機載雷達空時自適應檢測方法研究進展

王永良 劉維建 謝文沖 段克清 高 飛 王澤濤

①(空軍預警學院 武漢 430019)

②(國防科學技術大學電子科學與工程學院 長沙 410073)

1 引言

針對機載雷達空時2維濾波問題，Brennan等人[1]于 1973年首次提出了空時自適應處理(Space-Time Adaptive Processing, STAP)理論。在此基礎上，各種背景下的STAP技術被不斷提出。經過40年的不斷發展，STAP技術不斷完善，并形成理論體系[2－4]。更重要的是，該技術已經面向工程實用。根據有關報道，STAP技術已在美國生產的E-2D預警機上得到應用。

需要指出的是，STAP技術是機載雷達雜波抑制的有效途徑，但是雜波抑制僅是目標檢測的一個步驟，而不是機載雷達的最終目標。雷達最重要的作用是目標檢測與參數估計，任何信號處理方法都應以此為目的[5]。現有的機載雷達目標檢測方法通常是先利用脈沖多普勒技術或STAP技術進行雜波抑制，然后再利用諸如單元平均等恒虛警率(Constant False Alarm Rate, CFAR)處理進行目標檢測。文獻[6,7]把以空時聯合為框架、以機載雷達目標檢測為目的的自適應處理技術稱為空時自適應檢測(Space-Time Adaptive Detection, STAD)。STAD方法根據待檢測單元的數據及訓練樣本形成檢測統計量，直接判定有無目標。可以看出，STAP屬于濾波的范疇，而STAD屬于檢測的范疇。

STAD實現了雜波抑制與檢測的一體化，結構簡單，僅需要設計合理的檢測器即可，而不必設計濾波器。從本質上講，雜波抑制是數據白化的過程，對于STAD技術，這一過程隱含在檢測器中，而不需要額外的雜波抑制步驟。與先雜波抑制后檢測的方法相比，STAD具有3個主要的優點：

(1) STAD往往具CFAR特性，不需要額外的CFAR技術。這大大地簡化了檢測的流程和成本。例如，從濾波角度，根據最優輸出信雜噪比(SCNR)準則得到的采用協方差矩陣求逆(Sample Matrix Inversion, SMI)[8]算法可看做檢測器，但是 SMI不具有 CFAR特性。而根據兩步廣義似然比(Two-Step Generalized Likelihood Ratio Test, 2S-GLRT)準則得到的自適應匹配濾波器(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技術往往比先雜波抑制后檢測方法具有更高的檢測概率。例如，在信噪比(Signal-to-Noise Ratio, SNR)不是特別高時，基于GLRT準則得到的KGLRT (Kelly’s GLRT)[11]檢測器比從濾波角度得到SMI或AMF檢測器的檢測概率要高。

(3) STAD設計靈活，可根據不同的準則，基于不同的度量進行設計。常用的檢測器設計準則有 3種[12－14]：GLRT準則，Rao準則和Wald準則。對檢測器的度量指標包括：檢測概率的高低、對失配信號的穩健性和對失配信號的抑制能力，等等。

針對色噪聲下多通道信號的自適應檢測問題，國內外的學者展開了多方面的研究，并取得了大量成果，這些方法均可應用到STAD中。但很少有文獻針對STAD進行單獨研究，沒有深入地分析機載雷達STAD與常規色噪聲下多通道自適應檢測方法的區別。此外，值得指出的是，Klemm在其著作[15]中曾指出，STAP下一步的一個研究熱點為自適應檢測。

本文旨在對STAD這一技術進行簡要介紹，闡述STAD技術與現有STAP雜波抑制后檢測方法相比具有的優勢，并綜述可用到STAD中的現有自適應檢測方法，探討下一步的研究方向，起到拋磚引玉的作用。

2 STAD方法研究現狀

上文指出，STAD屬于檢測范疇。進一步講，STAD屬于色噪聲背景下的多通道信號自適應檢測。因此，現有的色噪聲背景下多通道信號檢測方法都可以應用到STAD中。自適應的含義指的是雜波加噪聲的協方差矩陣未知，這就需要利用訓練樣本來自適應地估計該協方差矩陣。訓練樣本必須與待檢測單元中雜波加噪聲的統計特性具有一定的相關性，否則訓練樣本不提供任何有價值的信息。

