Adaptive Robust Estimation of Model Parameters from Block Motion Vectors

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国际自动化与计算杂志.英文版.

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Robust Control and Estimation

Robust Control and Estimation Robust control and estimation are critical aspects of engineering and technology, particularly in the field of automation and control systems. These concepts are essential for ensuring the stability, performance, and reliability of complex systems in the presence of uncertainties and disturbances. Robust control and estimation techniques play a crucial role in various applications, including aerospace, automotive, robotics, manufacturing, and many others. One of the primary challenges in control and estimation is dealing with uncertainties in the system. These uncertainties can arise from various sources, such as modeling errors, external disturbances, sensor noise, and environmental changes. Robust control and estimation techniques are designed to address these uncertainties and ensure that the system behaves as intended under all operating conditions. This is particularly important in safety-critical applications, where the consequences of system failure can be severe. From a control perspective, robust control techniques aim to design controllers that can effectively handle uncertainties and variations in the system. This typically involves formulating control laws that are robust to uncertainties, such as H-infinity control, mu-synthesis, and robust model predictive control. These techniques are based on the idea of worst-case analysis, where the controller is designed to perform well under the most adverse conditions. This ensures that the system remains stable and meets performance requirements, even in the presence of uncertainties. On the other hand, robust estimation techniques are concerned with accurately estimating the state of the system in the presence of uncertainties and disturbances. This is essential for feedback control, where the state estimates are used to compute the control actions. Robust estimation methods, such as Kalman filtering, robust observers, and adaptive estimation, aim to provide accurate and reliable state estimates, even in the presence of noisy measurements and modeling errors. This is crucialfor ensuring the effectiveness of the control system and maintaining the desired performance. In addition to addressing uncertainties, robust control and estimation techniques also play a crucial role in ensuring the stability and performance of networked control systems. With the increasing integration of communication networks in control systems, there is a need to develop techniquesthat can effectively deal with network-induced delays, packet losses, and communication constraints. Robust control and estimation methods for networked control systems are designed to mitigate the effects of these issues and ensure the overall system stability and performance. Furthermore, the development of autonomous systems and artificial intelligence has brought new challenges to robust control and estimation. Autonomous systems, such as self-driving cars and unmanned aerial vehicles, require robust control and estimation techniques to ensure safe and reliable operation in dynamic and uncertain environments. Similarly, the integration of artificial intelligence in control systems introduces new uncertainties and complexities that need to be addressed through robust techniques. In conclusion, robust control and estimation are essential for ensuring the stability, performance, and reliability of complex systems in the presence of uncertainties and disturbances. These techniques play a crucial role in various applications, including aerospace, automotive, robotics, manufacturing, networked control systems, and autonomous systems. As technology continues to advance, the development of new robust control and estimation techniques will be essential for addressing the emerging challenges and ensuring the effectiveness of future control systems.。

军事通信装备PHM系统设计研究贾冠男

军事通信装备PHM系统设计研究贾冠男发布时间：2021-10-22T03:10:26.495Z 来源：《现代电信科技》2021年第10期作者：贾冠男潘申富[导读] PHM技术是提高军事通信装备可靠性和维修保障效率的有效途径。

本文开展了军事通信装备PHM系统设计研究，阐述了PHM技术的概念和内涵，设计了军事通信装备PHM系统的系统架构和工作流程，分析了其中的关键技术及实现方案，提出了军事通信装备PHM系统设计的几点建议。

（中国电子科技集团公司第五十四研究所河北石家庄 050081）摘要：PHM技术是提高军事通信装备可靠性和维修保障效率的有效途径。

关键词：军事通信装备，预测与健康管理，故障诊断，可靠性，维修保障A study of PHM system design for military communication equipmentAbstract：PHM is an effective method to improve the reliability and maintenance support efficiency of the military communication equipment. This paper focused on the study of the PHM system design for the military communication equipment. The concept and content of PHM were expounded，and the architecture and workflow of the military communication equipment’s PHM system were designed. Further，an analysis about key technologies and their solutions in this study was demonstrated. Finally，some suggestions for the PHM system design in the military communication equipment were propounded.Keywords：military communication equipment，PHM，fault diagnosis，reliability，maintenance support1 引言军事通信装备是构建战场网络信息体系的基础装备，在现代战争中发挥着至关重要的作用。

