Covariance Based Signal Detections for Cognitive Radio

阵形畸变对拖线阵三维探测性能的影响及补偿技术王思秀【摘要】针对拖曳阵阵形畸变导致的目标检测不准确问题,首先,分析了阵形畸变对拖线阵三维探测性能的影响,并论证了利用实际阵形在垂直方向形成的孔径实现对目标深度信息提取可行性;然后,依据拖线阵中姿态与深度传感器监测数据,提出一种基于阵形自动拟合的三维补偿技术;最后,通过三维补偿技术修正导向矢量,降低导向矢量与协方差矩阵之间不匹配度,解决阵形畸变所导致的目标检测不准确问题.数值仿真结果表明,对畸变阵形进行三维阵形估计和补偿,实现了对未知目标的三维探测,且避免了标校声源对拖线阵实时探测目标的影响,便于工程应用.%For the discontinuous problem of the target detection caused by the array shape distortion of the towed line array,firstly,the influence of the array shape distortion on the 3D detection performance is ana-lyzed,and the feasibility of extracting target depth information is demonstrated via the actual array shape forming the aperture in the vertical direction. Then,according to the monitoring data of the attitude sensor and depth sensor,a 3D compensation technique based on array shape automatic fitting is proposed. Final-ly,the steering vector is modified by the 3D compensation technique to reduce the mismatch between the steering vector and covariance matrix,and the discontinuous problem of the target detection caused by the array shape distortion is solved. The results of numerical simulation show that,estimation of the 3D array shape and compensation for the distortion array shape can achieve 3D detection of underwaterunknown tar-get,avoid the influence of calibration source on the real-time detecting target,and is convenient for engi-neering application.【期刊名称】《电讯技术》【年(卷),期】2018(058)002【总页数】7页(P145-151)【关键词】水下目标探测;拖线阵;阵形畸变;深度信息提取;三维补偿;三维探测【作者】王思秀【作者单位】新疆财经大学计算机科学与工程学院,乌鲁木齐830012【正文语种】中文【中图分类】TN911.71 引言受重力、浮力、流体阻力、海流、平台机动等多种因素影响，拖线阵在实际应用中，其实际阵形与理想阵形存在一定偏差，对探测性能存在一定影响。

Vol. 36 No. 12Dec72020第36卷第12期2020年12月信号处理Jouana-ooSogna-Paoce s ong文章编号：1003-0530(2020)12-2123-08结合场景分类的近岸区域SAR 舰船目标快速检测方法付晓雅王兆成(河北工业大学电子信息工程学院，天津300401)摘 要：合成孔径雷达(Synthetic Aperture Radar , SAR )图像场景通常较大，深层卷积网络用于SAR 舰船目标检测时通常需要密集滑窗提取子图像预处理，然后利用目标检测网络直接对子图像进行目标检测，该过程存在大量信息冗余，极大影响了目标检测效率的提升。

在近岸区域下陆地场景偏多且场景复杂，针对以上问题，本文提出了一种结合场景分类的近岸区域SAR 舰船快速目标检测方法(SC-SSD )，该方法主要包含两个阶段：场景分类 阶段和目标检测阶段。

它们分别是由场景分类网络(Convolutional Neural Network for Scene Classification ，SC-CNN ) 和目标检测网络(Singe Shot Detector ，SSD )构成。

其中SC-CNN 可以快速粗略筛选出可能包含舰船的子图像，然后将筛选出的子图像输入到SSD 网络中实现精细化的舰船目标检测。

基于高分辨率SAR 舰船检测数据集AIR-SARShip-C.0的实验结果表明，提出方法相比于传统舰船检测方法，在保持较高的检测精度的同时，具有明显更快的检测速度。

关键词：合成孔径雷达图像；场景分类；舰船目标检测中图分类号：TN957.51 文献标识码：A DOI ： 10. 16798/j. issn. 1003-0530. 2020.12.019引用格式：付晓雅，王兆成.结合场景分类的近岸区域SAR 舰船目标快速检测方法[J ].信号处理，2020, 36(12) : 2123-2130. DOI ： 10. 16798/j. issn. 1003-0530.2020.12.019.Reference format : Fu Xiaoya ，Wang Zhaocheng. SAR Ship Target Rapid Detection Method Combined with Scene Cmssifi- cation in the Inshore Region [ J ]. Journal of Signal Processing ，2020，36(12) : 2123-2130. DOI : 10. 16798/j. issn. 1003­0530.2020.12.019.SAR Ship Target Rapid Detection Method Combiner withSceee Classidcation in the Inshore RegionFu Xiaoyy Wang Zhaocheng(School of Electronics and Information Engineering ，Hebei University of Technology ，Tianjin 300401，China)Abshraeh : SyniheiocApeaiuaeRadaa ( SAR ) omagesceneosusua e yeaage ， deep coneoeuioonaeneiwoak ooaSARshop iaagei detection usua/y requires dense sliding window to extract sub-image pre-processing ，and then use the target detection net ­work to directly target detection sub-image ，the process has a large number of iformation redundancy ，which greatly a/ectsthe efficiency of target detection. In the inshore region ， there are many land scenes and complex scenes ，for the aboveproblems ，this paper proposes a fast target detection method ( SC-SSD ) for SAR ships in the near-shore region combinedwoih sceneceassooocaioon ， whoch maoneyconsosisooiwosiages : scenecea s ooocaioon siageand iaageideiecioon siage.TheyconsosiooConeoeuioonaeNeuaaeNeiwoak ooaSceneCea s ooocaioon ( SC-CNN ) and SongeeShoiDeiecioa ( SSD ) ， aespecioeeey.TheSC-CNNcan quockeyand coaaseeyooeieaouiihesub-omagesihaimayconiaon shops ， and ihen onpuiiheooeieaed sub-oma-收稿日期：2020-10-12"修回日期：2020-12-30基金项目：国家自然科学基金(62001155)2124信号处理第36卷ges to the SSD network to realize fine-coined ship target detection.The experimental results based on the high-resolution SAR ship detection dataset AIR-SARShip-1.0show that the proposed method X significantly faster than the WadiXonal ship detection method while maintaining a higher detection accuracy.Key words:SAR image；scene classification；ship target detection1引言合成孔径雷达(Synthetic Aperture Radar,SAR)是一种主动式的微波成像传感器，具有不受任何天气条件限制，全天时,全天候,作用距离远的技术优势，在军事和民用领域发挥着重要的作用*1+)其中，港口和海上区域的舰船检测是一个重要的研究方向，对SAR图像舰船进行有效的检测有利于海上运输管理，渔业管理，舰船油污探测等［2］)传统的SAR图像舰船目标检测方法包括两个步骤：检测，鉴别。