美國林肯實驗室的Kelly于1986年基于GLRT準則，提出了著名的KGLRT，這成為色噪聲中的多通道信號自適應檢測的奠基之作。上文指出，常用的檢測器設計準則有3種，即GLRT準則，Rao準則和 Wald準則1)需要注意的是，GLRT, Rao和 Wald并不是某一種特定的檢測器，而是通用的檢測器設計準則。在不同的環境下GLRT往往是不同的，Rao和Wald也是一樣。此外，當我們說“提出了一種GLRT檢測器、Rao檢測器或 Wald檢測器”時，指的是根據 GLRT準則、Rao準則或Wald準則，提出了相應的檢測器。這一用法在現有文獻中被普遍采用[24－27]。。此外，在實際中，三者對應的兩步檢測器設計準則也經常被應用。兩步檢測器設計準則的設計流程為：先假設協方差矩陣已知，然后根據相應的設計準則得到檢測器，最后用采樣協方差矩陣代替已得到檢測器中的未知協方差矩陣[9,16]。

2.1 均勻環境中的目標檢測

均勻環境指的是待檢測單元中雜波加噪聲的統計特性與訓練樣本中的統計特性完全相同[11]。在KGLRT的基礎上，Chen等人[10]與Robey等人[9]利用兩步GLRT設計準則在均勻環境下分別獨立提出了自適應匹配濾波器(Adaptive Matched Filter,AMF)。De Maio分別在文獻[17]和文獻[18]中根據Rao檢測器和Wald檢測器提出了相應的檢測器，并且證明了Wald檢測器與AMF等價。為敘述方便，記文獻[17]中的 Rao檢測器為 DMRao(De Maio’s Rao)。

2.2 非均勻環境中的目標檢測

由于載機飛行姿態的變化以及陣列結構擺放(共形陣、雙基地)的影響，在實際中機載雷達所面臨的環境往往是非均勻的。部分均勻環境是非均勻的一種，是指待檢測單元的協方差矩陣和訓練樣本的協方差矩陣具有相同的結構，但具有不同的功率。文獻[16]通過實測數據驗證了部分均勻環境模型適用于機載雷達所面臨的實際環境。基于2S-GLRT設計準則，Scharf于1996年提出了自適應相關估計器(Adaptive Coherence Estimator, ACE)[19]，該檢測器被證明是部分均勻環境中的 GLRT[19]，相應的Rao和Wald檢測器在文獻[20]中提出，并且均等價于ACE。

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

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

2.3 信號失配下的目標檢測

上述檢測器都是在目標導向矢量確知情況下得到的，在實際中，由于存在陣元校正誤差、指向誤差和多徑效應等影響，往往存在導向矢量失配的情況。文獻[31]從濾波的角度研究了導向矢量失配對輸出 SCNR的影響，并推廣了 RMB(Reed-Mallet-Brennan)準則[8]。通過理論分析，文獻[31]指出，當存在導向矢量失配時，只有通過增加訓練樣本數才能減小SCNR損失。信號失配下的檢測最早由Kelly開始研究，在文獻[32]中，Kelly指出信號失配對濾波和檢測的影響不同，通過合理的設計檢測器，可以降低信號失配對自適應檢測的影響。這一功能由檢測器的CFAR特性實現。

在Kelly的研究[32]基礎上不斷有新方法被提出，按照對失配信號的敏感程度可把檢測器分為兩類，一類為穩健檢測器，另一類為失配敏感檢測器。前者在導向矢量失配量相對較大的情況下，仍然能以較高的檢測概率檢測出目標。而對于后者，即使導向矢量失配較小，檢測器的檢測概率也會大為下降，即不把失配信號作為感興趣的目標。實際中究竟需要穩健檢測器還是失配敏感檢測器，要視具體情況而定。一般來說，當雷達工作在搜索模式時，需要選擇穩健檢測器，當雷達工作在跟蹤模式時，需要選擇失配敏感檢測器。