adaptive control

Desired Performance ComparisonDecision
Adaptation Mechanism
Performance Measurement
Adaptation scheme
Adaptive Control – Landau, Lozano, M’Saad, Karimi
Adaptive Control versus Conventional Feedback Control
y
u
Plant
Desired Performance
Adaptation Scheme
Reference Controller
u
Plant
y
An adaptive control structure
Remark: An adaptive control system is nonlinear since controller parameters will depend upon u and y
Adaptive Control – Landau, Lozano, M’Saad, Karimi
Conventional Control – Adaptive Control - Robust Control
Conventional versus Adaptive
Conventional versus Robust
Adaptive Control – Landau, Lozano, M’Saad, Karimi
Conceptual Structures
Desired Performance Controller Design Method Plant Model

matlab工具箱安装教程

1.1 如果是Matlab安装光盘上的工具箱，重新执行安装程序，选中即可；1.2 如果是单独下载的工具箱，一般情况下仅需要把新的工具箱解压到某个目录。

2 在matlab的file下面的set path把它加上。

3 把路径加进去后在file→Preferences→General的Toolbox Path Caching里点击update Toolbox Path Cache更新一下。

4 用which newtoolbox_command.m来检验是否可以访问。

如果能够显示新设置的路径，则表明该工具箱可以使用了。

把你的工具箱文件夹放到安装目录中“toolbox”文件夹中，然后单击“file”菜单中的“setpath”命令，打开“setpath”对话框，单击左边的“ADDFolder”命令，然后选择你的那个文件夹，最后单击“SAVE”命令就OK了。