第39卷第7期自动化学报Vol.39,No.7 2013年7月ACTA AUTOMATICA SINICA July,2013稀疏距离扩展目标自适应检测及性能分析魏广芬1苏峰2简涛2摘要在球不变随机向量杂波背景下,研究了稀疏距离扩展目标的自适应检测问题.基于有序检测理论,利用协方差矩阵估计方法,分析了自适应检测器(Adaptive detector,AD).其中,基于采样协方差矩阵(Sample covariance matrix,SCM)和归一化采样协方差矩阵(Normalized sample covariance matrix,NSCM),分别建立了AD-SCM和AD-NSCM检测器.从恒虚警率特性和检测性能综合来看,AD-NSCM的性能优于AD-SCM和已有的修正广义似然比检测器.最后,通过仿真实验验证了所提方法的有效性.关键词稀疏距离扩展目标,自适应检测,采样协方差矩阵,归一化采样协方差矩阵,有序统计量引用格式魏广芬,苏峰,简涛.稀疏距离扩展目标自适应检测及性能分析.自动化学报,2013,39(7):1126−1132DOI10.3724/SP.J.1004.2013.01126Sparsely Range-spread Target Detector and Performance AssessmentWEI Guang-Fen1SU Feng2JIAN Tao2Abstract In the background where the clutter is modeled as a spherically invariant random vector,the adaptive detection of sparsely range-spread targets is addressed.By exploiting the order statistics and the covariance matrix estimators,the adaptive detector(AD)is assessed.Herein,the detectors of AD-SCM and AD-NSCM are proposed based on the sample covariance matrix(SCM)and normalized sample covariance matrix(NSCM),respectively.In terms of constant false alarm rate properties and detection performance,the AD-NSCM outperforms the AD-SCM and the existing detector of modified generalized likelihood ratio.Finally,the performance assessment conducted by simulation confirms the effectiveness of the proposed detectors.Key words Sparsely range-spread target,adaptive detection(AD),sample covariance matrix(SCM),normalized sample covariance matrix(NSCM),order statisticsCitation Wei Guang-Fen,Su Feng,Jian Tao.Sparsely range-spread target detector and performance assessment.Acta Automatica Sinica,2013,39(7):1126−1132低分辨率雷达的目标尺寸小于距离分辨率,这种目标常称之为点目标[1].通过采用脉冲压缩技术,高分辨率雷达能够在空间上把一个目标分解成许多散射点[2−3],目标回波在雷达径向上的多个散射点分布在不同的距离分辨单元中,形成距离扩展目标[4].在许多情况下,距离扩展目标的散射点密度是稀疏的,可将这种目标简称为“稀疏距离扩展目标”.目前,高斯背景下的距离扩展目标检测已取得一定进收稿日期2011-12-28录用日期2012-08-27Manuscript received December28,2011;accepted August27, 2012国家自然科学基金(61174007,61102166),山东省优秀中青年科学家科研奖励基金(BS2010DX022)资助Supported by National Natural Science Foundation of China (61174007,61102166)and the Scientific Research Founda-tion for Outstanding Young Scientists of Shandong Province (BS2010DX022)本文责任编委韩崇昭Recommended by Associate Editor HAN Chong-Zhao1.山东工商学院信息与电子工程学院烟台2640052.海军航空工程学院信息融合技术研究所烟台2640011.School of Information and Electronics,Shandong Institute of Business and Technology,Yantai2640052.Research Insti-tute of Information Fusion,Naval Aeronautical and Astronauti-cal University,Yantai264001展,其中,针对估计参数空间过大的问题,文献[5]提出了一种无需辅助数据的检测器,简称为修正的广义似然比检验(Modified generalized likelihood ratio test,MGLRT)检测器,其在高斯背景下是有界恒虚警率(Constant false alarm rate,CFAR)的.但在高距离分辨率的条件下,背景杂波呈现出诸多的非高斯特性[1],高斯背景下获得的检测器已无法有效检测目标.在非高斯背景下,文献[6]研究了已知杂波协方差矩阵条件下的距离扩展目标检测;而通过利用不含目标信号的辅助数据,文献[7]和文献[8]分别针对距离扩展目标和距离–多普勒二维分布式目标展开了自适应检测研究.需要指出的是,以上自适应检测方法[7−8]都是基于辅助数据的.当无法获得满足条件的辅助数据时,实现非高斯背景下距离扩展目标的自适应检测具有重要意义.文献[9]基于迭代估计方法实现了自适应检测,但迭代估计计算量较大,如何在保证性能的同时减小计算量,也是值得探讨的问题.7期魏广芬等:稀疏距离扩展目标自适应检测及性能分析1127稀疏距离扩展目标的散射点只占据目标距离扩展范围的一部分,与含纯杂波的距离分辨单元幅值相比,含目标散射点的距离分辨单元幅值明显更高,这就为实现目标的自适应检测提供了条件.本文针对非高斯杂波中的稀疏距离扩展目标检测问题,在不需要辅助数据的条件下,首先,采用有序统计检测理论和协方差矩阵估计方法,粗略估计目标散射点单元集合;然后,进一步利用适当估计方法获得协方差矩阵的精确估计,设计了自适应检测器(Adaptivedetector,AD),并通过仿真实验验证了检测器的有效性.1问题观测数据来源于N个阵元的线性阵列天线,需跨过K个可能存在目标的距离分辨单元z t,t=1,···,K,判决一个距离扩展目标的存在与否.假设可能的目标完全包含在这些数据中,并且忽略目标距离走动的问题.在杂波背景下,待解决的检测问题可由以下二元假设检验公式来表达.H0:z t=c t,t=1,···,KH1:z t=αt p+c t,t=1,···,K(1)其中,p=(1,e jφ,e j2φ,···,e j(N−1)φ)T/√N表示已知单位导向矢量,即p H p=1,这里(·)H表示共轭转置,φ表示相移常量,(·)T表示转置,αt,t=1,···,K是反映目标幅度的未知参数.非高斯杂波可用球不变随机向量建模[10],由于中心极限定理在较小区域的杂波范围内仍是有效的,球不变随机向量可以表示为两个分量的乘积:一个是反映受照区域反射率的时空“慢变化”纹理分量,另一个是变化“较快”的“散斑”高斯过程.那么,距离分辨单元t的N维杂波向量c t为c t=√τt·ηt,t=1,···,K(2)其中,ηt=(ηt(1),ηt(2),···,ηt(N))T是零均值协方差矩阵为Σ的复高斯随机向量,非负的纹理分量τt与ηt相互独立,其用来描述杂波功率在不同距离分辨单元间的起伏,且服从未知分布fτ.另外,杂波协方差矩阵结构Σ可以表示为Σ=E{ηt ηHt}(3)距离扩展目标完全包含在K个距离分辨单元的滑窗中,假设一个等效散射点最多只占据一个距离分辨单元,即目标等效散射点数目与其所占据的距离分辨单元数目是相等的.通常目标散射点是稀疏分布的,与含纯杂波的距离分辨单元相比,有散射点的距离分辨单元幅值往往更高.含目标等效散射点的距离分辨单元数目用h0表示,而其所对应的距离分辨单元下标用集合Θh表示.为了简化分析,假设h0是已知的,若其未知,可利用模型阶数选择方法获得合适的估计值[11].如前所述,对距离扩展目标的检测只需在距离分辨单元Θh内进行,式(1)表示的假设检验问题可以进一步表示为H0:z t=c t,t∈ΘhH1:z t=αt p+c t,t∈Θh(4)在分布fτ未知的条件下,距离分辨单元t的杂波是条件高斯的,其相应的方差为τt.由于幅度αt 未知而向量p已知,针对不同假设,观测向量z t的联合概率密度可表示为t∈Θhf(z t|τt,H0)=t∈Θh1πNτN t det(Σ)×exp[−1τtz HtΣ−1z t](5)t∈Θhf(z t|αt,τt,H1)=t∈Θh1πNτN t det(Σ)×exp−1τt(z t−αt p)HΣ−1(z t−αt p)(6)其中,det(·)表示方阵的行列式.2检测器实现在未知集合Θh的条件下,为了获得估计的参数集合ˆΘh,这里先假设已知矩阵Σ.由于未知参数α={αt|t∈Θh}和τ={τt|t∈Θh},可利用广义似然比检验(GLRT)原理进行检测器设计[12].在矩阵Σ已知的条件下,根据GLRT原理,对于似然比中的未知参数,可用最大似然(Maximum likelihood,ML)估计进行替换,即考虑如下二元判决:maxτmaxαt∈Θhf(z t|αt,τt,H1)maxτt∈Θhf(z t|τt,H0)H1><H0T0(7)在H1假设下求得αt的ML估计为[13]ˆαt=p HΣ−1z tp HΣ−1p(8)将ˆαt代入式(7)后,可进一步在不同假设条件下求得τt的ML估计:H0:ˆτt=1Nz HtΣ−1z t(9) H1:ˆτt=1N(z t−ˆαt p)HΣ−1(z t−ˆαt p)(10)1128自动化学报39卷将式(8)∼(10)代入式(7)中,可得自然对数形式的GLRT判决为λ1=−Nt∈Θh0ln1−|p HΣ−1z t|2(z H tΣ−1z t)(p HΣ−1p)H1><H0T1(11)令w t=|p HΣ−1z t|2(z H tΣ−1z t)(p HΣ−1p)(12)值得注意的是,w t的结构类似于一个归一化匹配滤波器(权向量为Σ−1p)[14].可以看出,式(12)的分子部分p HΣ−1z t等效于给定距离分辨单元观测z t经过匹配滤波后的结果[14].而分母部分的两项z HtΣ−1z t和p HΣ−1p起到了归一化处理的作用,因此,w t是距离单元观测z t经过匹配滤波后模平方的归一化,可以看作是距离单元观测经归一化匹配滤波后的能量.由于目标完全包含在K个单元的距离滑窗中,且距离扩展目标等效散射点所占据的距离分辨单元幅值往往大于纯杂波的距离分辨单元幅值,因此,可通过归一化能量w t,t=1,···,K中最大的h0个值来确定未知集合ˆΘh.实际应用中协方差矩阵结构Σ往往是未知的,为了确定集合ˆΘh,需先对协方差矩阵结构进行估计.如前所述,纹理分量τt的分布fτ是未知的,因此,协方差矩阵结构Σ的ML估计不能通过期望最大化得到[13].本文考虑两种协方差矩阵估计方法.一种是高斯背景下的经典采样协方差矩阵(Sample covariance matrix,SCM),其可以表示为ˆΣSCM =1RRr=1y r y Hr(13)其中,y r,r=1,···,R表示可用于估计的R个数据.当R≥N时,SCM是以概率为1非奇异的,同时也是正定Hermitian矩阵[12].另外,在非高斯背景下,也常常利用辅助数据获得归一化采样协方差矩阵(Normalized sample covariance matrix, NSCM),可以表示为ˆΣNSCM =1RRr=1Ny Hry ry r y Hr(14)与文献[9]类似,针对稀疏距离扩展目标的自适应检测,AD检测器的实现分为如下三个步骤.步骤1.基于SCM或NSCM方法,利用K个待检测单元的观测数据获得初步估计矩阵ˆΣ1,进一步将估计矩阵ˆΣ1代入式(12)中,可得到初步估计ˆw(1)t.对ˆw(1)t,t=1,···,K按升序排列,可得如下有序序列:0≤ˆw(1)(1)≤···≤ˆw(1)(t)≤···≤ˆw(1)(K)≤1(15)步骤2.考虑有序序列的K−h0个最小值(即ˆw(1)(t),t=1,···,K−h0),并用Ωh表示相应距离分辨单元下标的集合.为了获得可逆的估计矩阵,需满足K−h0≥N.根据之前的分析,集合Ωh中的距离分辨单元极可能只包含纯杂波,故可以利用Ωh0对应的距离分辨单元观测值,精确估计矩阵Σ,并采用与初步估计中相同的估计方法(SCM或NSCM),进一步获得较为精确的协方差矩阵结构估计ˆΣ2.利用ˆΣ2代替式(12)中的未知矩阵Σ,得到w t的精确估计值用ˆw(2)(t)表示.对ˆw(2)(t),t=1,···,K按升序排列,可得如下有序序列:0≤ˆw(2)(1)≤···≤ˆw(2)(t)≤···≤ˆw(2)(K)≤1(16)考虑有序序列的h0个最大值(即ˆw(2)(t),t=K−h0+1,···,K),并用ˆΘh表示相应距离分辨单元下标的集合.步骤3.将距离分辨单元下标的集合ˆΘh和协方差矩阵的精确估计ˆΣ2代入式(11)中,获得自适应检测器AD的检测统计量可以表示为λ2=−NKt=K−h0+1ln(1−ˆw(2)(t))=−Nt∈ˆΘhln[1−|p HˆΣ−12z t|2(z H tˆΣ−12z t)(p HˆΣ−12p)]H1><H0T2(17)需要说明的是,在存在目标散射点的情况下,步骤1的初步估计矩阵不可避免地引入了估计误差,虽然这种误差在步骤2中得到了一定的抑制,但它仍将影响后续精确估计矩阵的精度.在存在辅助数据的前提下,为了获得良好的检测性能,一般要求辅助数据个数不小于阵元数N的两倍[15].在待检测单元数K不变的情况下,可利用的纯杂波单元数(K−h0)将随着散射点个数的增加而减小,因此,此处需等价满足(K−h0)≥2N.进一步考虑到步骤1中散射点单元所引起的估计误差,实际应用中可能需要更大的(K−h0)/N值以弥补步骤1中导致的性能损失,具体取值将在接下来的性能评估中给出.由于采用不同的估计方法会获得不同的自适应检测器,在这里,我们分别将采用SCM和NSCM估计方法获得的相应检测器简称为AD-SCM和AD-NSCM.由于本文的自适应检测器中ˆΘh和ˆΣ2均受到协方差矩阵估计方法的影响,因此,有必要评估自适应距离扩展目标检测器的CFAR特性,这将在接下来的性能分析中进行.7期魏广芬等:稀疏距离扩展目标自适应检测及性能分析1129 3性能评估本节对稀疏距离扩展目标自适应检测器AD-SCM和AD-NSCM进行了CFAR特性和检测性能评估,并与无需辅助数据的MGLRT检测器[5]进行了比较分析.利用Toeplitz矩阵对Σ进行建模,具体采用指数相关结构,在杂波一阶相关系数为γ的条件下,第m行第n列的矩阵元素为[Σ]m,n=γ|m−n|,1≤m,n≤N(18)利用Γ分布对纹理分量的分布fτ进行建模:fτ(x)=LbLΓ(L)x L−1e−(L b)x,x≥0(19)其中,Γ(·)是Gamma函数,均值b代表了平均杂波功率;参数L表示分布fτ的非高斯拖尾特征,具体来说,随着L的减小,函数fτ的拖尾将增大,而杂波的非高斯尖峰程度将增大.采用蒙特卡罗方法计算相应的检测概率P d和虚警概率P fa.根据前面的假设,在所有距离分辨单元均存在杂波的条件下,目标等效散射点只存在于h0个距离分辨单元中,且一个等效散射点最多只占据一个距离分辨单元.在所有K个距离分辨单元上,每个单元的目标或杂波的平均功率分别用σ2s 或σ2c表示.对于存在目标散射点的距离分辨单元(t∈Θh),用零均值独立复高斯变量对等效散射点建模,即目标散射点幅度在不同距离分辨单元间瑞利起伏;相应的方差表示为E{|αt|2}=εtσ2sK(εt表示单个散射点占目标总能量的比率).由|αt|2,t=1,···,K的独立性可知,检测性能与散射点在待检测单元中的位置无关.几种典型的散射点分布模型如表1所示.其中,Model 1中的目标能量等量分布在h0个距离分辨单元范围内;Model2∼4中某个距离分辨单元具有大部分能量,而剩下的能量在其余距离分辨单元中等量分布.Model5相当于点目标,是Model2∼4的极端特例.输入信杂比(Signal to clutter ratio,SCR)定义为K个距离分辨单元内的平均信杂比,即SCR=σ2sσ2cp HΣ−1p(20)为了便于CFAR特性评估,需针对杂波功率水平(对应于b)、尖峰程度(对应于L)和协方差矩阵结构(对应于γ)的不同情况,分析检测器的检测阈值与虚警概率间的关系.相关研究表明[9],在非高斯杂波下MGLRT是非CFAR的,即高斯背景下获得的MGLRT检测器不适用于非高斯背景.为了便于比较,在K=15,h0=3,N=2,L=0.1,1,γ=0,0.5,0.9和b=1,10条件下,图1和图2分别给出了AD-SCM和AD-NSCM的检测阈值(De-tection threshold)与虚警概率(False alarm prob-ability)的关系曲线.图1表明,AD-SCM检测器对杂波协方差矩阵结构和功率水平具有自适应性,但对杂波尖峰不具有适应能力.而图2说明,AD-NSCM对杂波尖峰和杂波功率水平具有CFAR特性,但其检测阈值仍受协方差矩阵结构的轻微影响.综合来看,AD-NSCM的检测阈值在不同杂波条件下的鲁棒性更好.图1K=15,N=2,L=0.1,1,γ=0,0.5,0.9,b=1,10,h0=3时,AD-SCM的CFAR特性曲线Fig.1CFAR curves of AD-SCM for K=15,N=2, L=0.1,1,γ=0,0.5,0.9,b=1,10,h0=3表1不同散射点分布模型的εt值Table1Values ofεt for typical scatters models目标距离分辨单元12···h0Model11h01h01h01h0Model20.50.5h0−10.5h0−10.5h0−1Model30.90.1h0−10.1h0−10.1h0−1Model40.990.01h0−10.01h0−10.01h0−1Model510001130自动化学报39卷图2K=15,N=2,L=0.1,1,γ=0,0.5,0.9,b=1,10,h0=3时,AD-NSCM的CFAR特性曲线Fig.2CFAR curves of AD-NSCM for K=15,N=2, L=0.1,1,γ=0,0.5,0.9,b=1,10,h0=3接下来分析AD检测器的检测性能.图3给出了MGLRT、AD-SCM和AD-NSCM的性能曲线.可以看出,AD-NSCM的检测性能最优,MGLRT 其次,而AD-SCM的检测性能最差.从以上分析综合来看,与MGLRT和AD-SCM相比,AD-NSCM 在CFAR特性和检测性能方面均具有一定的优势.下文将重点对AD-NSCM的检测性能展开分析.图3K=15,N=2,L=1,γ=0.9,h0=3,P fa=10−4, Model1时,MGLRT,AD-SCM和AD-NSCM的检测性能曲线Fig.3Detectability curves of MGLRT,AD-SCM and AD-NSCM for K=15,N=2,L=1,γ=0.9,h0=3,P fa=10−4,Model1首先,针对表1中5种不同模型,图4评估了散射点能量分布对AD-NSCM检测性能的影响.可以看出,随着距离分辨单元间散射点能量分布的均匀性增加,检测性能逐渐改善.为了便于分析,下文中主要针对Model1模型.另外,在不同的散射点密度条件下,图5分析了AD-NSCM检测性能.由图5可知,当h0<7时,协方差矩阵结构的估计误差较小,其对检测性能的影响也较小,当散射点数目增加时,检测器可利用的目标能量增大,AD-NSCM的检测性能得到一定的改善.当h0≥7时,协方差矩阵结构的估计误差影响较大,当散射点数目增加时,进行矩阵估计所用的观测数据量减少,估计矩阵的误差加大,导致较为严重的检测损失,且损失量高于增加散射点数目所获得的性能增益,并引起总检测性能的退化.综合来看,当h0<K/2时,AD-NSCM 的检测性能较好.图4K=15,N=2,L=1,γ=0.9,h0=3,P fa=10−4, Model1∼5对应的AD-NSCM检测性能曲线Fig.4Detectability curves of AD-NSCM for K=15, N=2,L=1,γ=0.9,h0=3,P fa=10−4,Model1∼5图5K=15,N=2,L=1,γ=0.9,P fa=10−4,Model 1时,h0=2,4,6,7,8,10,12对应的AD-NSCM检测性能曲线Fig.5Detectability curves of AD-NSCM for K=15, N=2,L=1,γ=0.9,P fa=10−4,Model1,h0=2,4,6,7,8,10,12在不同杂波尖峰条件下,图6给出了AD-NSCM检测性能.由图6可知,随着L的减小,杂波尖峰程度增大,AD-NSCM的检测性能有所改善.图7给出了不同杂波相关性对应的检测性能曲线.可以看出,杂波一阶相关系数的变化对检测性能几乎没有影响,说明AD-NSCM对杂波相关性7期魏广芬等:稀疏距离扩展目标自适应检测及性能分析1131的变化具有良好适应性.图8进一步分析了阵元数变化(N =2,4,6,8)对AD-NSCM 检测性能的影响.可以看出,在阵元数N ≤4的条件下,当N 增加时,检测性能有所提高;而在N >4的条件下,当N 增加时,检测性能反而有所下降.可能的原因是,当进行矩阵估计所用的观测数据量不变时(R =K −h 0=12),N 的增加会导致协方差矩阵维数变大,待估参量的数目增加,估计精度下降,并直接引起检测性能的退化.综合来看,当K −h 0≥3N 时,AD-NSCM 的检测性能较好.图6K =15,N =2,γ=0.9,h 0=3,P fa =10−4,Model 1时,L =0.5,1,2,10对应的AD-NSCM 检测性能曲线Fig.6Detectability curves of AD-NSCM for K =15,N =2,γ=0.9,h 0=3,P fa =10−4,Model 1,L =0.5,1,2,10图7K =15,N =2,L =1,h 0=3,P fa =10−4,Model 1时,γ=0,0.5,0.9对应的AD-NSCM 检测性能曲线Fig.7Detectability curves of AD-NSCM for K =15,N =2,L =1,h 0=3,P fa =10−4,Model 1,γ=0,0.5,0.94结论本文研究了非高斯杂波中的稀疏距离扩展目标检测问题.在不需要辅助数据的条件下,基于SCM 和NSCM 估计器,分别建立了AD-SCM 和AD-NSCM 检测器.从CFAR 特性和检测性能综合来看,AD-NSCM 的性能优于AD-SCM 和MGLRT.对于典型的非高斯杂波环境,随着杂波尖峰程度的增大,AD-NSCM 的检测性能得到提高,且其对杂波相关性的变化也具有良好适应性.另外,对于h 0<K/2的稀疏距离扩展目标,在K −h 0≥3N 条件下,AD-NSCM 能获得满意的检测性能.需要说明的是,与文献[9]中的检测器相比,AD-NSCM 虽然减小了计算量,但也牺牲了部分CFAR 特性.如何减小检测器对散射点信息的依赖性,是下一步需要研究的问题.图8K =15,L =1,γ=0.9,h 0=3,P fa =10−4,Model 1时,N =2,4,6,8对应的AD-NSCM 检测性能曲线Fig.8Detectability curves of AD-NSCM for K =15,L =1,γ=0.9,h 0=3,P fa =10−4,Model 1,N =2,4,6,8References1Zhou Yu,Zhang Lin-Rang,Liu Xin,Liu Nan.Adap-tive detection based on Bayesian approach in heteroge-neous environments.Acta Automatica Sinica ,2011,37(10):1206−1212(周宇,张林让,刘昕,刘楠.非均匀杂波环境下基于贝叶斯方法的自适应检测.自动化学报,2011,37(10):1206−1212)2He Chu,Liu Ming,Feng Qian,Deng Xin-Ping.PolIn-SAR image classification based on compressed sensing and multi-scale pyramid.Acta Automatica Sinica ,2011,37(7):820−827(何楚,刘明,冯倩,邓新萍.基于多尺度压缩感知金字塔的极化干涉SAR 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学校代码10701分类号TN95学号1702110045密级公开西安电子科技大学博士学位论文复合高斯海杂波背景雷达目标检测算法作者姓名：薛健一级学科：信息与通信工程二级学科：信号与信息处理学位类别：工学博士指导教师姓名、职称：水鹏朗教授学院：电子工程学院提交日期：2020年06月Radar target detection methods in compound-Gaussian sea clutterA Dissertation submitted toXIDIAN UNIVERSITYin partial fulfillment of the requirementsfor the degree of Doctor of Philosophyin Electrical EngineeringByXue JianSupervisor:Shui Penglang Title:ProfessorJune2020摘要摘要雷达在对海探测时会不可避免地接收到来自海面和各类目标的散射信号，海上目标种类繁多且海面回波特性复杂多变，因此在复杂海杂波背景下有效检测海面目标信号一直是雷达领域研究的热点。