針對導向矢量失配下的檢測，通常有4種檢測器設計方法：直接建模法[33－37]、增加虛擬信號/干擾法[38－42]、檢測器級聯法[17,22,43－49]和可調檢測器法[49－52]。直接建模法指的是確定失配角的范圍，假設目標實際導向矢量位于以陣列指向為軸心的真錐中，通過(凸)優化技術設計檢測器。增加虛擬信號/干擾法指的是在 H0假設檢驗下，假設存在確定(非隨機)信號或者虛擬隨機干擾。檢測器級聯法指的是檢測器由兩個子檢測器級聯組成，并且這兩個子檢測器分別為穩健檢測器和失配敏感檢測器。可調檢測器法指的是通過控制可調參數來控制檢測器對失配信號的敏感程度。

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/干擾法得到的檢測器對失配信號具有很好的抑制作用，但缺乏穩健性。檢測器級聯法和可調檢測器法的一個共同特點是，針對匹配信號，通過實際合理的選擇門限對或者可調參數，二者均可以達到比子檢測器(對于檢測器級聯法)或特例檢測器(對于可調檢測器法)更高的檢測概率。另外，檢測器級聯法對失配信號的穩健性和失配敏感性受制于子檢測器的穩健性和敏感性，而可調檢測器往往不受特例檢測器對失配信號敏感程度的影響，具有更高的靈活性。

2.4 小訓練樣本數下的目標檢測

機載雷達的自由度為陣元數與脈沖數的乘積。該自由度往往很大，導致雜波加噪聲的協方差矩陣維數很高。根據RMB準則[8]，要獲得滿意的協方差矩陣估計，至少需要兩倍于系統自由度維數的訓練樣本，然而這在實際中很難滿足。因此，有必要研究小訓練樣本數下的自適應檢測。

文獻[53]分析了級聯 STAD的性能，并與常規STAD進行了比較。文獻[54]把聯合域局域處理(Joint Domain Localised, JDL)與KGLRT結合，形成了JDL-GLRT檢測器。文獻[55]把對角加載[56]技術與 KGLRT結合，提出了對角加載 GLRT(Diagonally Loaded GLRT, DL-GLRT)。文獻[6,7]把對角加載技術與AMF和ACE結合，提出了對角加載AMF(Diagonally Loaded AMF, DL-AMF)和對角加載 ACE(Diagonally Loaded ACE, DLACE)。文獻[57]把主分量法[58]應用 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[59, 60]根據正交投影變換的思想，提出相應的降秩檢測器，文獻[61]把這一思想與ACE結合，提出了新的降秩檢測器。

共軛梯度(Conjugate Gradient, CG)[62]、多級維納濾波器(Multistage Wiener Filter, MWF)[63]和自適應輔助向量濾波器(Auxiliary-Vector Filtering,AVF)[64]屬于Krylov子空間技術(數值計算中的一類方法)。近年來，Krylov子空間技術被成功應用到自適應檢測中。文獻[65]把CG法應用到最優檢測器(即匹配濾波器，或稱為匹配檢測器，該檢測器在協方差矩陣已知的前提下得到)中。文獻[66]把MWF與AVF應用到自適應檢測中，提出了相應的檢測器。

上述新的檢測方法比常規的KGLRT, AMF和ACE等方法具有更高的檢測概率，尤其是在訓練樣本數小的情況下，這一優勢更為明顯。

3 結論與展望

通過上文的分析可以看出，STAP以雜波抑制為目標，而STAD以檢測目標的有無為目標。雜波抑制體現在STAD的中間過程中，而非作為一個獨立的步驟。下面列出自適應檢測的幾個亟待解決的問題或新的研究方向：

(1) 嚴重非均勻及非高斯環境下的檢測[67－69]；

(2) 結構化協方差矩陣下的檢測[70－74]；

(3) 擴展目標的檢測[14,16,75－79]；

(4) 機載MIMO或多基地檢測[80－84]；

(5) 壓縮感知檢測[85]；

(6) 認知雷達檢測[86]；

(7) 基于先驗知識的檢測[82,87－94]。

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