的檢測(cè)最早由Kelly開(kāi)始研究，在文獻(xiàn)[32]中，Kelly指出信號(hào)失配對(duì)濾波和檢測(cè)的影響不同，通過(guò)合理的設(shè)計(jì)檢測(cè)器，可以降低信號(hào)失配對(duì)自適應(yīng)檢測(cè)的影響。這一功能由檢測(cè)器的CFAR特性實(shí)現(xiàn)。

在Kelly的研究[32]基礎(chǔ)上不斷有新方法被提出，按照對(duì)失配信號(hào)的敏感程度可把檢測(cè)器分為兩類(lèi)，一類(lèi)為穩(wěn)健檢測(cè)器，另一類(lèi)為失配敏感檢測(cè)器。前者在導(dǎo)向矢量失配量相對(duì)較大的情況下，仍然能以較高的檢測(cè)概率檢測(cè)出目標(biāo)。而對(duì)于后者，即使導(dǎo)向矢量失配較小，檢測(cè)器的檢測(cè)概率也會(huì)大為下降，即不把失配信號(hào)作為感興趣的目標(biāo)。實(shí)際中究竟需要穩(wěn)健檢測(cè)器還是失配敏感檢測(cè)器，要視具體情況而定。一般來(lái)說(shuō)，當(dāng)雷達(dá)工作在搜索模式時(shí)，需要選擇穩(wěn)健檢測(cè)器，當(dāng)雷達(dá)工作在跟蹤模式時(shí)，需要選擇失配敏感檢測(cè)器。

針對(duì)導(dǎo)向矢量失配下的檢測(cè)，通常有4種檢測(cè)器設(shè)計(jì)方法：直接建模法[33－37]、增加虛擬信號(hào)/干擾法[38－42]、檢測(cè)器級(jí)聯(lián)法[17,22,43－49]和可調(diào)檢測(cè)器法[49－52]。直接建模法指的是確定失配角的范圍，假設(shè)目標(biāo)實(shí)際導(dǎo)向矢量位于以陣列指向?yàn)檩S心的真錐中，通過(guò)(凸)優(yōu)化技術(shù)設(shè)計(jì)檢測(cè)器。增加虛擬信號(hào)/干擾法指的是在 H0假設(shè)檢驗(yàn)下，假設(shè)存在確定(非隨機(jī))信號(hào)或者虛擬隨機(jī)干擾。檢測(cè)器級(jí)聯(lián)法指的是檢測(cè)器由兩個(gè)子檢測(cè)器級(jí)聯(lián)組成，并且這兩個(gè)子檢測(cè)器分別為穩(wěn)健檢測(cè)器和失配敏感檢測(cè)器?？烧{(diào)檢測(cè)器法指的是通過(guò)控制可調(diào)參數(shù)來(lái)控制檢測(cè)器對(duì)失配信號(hào)的敏感程度。

值得指出的是直接建模法往往得不到閉合解；增加虛擬信號(hào)/干擾法得到的檢測(cè)器對(duì)失配信號(hào)具有很好的抑制作用，但缺乏穩(wěn)健性。檢測(cè)器級(jí)聯(lián)法和可調(diào)檢測(cè)器法的一個(gè)共同特點(diǎn)是，針對(duì)匹配信號(hào)，通過(guò)實(shí)際合理的選擇門(mén)限對(duì)或者可調(diào)參數(shù)，二者均可以達(dá)到比子檢測(cè)器(對(duì)于檢測(cè)器級(jí)聯(lián)法)或特例檢測(cè)器(對(duì)于可調(diào)檢測(cè)器法)更高的檢測(cè)概率。另外，檢測(cè)器級(jí)聯(lián)法對(duì)失配信號(hào)的穩(wěn)健性和失配敏感性受制于子檢測(cè)器的穩(wěn)健性和敏感性，而可調(diào)檢測(cè)器往往不受特例檢測(cè)器對(duì)失配信號(hào)敏感程度的影響，具有更高的靈活性。