低分辨率或者大擦地角的海杂波往往使用高斯模型描述，然而随着分辨率的提高或者擦地角的减小，海杂波不再服从高斯模型，而是表现出强烈的非高斯特性。

传统针对高斯模型的自适应相干检测器在非高斯海杂波背景下会出现高的虚警概率或者低的检测概率。

再者，当在非均匀海杂波环境中用于估计杂波协方差矩阵的参考单元数量不足时，自适应相干检测器的检测性能会出现严重退化。

因此，为了在非高斯非均匀海杂波背景下提高雷达对目标的检测能力，本文进行了如下的工作：1、针对非高斯海杂波具有的重拖尾现象和参考单元不足时自适应相干检测器性能损失严重的问题，研究了协方差矩阵未知但具有斜对称结构的复合高斯海杂波背景下雷达点目标自适应相干检测方法。

在广义帕累托分布和逆高斯纹理复合高斯分布杂波下，基于两步广义似然比检验（Generalized Likelihood Ratio Test,GLRT）、Rao检验和Wald检验分别推导了相应的自适应相干检测器。

基于二次协方差矩阵的频谱感知算法韩仕鹏;赵知劲;戴绍港【摘要】协方差矩阵频谱感知算法不需要主用户先验信息,易于实现,但是,低信噪比时,协方差矩阵元素间差异变小,检测性能有待提高.为此,利用噪声的二次协方差矩阵方差大、主用户信号的二次协方差矩阵元素的相关性增强等特点,提出利用二次协方差矩阵方差和对角线元素的判决统计量,推导出判决门限.AWGN信道和Rayleigh信道下的仿真结果表明:新方法在低虚警概率条件下,检测性能有明显提升,同时抗噪声不确定度和抗频偏性能均有改进.【期刊名称】《杭州电子科技大学学报》【年(卷),期】2019(039)003【总页数】6页(P10-14,20)【关键词】认知无线电;频谱感知;二次协方差矩阵;低虚警概率【作者】韩仕鹏;赵知劲;戴绍港【作者单位】杭州电子科技大学通信工程学院,浙江杭州 310018;杭州电子科技大学通信工程学院,浙江杭州 310018;杭州电子科技大学通信工程学院,浙江杭州310018【正文语种】中文【中图分类】TN9250 引言认知无线电是一种提高频谱利用率的新技术，频谱感知[1]是认知无线电关键技术之一。

经典的频谱感知方法包括能量检测法(Energy Detection,ED)[2]、匹配滤波器检测法(Matching Filter Detection,MFD)[3]和循环平稳特征检测法(Cyclostationary Feature Detection,CFD)[4]。

能量检测法计算复杂度低，但需要得到噪声功率，对噪声不确定性敏感；匹配滤波器检测法可以最大化检测概率，但需要知道完整的主用户先验信息，实际应用难实现；循环平稳特征检测法有更好的盲检测性能，但算法复杂度高，信号检测时间长。