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This gives all the power of objects (reusability, plug together, share code) but also all the power of Matlab for machine learning research.http://www.kyb.tuebingen.mpg.de/bs/people/spider/index.htmlSchwarz-Christoffel Toolbox/matlabcentral/fileexchange/loadFile.do?objectId=1316&objectT ype=file#XML Toolbox/matlabcentral/fileexchange/loadFile.do?objectId=4278&object Type=fileFIR/TDNN Toolbox for MATLABBeta version of a toolbox for FIR (Finite Impulse Response) and TD (Time Delay) NeuralNetworks./interval-comp/dagstuhl.03/oish.pdfMisc.http://www.dcsc.tudelft.nl/Research/Software/index.htmlAstronomySaturn and Titan trajectories ... MALTAB astronomy/~abrecht/Matlab-codes/AudioMA Toolbox for Matlab Implementing Similarity Measures for Audiohttp://www.oefai.at/~elias/ma/index.htmlMAD - Matlab Auditory Demonstrations/~martin/MAD/docs/mad.htmMusic Analysis - Toolbox for Matlab : Feature Extraction from Raw Audio Signals for Content-Based Music Retrihttp://www.ai.univie.ac.at/~elias/ma/WarpTB - Matlab Toolbox for Warped DSPBy Aki Härmä and Matti Karjalainenhttp://www.acoustics.hut.fi/software/warp/MATLAB-related Softwarehttp://www.dpmi.tu-graz.ac.at/~schloegl/matlab/Biomedical Signal data formats (EEG machine specific file formats with Matlab import routines)http://www.dpmi.tu-graz.ac.at/~schloegl/matlab/eeg/MPEG Encoding library for MATLAB Movies (Created by David Foti)It enables MATLAB users to read (MPGREAD) or write (MPGWRITE) MPEG movies. That should help Video Quality project.Filter Design packagehttp://www.ee.ryerson.ca:8080/~mzeytin/dfp/index.htmlOctave by Christophe COUVREUR (Generates normalized A-weigthing, C-weighting, octave and one-third-octave digital filters)/matlabcentral/fileexchange/loadFile.do?objectType=file&object Id=69Source Coding MATLAB Toolbox/users/kieffer/programs.htmlBio Medical Informatics (Top)CGH-Plotter: MATLAB Toolbox for CGH-data AnalysisCode: http://sigwww.cs.tut.fi/TICSP/CGH-Plotter/Poster: http://sigwww.cs.tut.fi/TICSP/CSB2003/Posteri_CGH_Plotter.pdfThe Brain Imaging Software Toolboxhttp://www.bic.mni.mcgill.ca/software/MRI Brain Segmentation/matlabcentral/fileexchange/loadFile.do?objectId=4879Chemometrics (providing PCA) (Top)Matlab Molecular Biology & Evolution Toolbox(Toolbox Enables Evolutionary Biologists to Analyze and View DNA and Protein Sequences) James J. 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P.)http://webpages.ull.es/users/sympbst/pag_ing/pag_metmap/index.htmDoseLab - A set of software programs for quantitative comparison of measured and computed radiation dose distributions/GenBank Overview/Genbank/GenbankOverview.htmlMatlab: /matlabcentral/fileexchange/loadFile.do?objectId=1139CodingCode for the estimation of Scaling Exponentshttp://www.cubinlab.ee.mu.oz.au/~darryl/secondorder_code.htmlControl (Top)Control Tutorial for Matlab/group/ctm/AnotherCommunications (Top)Channel Learning Architecture toolbox(This Matlab toolbox is a supplement to the article "HiperLearn: A High Performance Learning Architecture")http://www.isy.liu.se/cvl/Projects/hiperlearn/Source Coding MATLAB Toolbox/users/kieffer/programs.htmlTCP/UDP/IP Toolbox 2.0.4/matlabcentral/fileexchange/loadFile.do?objectId=345&objectT ype=fileHome Networking Basis: Transmission Environments and Wired/Wireless Protocols Walter Y. Chen/support/books/book5295.jsp?category=new&language=-1MATLAB M-files and Simulink models/matlabcentral/fileexchange/loadFile.do?objectId=3834&object Type=file•OPNML/MATLAB Facilities/OPNML_Matlab/Mesh Generation/home/vavasis/qmg-home.htmlOpenFEM : An Open-Source Finite Element Toolbox/CALFEM is an interactive computer program for teaching the finite element method (FEM)http://www.byggmek.lth.se/Calfem/frinfo.htmThe Engineering Vibration Toolbox/people/faculty/jslater/vtoolbox/vtoolbox.htmlSaGA - Spatial and Geometric Analysis Toolboxby Kirill K. Pankratov/~glenn/kirill/saga.htmlMexCDF and NetCDF Toolbox For Matlab-5&6/staffpages/cdenham/public_html/MexCDF/nc4ml5.htmlCUEDSID: Cambridge University System Identification Toolbox/jmm/cuedsid/Kriging Toolbox/software/Geostats_software/MATLAB_KRIGING_TOOLBOX.htmMonte Carlo (Dr Nando)http://www.cs.ubc.ca/~nando/software.htmlRIOTS - The Most Powerful Optimal Control Problem Solver/~adam/RIOTS/ExcelMATLAB xlsheets/matlabcentral/fileexchange/loadFile.do?objectId=4474&objectTy pe=filewrite2excel/matlabcentral/fileexchange/loadFile.do?objectId=4414&objectTy pe=fileFinite Element Modeling (FEM) (Top)OpenFEM - An Open-Source Finite Element Toolbox/NLFET - nonlinear finite element toolbox for MATLAB ( framework for setting up, solving, and interpreting results for nonlinear static and dynamic finite element analysis.)