2.4 小訓(xùn)練樣本數(shù)下的目標(biāo)檢測(cè)

機(jī)載雷達(dá)的自由度為陣元數(shù)與脈沖數(shù)的乘積。該自由度往往很大，導(dǎo)致雜波加噪聲的協(xié)方差矩陣維數(shù)很高。根據(jù)RMB準(zhǔn)則[8]，要獲得滿意的協(xié)方差矩陣估計(jì)，至少需要兩倍于系統(tǒng)自由度維數(shù)的訓(xùn)練樣本，然而這在實(shí)際中很難滿足。因此，有必要研究小訓(xùn)練樣本數(shù)下的自適應(yīng)檢測(cè)。

文獻(xiàn)[53]分析了級(jí)聯(lián) STAD的性能，并與常規(guī)STAD進(jìn)行了比較。文獻(xiàn)[54]把聯(lián)合域局域處理(Joint Domain Localised, JDL)與KGLRT結(jié)合，形成了JDL-GLRT檢測(cè)器。文獻(xiàn)[55]把對(duì)角加載[56]技術(shù)與 KGLRT結(jié)合，提出了對(duì)角加載 GLRT(Diagonally Loaded GLRT, DL-GLRT)。文獻(xiàn)[6,7]把對(duì)角加載技術(shù)與AMF和ACE結(jié)合，提出了對(duì)角加載AMF(Diagonally Loaded AMF, DL-AMF)和對(duì)角加載 ACE(Diagonally Loaded ACE, DLACE)。文獻(xiàn)[57]把主分量法[58]應(yīng)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)。文獻(xiàn)[59, 60]根據(jù)正交投影變換的思想，提出相應(yīng)的降秩檢測(cè)器，文獻(xiàn)[61]把這一思想與ACE結(jié)合，提出了新的降秩檢測(cè)器。

共軛梯度(Conjugate Gradient, CG)[62]、多級(jí)維納濾波器(Multistage Wiener Filter, MWF)[63]和自適應(yīng)輔助向量濾波器(Auxiliary-Vector Filtering,AVF)[64]屬于Krylov子空間技術(shù)(數(shù)值計(jì)算中的一類(lèi)方法)。近年來(lái)，Krylov子空間技術(shù)被成功應(yīng)用到自適應(yīng)檢測(cè)中。文獻(xiàn)[65]把CG法應(yīng)用到最優(yōu)檢測(cè)器(即匹配濾波器，或稱(chēng)為匹配檢測(cè)器，該檢測(cè)器在協(xié)方差矩陣已知的前提下得到)中。文獻(xiàn)[66]把MWF與AVF應(yīng)用到自適應(yīng)檢測(cè)中，提出了相應(yīng)的檢測(cè)器。

上述新的檢測(cè)方法比常規(guī)的KGLRT, AMF和ACE等方法具有更高的檢測(cè)概率，尤其是在訓(xùn)練樣本數(shù)小的情況下，這一優(yōu)勢(shì)更為明顯。

3 結(jié)論與展望

通過(guò)上文的分析可以看出，STAP以雜波抑制為目標(biāo)，而STAD以檢測(cè)目標(biāo)的有無(wú)為目標(biāo)。雜波抑制體現(xiàn)在STAD的中間過(guò)程中，而非作為一個(gè)獨(dú)立的步驟。下面列出自適應(yīng)檢測(cè)的幾個(gè)亟待解決的問(wèn)題或新的研究方向：

(1) 嚴(yán)重非均勻及非高斯環(huán)境下的檢測(cè)[67－69]；

(2) 結(jié)構(gòu)化協(xié)方差矩陣下的檢測(cè)[70－74]；

(3) 擴(kuò)展目標(biāo)的檢測(cè)[14,16,75－79]；

(4) 機(jī)載MIMO或多基地檢測(cè)[80－84]；

(5) 壓縮感知檢測(cè)[85]；

(6) 認(rèn)知雷達(dá)檢測(cè)[86]；

(7) 基于先驗(yàn)知識(shí)的檢測(cè)[82,87－94]。

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