为了改进上述方法，提出了基于协方差矩阵频谱感知算法。

协方差矩阵频谱感知算法不需要主用户先验信息，计算简单，是一类更有效的频谱感知算法[5]。

文献[6]提出最大特征值检测(Maximum Eigenvalue Detection,MED)算法，采用样本协方差矩阵的最大特征值作为检验统计量，随机矩阵理论(Random Matrix,RMT)方法设置阈值，不需要信号的先验消息，可有效避免噪声波动。

a glimpse into the future of idby Tim Bass<bass@>Tim Bass is the CEO and managing director for Silk Road, a consulting business inWashington, D.C. specializing in network design, management, and security.and Dave Gruber<david.gruber@>Dave Gruber, Lt. Col., is the communications squadron commander at Hickam AFB,Hawaii.Cyberspace is a complex dimension of both enabling and inhibiting data flows in electronic data networks. Current-generation intrusion-detection systems (IDSes) are not technologically advanced enough to create the situational knowledge required to monitor and protect these networks effectively. Next-generation IDSes will fuse data, combining short-term sensor data with long-term knowledge databases to create cyberspace situational awareness. This article offers a glimpse into the foggy crystal ball of future ID systems.Before diving into the technical discussion, we ask the reader to keep in mind the generic model of a datagram traversing the Internet. Figure 1 illustrates an IP datagram moving in a store-and-forward environment from source to destination; it is routed on the basis of a destination address with an uncertain source address decrementing the datagram time-to-live (TTL) at every router hop[1]. The datagram is routed through major Internet and IP transit providers.There is a striking similarity between the transit of a datagram on the Internet and an airplane through airspace, between future network management and air traffic control (ATC). At a very high abstract level, the concepts used to monitor objects in airspace apply to monitoring objects in networks. The Federal Aviation Administration (FAA) divides airspace management into two distinct entities. On the one hand, local controllers guide aircraft into and out of the airspace surrounding an airport. Their job is to maintain awareness of the location of all aircraft in their vicinity, ensure properseparation, identify threats to aircraft, and manage the overall safety of passengers. Functionally, this is similar to the role of network controllers, who must control the environment within their administrative domains. The network administrator must ensure that the proper ports are open and that the information is not delayed, that collisions are kept to a minimum, and that the integrity of the delivery systems is not compromised.Figure 1. Network object flow pathThis is similar to the situational awareness required in current-generation ATC. The FAA controls the routes between source and destination (airports), and airport authorities control the airports (as both router and host), maintaining the safety of the payload (passengers) and the transport agent (the airplane). The success of ATC depends on the fusion of data and information from short-term and long-term knowledge sources to create airspace situational awareness. This role is remarkably similar to network operators in future complex internetwork environments. As an example, consider the FAA and the National Weather Service as they monitor the weather. A change in environment can cause the FAA to make changes in air routes and landing criteria. This is similar to service providers keeping an eye out for unfavorable conditions in networks — for example, the loss of a major Internet transit network; severe congestion on major interdomain links; or attacks against routers, computers, and information. The same data-fusion concepts are shared across the airspace management functions and organizations. We expect that a similar fusion paradigm will occur with network management, Internet Traffic Control (ITC), and future intrusion-detection systems. Of course, this will not occur overnight (and may never become as comprehensive as ATC), but the analogy does help provide a glimpse into the future of ID.Figure 2. Hierarchy of IDS data-fusion inferencesFigure 2 illustrates the levels of situational knowledge inference required to support both the air traffic controller and the network manager. Sophisticated electronics must identify objects against a noise-saturated environment, track the objects, calculate their velocity, and estimate the projected threat. These are nontrivial technical requirements.Figure 3. Cyberattack with multiple sources andtargetsFigure 4. Intrusion-detection data fusionExperienced network-security professionals generally agree that current-generation intrusion-detection systems are not technically advanced enough to detect multiple, complex non-signature-based cyberattacks, illustrated in Figure 3. Next-generation cyberspace IDSes require the fusion of data from heterogeneous distributed network sensors, modeled in Figure 4.Historical Intrusion Detection SystemsWe offer a brief review of the state of the art of current-generation ID systems, from our recent ACM paper[2].Internet ID systems historically examine operating-system audit trails and Internet traffic[5, 6] to help insure the availability, confidentiality, and integrity of critical information infrastructures. ID systems attempt to protect information infrastructures against denial-of-service attacks, unauthorized disclosure of information, and the modification or destruction of data. The automated detection and immediate reporting ofthese events are required to respond to information attacks against networks and computers. The basic approaches to intrusion detection today may be summarized as: known pattern templates, threatening behavior templates, traffic analysis,statistical-anomaly detection, and state-based detection. These systems have not matured to a level where sophisticated network-centric attacks are reliably detected, verified, and assessed.[2]Computer intrusion-detection systems were introduced in the mid-1980s to complement conventional approaches to computer security. IDS designers often cite Denning's[5] 1987 intrusion-detection model built on host-based subject profiles, systems objects, audit logs, anomaly records, and activity rules. The underlying ID construct is arules-based pattern-matching system whereby audit trails are matched against subject profiles to detect computer misuse based on logins, program executions, and file access. The subject-anomaly model was applied in the design of many host-based IDSes, among them Intrusion Detection Expert System (IDES)[7]; Network Intrusion Detection Expert System (NDIX)[9]; and Wisdom & Sense (W&S), Haystack, and Network Anomaly Detection and Intrusion Reporter (NADIR) [10]. Other ID systems are also based on the Denning model; an excellent survey of them may be found in Mukherjee et al.[6]. The basic detection algorithms used in these systems include:weighted functions to detect deviations from normal usage patterns qcovariance-matrix—based approaches for normal usage profiling qrules-based expert-systems approach to detect security eventsqThe second-leading technical approach to present-day intrusion detection is themulti-host network-based IDS. Heberlein et al. extended the Denning model to traffic analysis on Ethernet-based networks with the Network Security Monitor (NSM) framework[11]. This was further extended with the Distributed Intrusion Detection System (DIDS), which combined host-based intrusion detection with network-traffic monitoring[6, 8]. Current commercial IDSes such as Real Secure by ISS and Computer Misuse Detection System (CMDS) by SAIC have distributed architectures using either rules-based detection, statistical-anomaly detection, or both.A significant challenge remains for IDS designers to fuse sensor, threat, and situational information from numerous heterogeneous distributed agents, system managers, and databases. Coherent pictures that can be used by network controllers to visualize and evaluate the security of cyberspace is required. Next, we review the basic principles of the art and science of multisensor data fusion applied to future ID systems in Bass[2] and Bass[3] to create highly reliable next-generation intrusion-detection systems that identify, track, and assess complex threat situations.Internet Situational Data FusionIn a typical military command-and-control (C2) system, data-fusion sensors are used to observe electromagnetic radiation, acoustic and thermal energy, nuclear particles, infrared radiation, noise, and other signals. In cyberspace ID systems the sensors are different because the environmental dimension is different. Instead of a missile launch and supersonic transport through the atmosphere, cyberspace sensors observeinformation flowing in networks. However, just as C2 operational personnel are interested in the origin, velocity, threat, and targets of a warhead, network-security personnel are interested in the identity, rate of attacks, threats, and targets of malicious intruders and criminals[2]. Input into next-generation IDSes consists of sensor data, commands, and a priori data from established databases. For example, the system input would be data from numerous distributed packet sniffers, system log files, SNMP traps and queries, signature-based ID systems, user-profile databases, system messages, threat databases, and operator commands. (See Figure 4.)The output of fusion-based ID systems consists of estimates of the identity (and possibly the location) of a threat source, the malicious activity, taxonomy of the threats, the attack rates, and an assessment of the potential severity of damage to the projected target(s). We extrapolated from Waltz[12] to suggest possible generic sensor characteristics of next-generation network fusion systems[2]:Detection Performance is the detection characteristics — false-alarm rate, qdetection probabilities, and ranges — for an intrusion characteristic against agiven network-centric noise background. For example, when detecting malicious activity, nonmalicious activity is typically modelled as noise.Spatial/Temporal Resolution is the ability to distinguish between two or more qnetwork-centric objects in space or time.Spatial Coverage is the span of coverage, or field of view, of the sensor (i.e., the qspatial coverage of a system log file is the computer system processes and system calls being monitored).Detection/Tracking Mode is the mode of operation of the sensor (i.e., scanning, qsingle or multiple network object tracking).Target Revisit Rate is the rate at which a network object or event is revisited by qthe sensor to perform measurements.Measurement Accuracy is the statistical probability that the sensor measurement qor observation is accurate and reliable.Measurement Dimensionality is the number of measurement variables for network qobject categories.Hard vs. Soft Data Reporting is the decision status of the sensor reports. (I.e., can qa command decision be made without correlation, or does the sensor requireconfirmation?)Detection/Tracking Reporting is the characteristic of the sensor with regard to qreporting events. (Does the sensor maintain a time-sequence of the events? type of historical event buffers?)In our fusion model, situational data is collected from network sensors with elementary observation primitives; identifiers, times of observation, and descriptions. The raw data requires calibration and filtering, referred to as Data Refinement (short-term knowledge). Object Refinement is a process that correlates data in time (and space if required); the data is assigned appropriate weighted metrics. Observations may be associated, paired, and classified according to intrusion-detection primitives.Situation Refinement (mid-term knowledge) provides situational knowledge and awareness after objects have been aligned, correlated, and placed in context in an object base. Aggregated sets of objects are detected by their coordinated behavior, dependencies, common points of origin, common protocols, common targets, correlated attack rates, or other high-level attributes.In the interdomain construct of Figure 1, network objects and data flows will be identified and tracked by placing sensors at or between the interdomain gateways. Without going into the details, it can be shown that temporal resolution of the cyberspace situational awareness is directly proportional to the ratio of the transit time of the datagram and the sensory fusion process and inference time.As an analogy we offer the tracking of an object in aerospace — for example, a projectile. If the intercept time of a projectile is greater than the time used by radar or another tracking system and other required processing, then it is not possible to track and react to the object before the projectile hits the target. For example, if the datagram will reach its destination in 30ms, then the decision-fusion process required for network situational awareness must be much less than 30ms. Highly critical situational awareness can be achieved by networking the sensors (and optional command and control links) out-of-band. Current-generation systems use in-band processing, which can only achieve limited temporal resolution.Extensible Threat Taxonomy FusionThe number of IP packets processed by the Internet gateways of Figure 5 is enormous. Gateway sensors acquire and forward proportionally large amounts of data to packet analysis and correlation processes. For example, a router processing 100,000 packets per second on a high-speed interface, logging 14 bytes of information per packet, produces approximately 1.4 MBPS of data per sensor. It is clear that distributed sensors in network-centric IP fusion systems require local processing. Consequently, sensor output data should be reduced at the sensor to minimize central fusion processing and transport overhead costs.Figure 5. Gateway sensors on ID fusion networkWe focus here on the sensor output by outlining an example extensible taxonomy framework of TCP/IP-based threats. Antony[14] discusses database requirements for fusion system and situational knowledge. He states that knowledge is either declarativeor procedural. Declarative knowledge is passive factual knowledge or knowledge of relationships (e.g., files). Procedural knowledge is a special case of declarative knowledge represented as patterns, algorithms, and transformations.Entity relationships are the most fundamental declarative models for sensor data representation. Binaries trees, family trees, and general taxonomies are examples of the elemental database relationships required for situational analysis; the vast majority can be represented by the SQL command[14]:SELECT(attribute) FROM (table) WHERE (condition)With this basic database model and data-selection primitives in mind, we offered a framework TCP/IP threat taxonomy[3]. This framework was offered as an extensible context-dependent TCP/IP threat tree based on the SNMP management information base (MIB) concept. The SNMP MIB concept for representing context-dependent data is well suited for network-centric threats (and countermeasures).Threats to TCP/IP at the physical layer are service disruptions caused by natural disasters such as fires or flooding, cuts to cables, malfunctioning transceivers, and other hardware failures. Threats to the network layer include IP source-address spoofing and route-cache poisoning. An extensible context-dependent framework for this is illustrated in Figures 6, 7, and 8.Figure 6. Example TCP/IP threat subtreeFigure 7. Example IP transport threat subtreeFigure 8. Example TCP transport threat subtreeThree primary data flows (services) exist on the Internet: User Datagram Protocol (UDP), Transmission Control Protocol (TCP), and Internet Control Message Protocol (ICMP)[1]. Domain Name System (DNS) cache poisoning and UDP port-flooding denial-of-service attacks are examples of two vulnerabilities exploited using UDP services. The ping-of-death and ICMP redirect bombs are examples of Internet attacks based on ICMP. TCP vulnerabilities include TCP sequence number and SYN flood attacks, as illustrated in Figure 8.Security threats and countermeasures can be represented using the ASN.1 MIB notation. For example, a TCP SYN flood attack could be represented with the following OBJECT IDENTIFIER (OID):tcpSYNFlood OID ::= { iso 3.6.1.5.1.3.1.1 }Additional sub-object examples for tcpSYNFlood OID could be the source address or the target address of the malicious SYN packet and a counter with the number of SYN floods:tcpSYNFlood.source OID ::= { iso 3.6.1.5.1.3.1.1.1 } tcpSYNFlood.dest OID ::= { iso 3.6.1.5.1.3.1.1.1.2 } tcpSYNFlood.number OID ::= { iso 3.6.1.5.1.3.1.1.1.3 } Developing an extensible TCP/IP security threat MIB is a solid first step on the road to creating Internet ID fusion systems. Other long-term knowledge databases include context-dependent countermeasure, threat profiles, and attack-capabilities databases. ConclusionFuture reliable services that provide long-term threat, countermeasure, and other security-related information to fusion systems are similar to the current state of the art of weather forecasting and threat assessment. Fusion from multiple short-term sensors further processed with long-term knowledge creates short mid-term situational awareness. Situational awareness is required to operate and survive in a complex world with both friendly and hostile activities.All intelligent biological organisms fuse short-term and long-term knowledge to create situational awareness. Humans continually create and redefine systems that help us increase and refine our situational knowledge. These systems include air traffic control, battlefield management, early-warning systems, and robotics. There are strong indications, based on our work in both the Air Force and commercial industry, that future ID systems will shift toward more advanced fusion-based models.Our crystal ball is as foggy as yours, but if the developments in situational awareness systems in air traffic control over the past 40 years are any indication, then Internet traffic-control systems and next-generation intrusion-detection systems have a significant and challenging future in store for all of us.References[1] Stevens, R. TCP/IP Illustrated, Volume 1: The Protocols. Reading, MA:Addison-Wesley, 1994.[2] Bass, T. "Intrusion Detection Systems and Multisensor Data Fusion: Creating Cyberspace Situational Awareness." Communications of the ACM. Forthcoming, 1999.[3] Bass, T. "Multisensor Data Fusion for Next Generation Distributed Intrusion Detection Systems." 1999 IRIS National Symposium on Sensor and Data Fusion, May 1999.[4] Bass, T.; Freyre, A.; Gruber, D.; and Watt., G. "E-Mail Bombs and Countermeasures: Cyber Attacks on Availability and Brand Integrity." IEEE Network, March/April 1998, pp. 10-17.[5] Denning, D. "An Intrusion-Detection Model." IEEE Transactions on Software Engineering, February 1987, pp. 222-232.[6] Mukherjee, B.; Heberlein, L.; and Levitt, K. "Network Intrusion Detection." IEEE Network Magazine, May/June 1994, pp. 26-41.[7] Denning, D., et al. "A Prototype IDES: A Real Time Intrusion Detection Expert System." Computer Science Laboratory, SRI International, August 1987.[8] Snapp. S. et al. "A System for Distributed Intrusion Detection." Proceedings of IEEE COMPCON, March 1991, pp. 170-176.[9] Bauer, D. and Koblentz, M. "NDIX — An Expert System for Real-Time Network Intrusion Detection." Proceedings of the IEEE Computer Networking Symposium, April 1988, pp. 98-106.[10] Hochberg et al. "NADIR: An Automated System for Detecting Network Intrusion and Misuse." Computers & Security, Elsevier Science Publishers, 1993, pp. 235-248. [11] Heberlein, L. et al. "A Network Security Monitor." Proceedings of the IEEE Computer Society Symposium, Research in Security and Privacy, May 1990, pp.296-303.[12] Waltz, E., and Llinas, J. Multisensor Data Fusion. Boston: Artech House, 1990.[13] Waltz, E. Information Warfare Principles and Operations. Boston: Artech House, 1998.[14] Antony, R. Principles of Data Fusion Automation. Boston: Artech House, 1995.Need help? Use our Contacts page. Last changed: 16 Nov. 1999 mc Issue index;login: indexUSENIX home。

第39卷第8期自动化学报Vol.39,No.8 2013年8月ACTA AUTOMATICA SINICA August,2013一种基于最优未知输入观测器的故障诊断方法胡志坤1,2孙岩1姜斌2何静3张昌凡3摘要针对含有未知输入干扰和噪音的不确定动态系统,使用全阶未知输入观测器(Unknown input observer,UIO)来消除干扰项,实现状态估计,结合Kalman滤波器算法来求解状态反馈矩阵,以使得输出残差信号的协方差最小,从而增强系统对噪声的鲁棒性,实现了一种基于最优未知输入观测器的残差产生器.采用极大似然比(Generalized likelihood ratio,GLR)的方法对残差信号进行评估,通过设定的阈值来提高诊断率.最后以风力发电机组传动系统出现加性传感器故障和乘性传感器故障为例,进行了残差信号的仿真,仿真结果说明了该方法的有效性.关键词故障诊断,未知输入观测器,Kalman滤波器,极大似然比引用格式胡志坤,孙岩,姜斌,何静,张昌凡.一种基于最优未知输入观测器的故障诊断方法.自动化学报,2013,39(8): 1225−1230DOI10.3724/SP.J.1004.2013.01225An Optimal Unknown Input Observer Based Fault Diagnosis Method HU Zhi-Kun1,2SUN Yan1JIANG Bin2HE Jing3ZHANG Chang-Fan3Abstract A full-order unknown input observer(UIO)is employed for uncertain dynamic systems with unknown input interference and noise to eliminate the interference and achieve state estimation,combine with the Kalmanfilter algorithm to solve the state feedback matrix to minimum the covariance of the residual signal,so as to enhance the robustness of the system noise,thus an optimal unknown input observer is achieved as a residual generator.The threshold is designed based on the generalized likelihood ratio(GLR)method to evaluate the residual signals and achieve a high fault detection rate.Finally,the drive train system of the wind turbine with additive sensor faults and multiplicative sensor faults is used as an example.The residual signals are simulated and the results shows the effectiveness of the proposed method.Key words Fault detection,unknown input observer(UIO),Kalmanfilter,generalized likelihood ratio(GLR) Citation Hu Zhi-Kun,Sun Yan,Jiang Bin,He Jing,Zhang Chang-Fan.An optimal unknown input observer based fault diagnosis method.Acta Automatica Sinica,2013,39(8):1225−1230自20世纪70年代以来,基于模型的故障诊断方法一直受到学术界与工程应用领域研究人员的高度重视,利用现代控制理论,基于被监控过程的数学模型,研究出了各种故障诊断方法[1−3].基于解析模型的故障诊断方法利用系统精确的数学模型和可观测的输入输出量构造残差信号来反映系统期望行为与实际运行模式之间的不一致,然后,对残差信号进行分析,实现故障诊断[4].基于解析模型的故障诊断方法通常采用观测器技术,将观测器的输出值与系收稿日期2012-05-16录用日期2012-09-29Manuscript received May16,2012;accepted September29, 2012国家自然科学基金(61273159,61104024,60904077),中国博士后科学基金(2012M511752)资助Supported by National Natural Science Foundation of China (61273159,61104024,60904077),China Postdoctoral Science Foundation(2012M511752)本文责任编委王宏Recommended by Associate Editor WANG Hong1.中南大学物理与电子学院长沙4100832.南京航空航天大学自动化学院南京2100163.湖南工业大学电气工程学院株洲412001 1.School of Physics and Electronics,Central South Univer-sity,Changsha410083 2.College of Automation Engineering, Nanjing University of Aeronautics and Astronautics,Nanjing 210016 3.School of Electrics Engineering,Hunan University of Technology,Zhuzhou412001统实际输出值对比,产生残差信号,通过残差信号评估系统是否发生故障,其核心在于观测器的设计.由于在建模过程中总要做一些近似化,而且系统通常都存在一些未知的输入干扰,再加上环境中各种噪声的影响,都会直接影响到检测系统的性能指标,特别是会导致误报和系统的灵敏度降低.为了解决这一问题,自80年代末开始,人们就把研究的重点放在了基于观测器的残差产生器的鲁棒性上,并产生了一些理论的成果,如未知输入的故障诊断鲁棒性设计[5−6].在解耦干扰方面,未知输入方法已发展出了很多方法,如频域方法、未知输入故障检测滤波器(Unknown input fault detectfilter,UIFDF)方法、未知输入诊断观测器(Unknow input detect observer,UIDO)方法、几何方法等,Ding和Frank 在文献[7−8]中最早提出频域方法,用于解决未知输入干扰的解耦问题,几何方法则由Massoumnia 在文献[9]中最早提出的,但这些方法的实现方式复杂.在近几十年,UIDO方法在未知输入解耦方面得到的关注度最高,Chow等采用了等价空间法设计了未知输入观测器(Unknown input observer,1226自动化学报39卷UIO)[10],从此开始形成未知输入观测器的设计思想,在最近几年,在未知输入观测器的设计中,Frisk 等采用基于多项式分解的方法来解决干扰解耦的问题[11],李振营等[12]采用了一种全阶比例积分观测器的方法进行干扰解耦.但是在针对系统中既存在未知输入干扰,又存在噪声的情况,目前还很少有研究.针对系统和环境噪声的影响,Kalman滤波器作为一种高效率的递归滤波器,提供了一种高效可计算的方法来估计过程的状态,并使估计均方误差最小,是一种常用的用于滤除高斯白噪声的滤波器.但是由于Kalman滤波器达不到干扰解耦的作用,所以在系统中还存在未知输入干扰时,就很难应用于残差产生器中.针对系统存在未知干扰和噪声的情况下,通过配置伦伯格观测器的系数来达到解耦干扰且降低噪声的效果[13−14].近几年来,风力发电的发展速度非常快.然而,由于长期处于恶劣的天气条件,风力发电机组的传感器、执行器等极易发生卡死、偏移等故障.Odgaard等[15−16]建立了风力发电机的转换器系统和传动系统的控制模型,并采用基于Kalman滤波器的方法生产残差,进行故障诊断.但是,由于风力发电系统在极其恶劣的环境下运行,系统会受到严重的噪音干扰.而且由于风力发电系统的风速不稳定,使得其测量值不准确,会影响模型的精确度.综合实际的故障检测需求,即系统经常存在未知干扰的影响,但又不能避免高斯白噪声的影响,本文将未知输入观测器和Kalman滤波算法的优点结合起来,以文献[17]提出的一种三叶片水平轴风力发电机组的传动系统为对象,考虑到系统模型中存在由于风速测量误差带来的不确定性以及系统中不可避免的外界噪声,采用本文提出的最优未知输入观测器设计残差产生器,采用极大似然比(Generalized likelihood ratio,GLR)的方法来设定阈值,以判断系统是否确定发生故障.1优化未知输入观测器设计1.1未知输入观测器在不考虑系统噪声的情况下,一个带有未知输入干扰的线性时不变系统的状态空间方程为x(k+1)=Ax x(k)+Bu u(k)+E d d(k)y(k)=Cx x(k)(1)由上式可得:y(k+1)−CAx x(k)−CBu u(k)=CE d d(k)(2)在未知输入观测器的设计中,为了消除未知干扰的影响,首先,通过对干扰矢量进行重构,然后,在状态方程中通过重构的干扰项来解耦干扰,所以必须要满足rank(CE d)=rank(E d)=k d的条件下,才能达到完全重构干扰项的目的.在这样的条件下,存在M ce满足:M ce CE d=I kd×k d(3)用M ce同时乘式(2)的左右两边可得:M ce(y(k+1)−CAx x(k)−CBu u(k))=d(k)(4)因此,可以由上式估计出未知输入干扰d(k)的值:ˆd(k)=Mce(y(k+1)−CAx x(k)−CBu u(k))(5)根据输出y(k+1),对观测器进行干扰项的补偿,可以得到观测器的表达式为ˆx(k+1)=Aˆx(k)+Bu u(k)+E d M ce(y(k+1)−CAx x(k)−CBu u(k))+L(y(k)−Cˆx(k))(6)在上述的观测器方程中,无法事先知道y(k+1)的数值.为了解决这一问题,我们引入新的矩阵矢量来消掉y(k+1),令:z(k)=ˆx(k)−E d M ce y(k)(7)T=I−E d M ce C(8)将上述式子代入观测器方程(6)中可得:z(k+1)=Aˆx(k)+Bu u(k)−E d M ce CAx x(k)−E d M ce CBu u(k)+L(y(k)−Cˆx(k))=T Aˆx(k)+T Bu u(k)+Ly y(k)−LCˆx(k)=(T A−LC)z(k)+Ly y(k)+T Bu u(k)+(T A−LC)EdM ce y(k)(9)即可得观测器的方程为z(k+1)=(T A−LC)z(k)+T Bu u(k)+((T A−LC)E d M ce+L)y(k)ˆx(k)=z(k)+E d M ce y(k)(10)令F=T A−LC,G=T B,H=E d M ce,则观测器方程可以写为z(k+1)=Fz z(k)+Gu u(k)+(F H+L)y(k)ˆx(k)=z(k)+Hy y(k)(11)在上面观测器的设计过程中,可以看到,在不考虑系统噪声的情况下,系统中的干扰项已经可以通过对干扰项的重构过程得到补偿,达到干扰解耦的效果.然而,在实际系统中,噪声往往和干扰同时存在.8期胡志坤等:一种基于最优未知输入观测器的故障诊断方法12271.2反馈矩阵的设计在同时考虑干扰和噪声的情况下,离散系统的状态空间方程表示如下:x(k+1)=Ax x(k)+Bu u(k)+E d d(k)+ζ(k)y(k)=Cx x(k)+η(k)(12)式中,x(k)∈R n为状态向量,u(k)∈R q为控制输入向量,y(k)∈R p为系统输出向量,d(k)∈R m为干扰信号(未知输入向量),ζ(k)和η(k)是独立的零均值白噪声序列,其协方差矩阵分别为Q和R,矩阵A,B,C和E d是具有相应维数的系统矩阵.通常在未知输入观测器中,状态反馈矩阵L的选择只要满足使系统极点分配在左半平面,即系统为稳定系统即可,并没有考虑到系统噪声的影响.在本文的设计中,核心思想就是考虑到系统中存在的噪声信号,通过配置状态反馈矩阵L来减小噪声信号的影响.在式(11)的观测器表达式的基础上,残差信号可以表示为e(k+1)=x(k+1)−ˆx(k+1)=x(k+1)−(z(k+1)+Hy y(k+1))=(I−HC)x(k+1)−Hηη(k+1)−(Fz z(k)+Gu u(k)+(F H+L)y(k))=Fe e(k)−Lηη(k)+(I−HC)ζ(k)+((I−HC)A−F−LC)x(k)+(I−HC)E d d(k)−Hηη(k+1)+((I−HC)B−G)u(k)而设计的观测器满足:G=(I−HC)B,E d=HCE dF=(I−HC)A−LC所以残差信号可以表示为E(k+1)=Fe e(k)−Hηη(k+1)−Lηη(k)+(I−HC)ζ(k)(13)残差信号的协方差可以表示为p(k)=ε{(x(k)−ˆx(k))(x(k)−ˆx(k))T}为了简化计算,令A1=A−HCA=T A,则残差信号协方差的更新过程为p(k+1)=Fp p(k)F T+(I−HC)Q(I−HC)T+ HRH T+LRL T=(A1−LC)p(k)(A1−LC)T+LRL T+(I−HC)Q(I−HC)T+HRH T=A1p(k)A T1+(I−HC)Q(I−HC)T+HRH T−A1p(k)C T L T−LCp p(k)A T1+L(Cp p(k)C T+R)L T式中的Q和R分别为高斯白噪声ζ(k)和η(k)的协方差矩阵.因为R和Cp(k)C T都为正定矩阵,因而存在矩阵S使得SS T=CP C T+R,令D=A1p(k)C T(S T)−1,则协方差矩阵可以表示为p(k+1)=A1p(k)A T1+(I−HC)Q(I−HC)T+HRH T−A1p(k)C T L T−LCp p(k)A T1+L(Cp p(k)C T+R)L T=A1p(k)A T1+(I−HC)Q(I−HC)T+HRH T+(LS−d)(LS−d)T−DD T在上式中,如果LS−D=0,就可以使得残差信号的协方差矩阵达到最小,这样就可以得到:L=A1p(k)C T(Cp p(k)C+R)−1(14)此时,可以保证残差信号的协方差为最小:p(k+1)=A1p(k)A T1+(I−HC)Q(I−HC)T+ HRH T−DD T(15) DD T=LSS T L T=LSS T(A1p(k)C T(SS T)−1)T=LSS T(SS T)−1Cp p(k)A T1=LCp p(k)A T1将DD T=LCp p(k)A T1带入式(15)可得:p(k+1)=A1p(k)A T1+(I−HC)Q(I−HC)T+HRH T−LCp p(k)A T1(16)通过上面的推导过程,可以得出这种最优未知输入观测器的整个设计过程为:步骤1.检验系统是否满足式(3)中的条件,即rank(CE d)=rank(E d)=k d,如果满足,进行下一步;否则,停止计算.步骤2.根据式(3)和式(8)计算M ce,T.步骤3.根据式(14)和式(16)计算反馈矩阵L.步骤4.根据式(10)和式(11)构造出最优未知输入观测器.在上述推导过程中可以看出,最后得出的反馈矩阵和协方差矩阵的形式与标准卡尔曼滤波器算法是相同的,这也从另一方面说明了采用这种观测器可以将未知输入观测器和卡尔曼滤波算法的优点结合起来.另外,在实际应用中,如果面对数据量很大1228自动化学报39卷的情况,其反馈矩阵也可以通过直接求稳态卡尔曼滤波器系数的方法求出来,这样不但简化了计算过程,也降低了计算量.2故障检测与隔离考虑如下传感器故障模型:x(k+1)=Ax x(k)+Bu u(k)+E d d(k)+ζ(k)y(k)=Cx x(k)+F s(k)+η(k)(17)式中,F s(k)是未知传感器故障信号.利用公式计算得到状态估计值ˆx(k),可以计算出残差信号R(k)=y(k)−Cˆx(k)的幅值,来实现传感器系统故障的检测.理论上,在无故障时,残差r(k)应该近似为零,而当出现故障时,残差会偏离零值.由于实际中受系统建模精度的影响,无故障情形下的残差难于严格保持零值,故采用阈值门限的方法进行分析判断.考虑系统本身的噪音带来的随机性,采用极大似然比(GLR)来对残差信号进行评估,极大似然估计的表达式为J G(k)=1σ2R(k)2(18)其中,R(k)代表系统实际输出残差信号的方差,σ2表示系统在无故障时输出残差信号的方差,J G(k)服从自由度为1的χ2分布.设定误报率P f后,阈值T r就可以根据χ2分布表来确定:Probability{J G(k)>T r|fault−free}=P f(19)因此,在判定系统是否发生故障时,就可以根据以下逻辑进行判定:J G(k)>T r⇒faultyJ G(k)<T r⇒fault−free当检测出传动系统的控制系统传感器出现故障时,接下来就需要对传感器故障进行定位和隔离.在本文中,采用双传感器冗余的方法来进行故障隔离.在传动系统中,需要测量的变量为ωr和ωg.其中,ωr 为转子转速,ωg为发电机转速,其测得的值分别为ωr,i(i=1,2)和ωg,j(j=1,2).采用本文提出的方法在每个测量变量的2个测量位置分别建立2个优化未知输入观测器,故共用4个观测器,设为ΩUIO,γ,i和ΩUIO,g,j,则不同的残差产生器会产生4个残差队列Rγ,i(k)和r g,j(k),通过分析残差队列的逻辑状态,来完成传感器的故障隔离.4个不同的残差产生器在不同的ωγ,i和ωg,j的组合下可以写为zα,β(k+1)=Fz zα,β(k)+Gu u(k)+(F H+L)yα,β(k)ˆxα,β(k)=zα,β(k)+Hy yα,β(k)(20)式中,α=γ或α=g,β=i或β=j.即可根据式(20)得到状态估计,然后,计算出残差rγ,i(k)和R g,j(k),然后,获得通过式(18)和(19)分别计算J G,α,β和T r d,即可进行传感器故障的定位.3实例仿真采用文献[18]的风力发电机组的传动系统模型,对式(17)进行仿真,得到:A=−B d tJγB d tN g Jγ−K d tJγηd tB d tN g J g−ηηd t B d tN2gJ gηd tK d tN g J G1−1N gB=00−1J g00,E d=1Jγ0000C=100010,x(k)=ωγωgθ∆u(k)=τg,d=τrr(k)=y(k)−Cˆx(k),E d=1/J r,d=τr,其中,τr为转子的扭矩,其值要受到风速测量的影响,x=[ωγωgθ∆]T,ζ(k)和η(k)均值为0,协方差矩阵分别为Q=0.10000.10000.1,R=0.1000.1的高斯白噪声,ωr为转子转速,ωg为发电机转速,θ∆为扭转角,J r为低速轴的转动惯性,K d t为抗扭劲度,B d t为转矩(扭转)阻尼系数,N g为传动比(齿轮比),J g为高速轴转动的转动惯性,ηd t为传动系统的效率,θ∆(t)为传动系统的扭转角.设B d t=9.45N·ms,N g=95,K d t=2.7×109N·m,ηd t=0.97,ηd t2=0.92,J g=390N·ms2,Jγ=55×106N·ms2,将上述参数带入到系统模型中,可得其系统矩阵为A=−1.718×10−71.809×10−9−49.0912.474×10−4−2.604×10−6706.8831−0.010508期胡志坤等:一种基于最优未知输入观测器的故障诊断方法1229B =0002.564×10−300,C =100010E d = 1.818×10−800000在系统仿真中使用的故障信号如表1所示,其中w γ,m 为实际测得的转子转速.表1仿真中用到的故障信号Table 1The fault signal used in the simulation编号故障类型描述表现形式F1传感器故障ωγ,m,1=2(rad/s)固定值F2传感器故障w γ,m,2=1.05·w γ,m (rad/s)增益值在无故障时,采用上述算法进行仿真,得到的结果如图1所示.从仿真图中可以看出,普通的未知输入观测器的残差信号明显比本文提出的改进的未知输入观测器的幅值要大,容易误报警,这对于正确的故障诊断很不利.通过采用GLR 来对残差信号进行评估,选定误报率P f =0.0003,根据分布表得到阈值T r =13.0704,根据式(15),对上述传感器故障进行评估的仿真图如图2所示.图1无故障时系统的残差信号Fig.1The residual signal without fault图2所示是系统在t =100s 时,发生加性故障时的仿真图,从仿真图中可以看出,在t =100s,系统产生故障信号时,残差产生器仿真出来的残差信号明显比设置的阈值要大,即系统可以正确地隔离故障.对于乘性故障,在出现故障时残差信号会产生很大的变化,这种变化很不利于观察,所以将信号在时间轴上进行放大,系统在t =100∼150s 时,出现乘性故障时的残差信号如图3所示.从仿真图中可以看出来,在系统出现故障时,J G (k )明显大于阈值,表明可以正确地隔离故障.所以采用这种基于观测器和卡尔曼滤波器的故障诊断方法可以较好地达到故障诊断的效果,而且由于乘性故障信号在残差信号中表现得更加明显,所以可以更简单地进行故障的隔离.图2故障F1的GLR 估计和阈值对比Fig.2Comparing GLR estimation with threshold ofFaultF1图3故障F2的GLR 估计和阈值对比Fig.3Comparing GLR estimation with threshold ofFault F24结论在本文中,通过数学的方法推导证明了将卡尔曼滤波器和未知输入观测器结合所设计的残差产生器的鲁棒性更强,可以使残差信号更好地抑制噪声的影响,并可以达到隔离干扰的效果.同时,通过残差产生器对加性和乘性故障信号所产生的残差信号进行仿真,证明所设计的观测器可以达到将不同的故障信号进行隔离的目的.1230自动化学报39卷References1Ding S X.Model-based Fault Diagnosis Techniques:Design Schemes,Algorithms,and Tools.Berlin:Springer,2008.10−3432Zhou Dong-Hua,Hu Yan-Yan.Fault diagnosis techniques for dynamic systems.Acta Automatica Sinica,2009,35(6): 748−758(周东华,胡艳艳.动态系统的故障诊断技术.自动化学报,2009, 35(6):748−758)3Venkatasubramanian V,Rengaswamy R,Yin K,Kavuri S N.A review of process fault detection and diagnosis,Part I: quantitative model-based puters and Chemi-cal Engineering,2003,27(3):293−3114Patton R J,Chen J,Nielsen S B.Model-based methods for fault diagnosis:some guide-lines.Transactions on the Institute of Measurement and Control,1995,17(2):73−83 5Zhou Dong-Hua,Ye Hao,Wang Gui-Zeng.Discussion of some important issues of observer based fault diagnosis tech-nique.Acta Automatica Sinica,1998,24(3):338−344(周东华,叶昊,王桂增.基于观测器方法的故障诊断技术若干重要问题的探讨.自动化学报,1998,24(3):338−344)6Chen J,Patton R J.Robust Model-based Fault Diagnosis for Dynamic Systems.London:Kluwer Academic Publishers, 1999.10−2007Ding X C,Frank P M.Fault detection via factorization ap-proach.Systems&Control Letters,1990,14(5):431-436 8Frank P M,Ding X C.Frequency domain approach to opti-mally robust residual generation and evaluation for model-based fault diagnosis.Automatica,1994,30(5):789−904 9Massoumnia M A.A geometric approach to the synthesis of failure detectionfilters.IEEE Transactions on Automatic Control,1986,31(9):839−84610Chow E Y,Willsky A S.Analytical redundancy and the design of robust failure detection system.IEEE Transactions on Automatic Control,1984,29(7):603−61411Frisk E,Nyberg M.A minimal polynomial basis solution to residual generation for fault diagnosis in linear systems.Automatica,2001,37(9):1417−142412Li Zhen-Ying,Shen Yi,Hu Heng-Zhang.Design of observers for system with unknown inputs.Acta Aeronautica Et As-tronautica Sinica,2000,21(5):471−473(李振营,沈毅,胡恒章.具有未知输入干扰的观测器设计.航空学报,2000,21(5):471−473)13Wang H,Daley S.Actuator fault diagnosis:an adaptive observer-based technique.IEEE Transactions on Automat-ics Control,1996,41(7):1073−107814Jiang Bin,Mao Ze-Hui,Yang Hao,Zhang You-Min.Fault Diagnosis and Fault Regulation of Control System.Beijing: National Defence Industry Press,2009.51−153(姜斌,冒泽慧,杨浩,张友民.控制系统的故障诊断与故障调节.北京:国防工业出版社,2009.51−153)15Odgaard P F,Stoustrup J.Unknown input observer based scheme for detecting faults in a wind turbine converter.In: Proceedings of the7th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes.Barcelona, Spain:IFAC,2009.162−16616Odgaard P F,Stoustrup J,Nielsen R.Observer based de-tection of sensor faults in wind turbines.In:Proceedings of the2009European Wind Energy Conference.Marseille, France,2009.1−1017Odgaard P F,Stousturp J,Kinnaert M.Fault tolerant con-trol of wind turbines—a benchmark model.In:Proceedings of the7th IFAC Symposium on Fault Detection Supervision and Safety of Technical Processes.Barcelona,Spain:IFAC, 2009.155−16018Seiler P,Bokor J,Vanek B,Balas G J.Robust model match-ing for geometric fault detectionfilters.In:Proceedings of the2011American Control Conference.San Francisco,USA: IEEE,2011.226−231胡志坤中南大学物理与电子学院副教授.主要研究方向为复杂过程在线监测与故障诊断.本文通信作者.E-mail:************.cn(HU Zhi-Kun Associate professorat the School of Physics and Electron-ics,Central South University.His re-search interest covers online monitoring and fault diagnosis for complex technical process.Corre-sponding author of this paper.)孙岩中南大学物理与电子学院硕士研究生.主要研究方向为计算机测控技术与故障诊断.E-mail:*****************(SUN Yan Master student at theSchool of Physics and Electronics,Cen-tral South University.Her researchinterest covers computer measurement and fault diagnosis theory.)姜斌南京航空航天大学自动化学院教授.主要研究方向为故障诊断与容错控制.E-mail:*****************.cn(JIANG Bin Professor at the Col-lege of Automation Engineering,Nan-jing University of Aeronautics and As-tronautics.His research interest coversfault diagnosis and fault tolerant con-trol.)何静湖南工业大学教授.主要研究方向为机电系统和工业过程控制.E-mail:*********************(HE Jing Professor at HunanUniversity of Technology.Her researchinterest covers fault diagnosis onmechatronics and industrial processcontrol.)张昌凡湖南工业大学教授.主要研究方向为电机故障诊断和工业过程制.E-mail:*********************(ZHANG Chang-Fan Professor atHunan University of Technology.Hisresearch interes covers fault diagnosison electric machines and industrial pro-cess control.)。

信号接收与检测算法信号接收与检测算法是用于从接收到的信号中提取信息和判断所传递信息的算法。

这些算法在无线通信、雷达、无线传感器网络等领域中起着关键作用。

以下是一些常见的信号接收与检测算法：匹配滤波器（Matched Filter）：用于在噪声环境中检测目标信号，将接收信号与预先已知的信号模板进行匹配，从而提高信号的信噪比。

能量检测（Energy Detection）：在无法确定信号波形的情况下，通过测量接收信号的能量来判断是否存在信号。

适用于低信噪比环境。

协方差矩阵检测（Covariance Matrix Detection）：用于多天线接收系统中，通过计算接收信号的协方差矩阵来进行信号检测，适用于多径衰落信道。

信号特征提取：提取信号的特征，如频率、相位、幅度等，然后使用这些特征进行信号分类和检测。

最小均方误差检测（Minimum Mean Square Error Detection）：利用统计学方法，通过最小化均方误差的方法来进行信号检测，可以适用于多样的信号情况。

信号假设测试（Hypothesis Testing）：根据事先建立的假设，比较接收信号在不同假设下的概率，选择最可能的假设。

贝叶斯检测（Bayesian Detection）：基于贝叶斯定理，结合事先知识和接收信号信息，进行信号检测和估计。

循环相关检测（Cyclostationary Detection）：适用于周期性信号，通过分析接收信号的循环自相关性来进行信号检测。

机器学习方法：使用机器学习算法，如神经网络、支持向量机等，对接收信号进行学习和分类，适用于复杂的信号环境。

这些算法根据不同的应用和信号情况有不同的适用性。

在实际应用中，根据信道环境、信号特性以及噪声情况，选择合适的信号接收与检测算法非常重要。

基于相关系数的两级盲频谱感知算法包志强;徐笑【摘要】针对盲频谱感知检测概率低下的问题,提出一种多天线系统基于相关系数的两级感知算法.首先,通过多天线系统获得采样协方差矩阵获得相关系数;其次,用最大和最小相关系数作第一级检测的两个检验统计量;最后,对双门限之间的部分重新构造新的检验统计量进行第二级检测.蒙特卡罗仿真的结果表明,在采样次数较少的情况下,尤其是在低信噪比条件下,随着用户的增加,检测性能更优,与传统的双门限检测算法相比,不需要增加采样次数,节省运算成本.%Aiming at the problem of low probability of blind spectrum sensing detection,a tw o level spec-trum sensing algorithm based on correlation coefficient for multi-antenna system is proposed.Firstly,the corre-lation coefficient is obtained by sampling the covariance matrix of multi-antenna system.Secondly,take the maximum and minimum correlation coefficients as the first detection statistics.Finally,make the seconde detec-tion by reconstructing the new test statistics between the threshold.Monte Carlo simulation shows that in the case of few sampling times,especially in low signal to noiseratio(SNR)conditions,with the increase of the number of users,the detection performance is pared with the traditional double threshold detection, the algorithm does not need to increase the number of sampling time and it saves operation cost.【期刊名称】《系统工程与电子技术》【年(卷),期】2018(040)005【总页数】5页(P1124-1128)【关键词】盲频谱感知;协方差矩阵;相关系数【作者】包志强;徐笑【作者单位】西安邮电大学通信与信息工程学院,陕西西安710121;西安邮电大学通信与信息工程学院,陕西西安710121【正文语种】中文【中图分类】TN9250 引言无线通信中的认知无线电(cognitive radio,CR)[1-2]被普遍认为是解决当前频谱资源紧张的核心问题。

修正的干扰噪声自相关矩阵重构波束形成算法丛凤翔;王伟;魏东兴【摘要】为改善采样自相关矩阵求逆( SMI)算法中期望信号存在于接收信号所引起的性能下降，提出一种修正干扰噪声自相关矩阵重构( CMR)算法。

该算法首先选取采样自相关矩阵特征分解的最小特征值对应的特征向量构造空间分布系数，再对其在非期望信号波达方向上进行累加实现矩阵的重构。

当存在相干信号时，可采取先利用特征向量元素对协方差矩阵进行托普利兹化处理实现解相干，再进行矩阵重构的托普利兹矩阵重构( TCMR)算法。

计算机仿真与实验结果证明适用于非相干信号条件下的CMR算法与适用于相干信号条件下的TCMR算法具有更好的输出性能。

%To improve the performance reduction of sample matrix inversion( SMI) algorithm as the desired signal exists in training data,a modified interference-plus-noise covariance matrix reconstructing( CMR) algorithm is proposed in this paper. The algorithm firstly uses the eigenvector corresponding to the mini-mum eigenvalue of the sample autocovariance matrix to structure the space distribution coefficient,and then accumulates it on the range except the direction of the desired signal to reconstruct the interference-plus-noise covariance matrix. In the presence of coherent signals,the element in the max eigenvector can be uti-lized to make the covariance matrix a Toeplitz matrix,and then the CMR algorithm( Toeplitz CMR,TCMR) can be used. Simulation and experiment results demonstrate that the CMR algorithm applied in incoherent signal circumstance and the TCMR algorithm applied in coherent signal circumstance have better output performance.【期刊名称】《电讯技术》【年(卷),期】2014(000)005【总页数】5页(P584-588)【关键词】波束形成;特征空间分解;自相关矩阵重构;相干信号;托普利兹矩阵【作者】丛凤翔;王伟;魏东兴【作者单位】大连理工大学信息与通信工程学院，辽宁大连116024;解放军66440部队，石家庄050081;大连理工大学信息与通信工程学院，辽宁大连116024【正文语种】中文【中图分类】TN911.7波束形成算法是阵列信号处理领域的主要研究内容，在雷达、声纳、地震勘测以及移动通信领域得到了迅速发展和广泛应用［1］，算法按类别可以分为利用信号先验知识的盲波束形成算法以及需要导频信号或波达方向角（Direction of Arrival，DOA）的非盲算法［2］。

认知无线电中基于阵列天线和协方差矩阵的频谱感知算法赵晓晖;李晓燕【期刊名称】《电子与信息学报》【年(卷),期】2014(36)7【摘要】该文提出一种基于阵列天线和协方差矩阵的频谱感知算法，该算法能够在噪声不确定性的条件下进行盲频谱感知。

该算法在协方差矩阵的基础上，构建新的检测统计量，推导判决门限，对检测统计量与判决门限进行比较进而做出最终判决；在主用户信号到达方向与认知用户接收天线法线方向不一致的情况下，为使认知用户能完全接收主用户信号，利用了阵列天线技术。

仿真结果表明，与Zeng等人(2009)提出的绝对值协方差矩阵频谱感知算法(Covariance Absolute Value Spectrum Sensing, CAVSS)相比，该算法判决门限的计算方法更加准确；在相同条件下，该算法的检测概率高于CAVSS。

%A spectrum sensing algorithm based on covariance matrix and array antenna is reported. It can perform blind spectrum sensing under a condition of uncertainty noise. The new test statistics for spectrum sensing based on the covariance matrix is constructed and the decision threshold based on the test statistics is derived, thus allowing the comparison of the test statistics with the decision threshold to make a final decision. In order to enable cognitive users to fully receive signals of cognitive primary user in the case that the arrival direction of primary signal and the receiving antenna of cognitive users is not consistent, this algorithm applies array antenna to the spectrum sensing based on covariance matrix. Simulation results show thatthe performance of the proposed spectrum sensing algorithm is superior to the Covariance Absolute Value Spectrum Sensing (CAVSS) algorithm proposed by Zeng (2009).【总页数】6页(P1693-1698)【作者】赵晓晖;李晓燕【作者单位】吉林大学通信工程学院长春 130012;吉林大学通信工程学院长春130012【正文语种】中文【中图分类】TN929.5【相关文献】1.基于非理想感知的认知无线电系统感知时间与频谱分配联合优化算法 [J], 任丙印;许光飞;王大鸣;胡捍英2.利用协方差矩阵信息的多天线频谱感知算法 [J], 毛翊君;赵知劲;沈雷;王海泉3.认知无线电中一种基于秩准则的鲁棒多天线盲频谱感知算法 [J], 张军;杨喜;王向明4.认知无线电中基于压缩感知的非重构频谱检测算法 [J], 安爽; 邵建华5.认知无线电中基于机器学习的频谱感知算法研究 [J], 胡浩;屈少晶因版权原因，仅展示原文概要，查看原文内容请购买。

方差的计算简式如式（2）所示。

火灾图像特征的处理
图1 算法模型
3.2 基于支持向量机的隧道火灾识别系统
基于支持向量机的隧道火灾识别系统的主要流程分为以下几点：
第一，红外图像特征的提取。

对红外图像进行预处理和分割，并根据上文给出的两个特征描述子进行提取
图2 SVM分类器运行结果
（2）分类结果评价。

运行结果如图3所示。

图3 分类结果评价
从上面的测试正确率结果来看，该分类器能够在大量的样本识别训练后，在投入隧道火灾识别应用环境中也能得到较为不错的结果。

实验结果表明，该隧道火灾识别系统通过采集红外图像进行识别能够有效地排除掉以上干扰源对火焰识别精准度的影响，满足对实际应用中的精准度要求。

从结果正确率数值来看，正确率为93.66%，还存在需要改进完善的地方。

经过对算法以及样本的反复分析，导致SVM分类器识别性能不完善的原因可能有以下几点：（1）实验样本的本质不是可燃物在真实隧道环境下产生的火灾火焰。

（2）火灾训练样本存在着干扰源影响了识别的精准度。

（3）火灾特征的选择未能完全地反映火灾的所有信息。

5 结语
从理论上分析了隧道火灾的演变过程、火灾红外热
曳引式电梯轮槽磨损与检验检测的分析。

学术报告复合高斯海杂波背景下的最优及近最优相参恒虚警目标检测由中国电子学会主办，中国电子学会雷达分会和雷达信号处理国家重点实验室承办的“2021 CIE国际雷达会议”于2021年12月15日至20日在海南省海口市亚特国际会议中心酒店召开。

西安电子科技大学许述文教授于12月17日在会上做了题为《Optimum and near-optimum coherent CFAR detection of radar targets in compound-Gaussian sea clutter》的报告。

报告简介In this report, we propose optimum and near-optimum adaptive coherent detectors of radar targets in compound-Gaussian clutter with generalized inverse Gaussian texture. The target amplitude and the speckle covariance matrix are modeled as unknown quantities to be estimated. On the basis of the two-step generalized likelihood ratio test (GLRT) and the estimate of the speckle covariance matrix, the optimum coherent detector and its adaptive version are designed. It is demonstrated that the proposed optimum coherent detector contains three common detectors, which are the optimum K detector (OKD), the generalized likelihood ratio test linear-threshold detector (GLRT-LTD), and the generalized likelihood ratio test detector for compound-Gaussian clutter with inverse Gaussian texture (GLRT-IG). The proposed near-optimum coherent detector contains two common detectors, the GLRT-LTD and the alpha-MF detector in K-distributed clutter, and has a comparable detection performance of the near-optimum detector in CG-IG clutter which was proposed before. Theoretical analysis and numerical experiments illustrate that the proposed two detectors for CG-GIG clutter have the constant false alarm ratio (CFAR) property relative to the estimate of the speckle covariance matrix and Doppler steering vector. Moreover, the detection performance of the two coherent detectors are evaluated by the simulated and real data.报告PPT本报告PPT共35张。

smn是什么意思_单词解释SMN是一个多义词：1.英语单词;2. SDH管理子网(SDH management network);3. 全称School Multifunction Networkservice，是亿龙公司推出的教育管理、交流网络服务开放性集成平台。

英语单词SMNabbr. spinal motor neurons 脊髓运动神经元;sonic motor nucleus 声运动核;survival of motor neuron 运动神经元生存率;supravital micronucleus 超生[命]微核双语例句以下例句来源于网络，仅供参考1 After considering some characteristics of the SMN, we consider a new type of network growing protocol: local-preference connecting protocol.本文提出了一个生长机制&amp;局部优先连接机制，并用这个机制构造了一个生长网络模型。

2 Objective To investigate the relationship between survival motor neuron ( SMN) gene and the clinical features of childhood spinal muscular atrophy ( SMA).目的探讨运动神经元存活基因与儿童期脊肌萎缩症临床特征的关系。

3 The diagnosis value of SMN gene deletions in progressive spinal muscular atrophy运动神经元存活基因对进行性脊肌萎缩症的诊断价值4 Detection of SMN gene deletions in spinal muscular atrophy脊肌萎缩症基因缺失的初步研究5 Effects of Ultraviolet on Human SMn Fibroblasts紫外线对人皮肤成纤维细胞的影响6 Systems with Multiplicative Noises ( SMN) universally exist in many application fields, such as oil seismic exploration, underwater remote targets detection, engineering of telecommunication and speech signal processing, etc.带乘性噪声系统普遍存在于石油地震勘探、水下目标探测、通讯工程和语音处理等诸多应用领域。

pca的使用方法和注意事项-回复Principal Component Analysis (PCA) is a widely used technique for dimensionality reduction and data visualization in various fields such as statistics, machine learning, and signal processing. In this article, we will discuss the methods and considerations involved in using PCA.1. Introduction to PCA:Principal Component Analysis is a statistical technique that transforms a dataset into a new coordinate system, where the first axis represents the direction of maximum variance in the data. This axis is called the first principal component (PC), and subsequent PCs represent orthogonal directions with decreasing variance. The main objective of PCA is to find a low-dimensional representation of high-dimensional data while preserving important patterns or structures in the data.2. Steps to perform PCA:The PCA algorithm consists of several steps, as outlined below:Step 1: Data PreprocessingPreprocessing the data is an essential step in PCA. Firstly, ensurethat the data is in numerical format. If there are categorical variables, they need to be encoded as numerical values using techniques like one-hot encoding or label encoding. Secondly, standardize or normalize the data if necessary. PCA is sensitive to the scale of the features, so scaling the data to have zero mean and unit variance can help in obtaining better results.Step 2: Covariance Matrix CalculationNext, calculate the covariance matrix of the standardized data. The covariance matrix measures the relationship between pairs of variables and is crucial for determining the principal components. The covariance between two variables x and y is given by the formula:cov(x, y) = Σ((x[i] - mean(x)) * (y[i] - mean(y))) / (n - 1)where x[i] and y[i] represent the values of x and y for each data sample, and n is the number of data samples.Step 3: Eigenvalue DecompositionPerform eigenvalue decomposition on the covariance matrix to obtain its eigenvectors and eigenvalues. The eigenvectorsrepresent the directions along which the data vary the most, while the eigenvalues denote the amount of variance explained by each eigenvector. This decomposition can be done using various numerical methods, such as the power method or singular value decomposition (SVD).Step 4: Selecting Principal ComponentsSort the eigenvalues in descending order and choose the top k eigenvectors corresponding to the largest eigenvalues as the principal components. These k eigenvectors constitute the new coordinate system in which the data will be projected. Generally, the number of principal components chosen depends on the cumulative explained variance, which is the sum of the eigenvalues and represents the proportion of the total variance explained by each PC.Step 5: Projecting Data onto Principal ComponentsFinally, project the original data onto the selected principal components to obtain the reduced-dimensional representation. The projection can be calculated by multiplying the standardized data matrix with the matrix formed by stacking the selected eigenvectors column-wise. This projection will result in a newdataset with fewer dimensions, where each dimension represents a principal component.3. Considerations when using PCA:When utilizing PCA, there are several important considerations to keep in mind:Data Interpretability: PCA creates a linear combination of the original features, which may make the resulting components less interpretable. It is crucial to ensure that the derived components make sense in the context of the problem at hand.Explained Variance: The cumulative explained variance helps determine the number of principal components to retain. It is essential to strike a balance between dimensionality reduction and retained information. Choosing too few components may result in significant loss of information, while selecting too many may lead to overfitting.Outliers: PCA is sensitive to outliers as they can heavily influence the estimation of covariance matrix and the subsequent principal components. It is advisable to handle outliers appropriately, suchas using robust PCA or outlier detection techniques, to ensure accurate results.Data Scaling: Scaling the data to have zero mean and unit variance is generally recommended. However, if the data has a meaningful scale, such as physical measurements, it may be appropriate to skip this step.Linear Assumption: PCA assumes a linear relationship between variables. If the data contains highly nonlinear relationships, nonlinear dimensionality reduction techniques like Kernel PCA may be more suitable.4. Applications of PCA:PCA has numerous applications, including data visualization, feature extraction, and noise reduction. In data visualization, PCA can be used for projecting high-dimensional data onto alower-dimensional space to facilitate visualization and exploration. In feature extraction, PCA can be employed to transform a large number of features into a smaller set of uncorrelated features, reducing computational complexity and improving model performance. Additionally, PCA can be used for noise reduction byremoving components with low eigenvalues, assuming that noise has a relatively smaller impact on these components.In conclusion, PCA is a powerful technique for dimensionality reduction and data visualization, with broad applications across various fields. By following the outlined steps and considering important factors, users can effectively leverage PCA to extract valuable insights and better understand complex datasets.。