/GetFEM - C++ library for finite element methods elementary computations with a Matlabinterfacehttp://www.gmm.insa-tlse.fr/getfem/FELIPE - FEA package to view results ( contains neat interface to MATLA/~blstmbr/felipe/Finance (Top)A NEW MATLAB-BASED TOOLBOX FOR COMPUTER AIDED DYNAMIC TECHNICAL TRADINGStephanos Papadamou and George StephanidesDepartment of Applied Informatics, University Of Macedonia Economic & Social Sciences, Thessaloniki, Greece/fen31/one_time_articles/dynamic_tech_trade_matlab6.htm Paper: :8089/eps/prog/papers/0201/0201001.pdfCompEcon Toolbox for Matlab/~pfackler/compecon/toolbox.htmlGenetic Algorithms (Top)The Genetic Algorithm Optimization Toolbox (GAOT) for Matlab 5/mirage/GAToolBox/gaot/Genetic Algorithm ToolboxWritten & distributed by Andy Chipperfield (Sheffield University, UK)/uni/projects/gaipp/gatbx.htmlManual: /~gaipp/ga-toolbox/manual.pdfGenetic and Evolutionary Algorithm Toolbox (GEATbx)/Evolutionary Algorithms for MATLAB/links/ea_matlab.htmlGenetic/Evolutionary Algorithms for MATLABhttp://www.systemtechnik.tu-ilmenau.de/~pohlheim/EA_Matlab/ea_matlab.html GraphicsVideoToolbox (C routines for visual psychophysics on Macs by Denis Pelli)/VideoToolbox/Paper: /pelli/pubs/pelli1997videotoolbox.pdf4D toolbox/~daniel/links/matlab/4DToolbox.htmlImages (Top)Eyelink Toolbox/eyelinktoolbox/Paper: /eyelinktoolbox/EyelinkToolbox.pdfCellStats: Automated statistical analysis of color-stained cell images in Matlabhttp://sigwww.cs.tut.fi/TICSP/CellStats/SDC Morphology Toolbox for MATLAB (powerful collection of latest state-of-the-art gray-scale morphological tools that can be applied to image segmentation, non-linear filtering, pattern recognition and image analysis)/Image Acquisition Toolbox/products/imaq/Halftoning Toolbox for MATLAB/~bevans/projects/halftoning/toolbox/index.htmlDIPimage - A Scientific Image Processing Toolbox for MATLABhttp://www.ph.tn.tudelft.nl/DIPlib/dipimage_1.htmlPNM Toolboxhttp://home.online.no/~pjacklam/matlab/software/pnm/index.htmlAnotherICA / KICA and KPCA (Top)ICA TU Toolboxhttp://mole.imm.dtu.dk/toolbox/menu.htmlMISEP Linear and Nonlinear ICA Toolboxhttp://neural.inesc-id.pt/~lba/ica/mitoolbox.htmlKernel Independant Component Analysis/~fbach/kernel-ica/index.htmMatlab: kernel-ica version 1.2KPCA- Please check the software section of kernel machines.KernelStatistical Pattern Recognition Toolboxhttp://cmp.felk.cvut.cz/~xfrancv/stprtool/MATLABArsenal A MATLAB Wrapper for Classification/tmp/MATLABArsenal.htmMarkov (Top)MapHMMBOX 1.1 - Matlab toolbox for Hidden Markov Modelling using Max. Aposteriori EM Prerequisites: Matlab 5.0, Netlab. Last Updated: 18 March 2002./~parg/software/maphmmbox_1_1.tarHMMBOX 4.1 - Matlab toolbox for Hidden Markov Modelling using Variational Bayes Prerequisites: Matlab 5.0,Netlab. Last Updated: 15 February 2002../~parg/software/hmmbox_3_2.tar/~parg/software/hmmbox_4_1.tarMarkov Decision Process (MDP) Toolbox for MatlabKevin Murphy, 1999/~murphyk/Software/MDP/MDP.zipMarkov Decision Process (MDP) Toolbox v1.0 for MATLABhttp://www.inra.fr/bia/T/MDPtoolbox/Hidden Markov Model (HMM) Toolbox for Matlab/~murphyk/Software/HMM/hmm.htmlBayes Net Toolbox for Matlab/~murphyk/Software/BNT/bnt.htmlMedical (Top)EEGLAB Open Source Matlab Toolbox for Physiological Research (formerly ICA/EEG Matlabtoolbox)/~scott/ica.htmlMATLAB Biomedical Signal Processing Toolbox/Toolbox/Powerful package for neurophysiological data analysis ( Igor Kagan webpage)/Matlab/Unitret.htmlEEG / MRI Matlab Toolbox/Microarray data analysis toolbox (MDAT): for normalization, adjustment and analysis of gene expression_r data.Knowlton N, Dozmorov IM, Centola M. Department of Arthritis and Immunology, Oklahoma Medical Research Foundation, Oklahoma City, OK, USA 73104. We introduce a novel Matlab toolbox for microarray data analysis. This toolbox uses normalization based upon a normally distributed background and differential gene expression_r based on 5 statistical measures. The objects in this toolbox are open source and can be implemented to suit your application. AVAILABILITY: MDAT v1.0 is a Matlab toolbox and requires Matlab to run. MDAT is freely available at:/publications/2004/knowlton/MDAT.zipMIDI (Top)MIDI Toolbox version 1.0 (GNU General Public License)http://www.jyu.fi/musica/miditoolbox/Misc. (Top)MATLAB-The Graphing Tool/~abrecht/matlab.html3-D Circuits The Circuit Animation Toolbox for MATLAB/other/3Dcircuits/SendMailhttp://carol.wins.uva.nl/~portegie/matlab/sendmail/Coolplothttp://www.reimeika.ca/marco/matlab/coolplots.htmlMPI (Matlab Parallel Interface)Cornell Multitask Toolbox for MATLAB/Services/Software/CMTM/Beolab Toolbox for v6.5Thomas Abrahamsson (Professor, Chalmers University of Technology, Applied Mechanics,Göteborg, Sweden)http://www.mathworks.nl/matlabcentral/fileexchange/loadFile.do?objectId=1216&objectType =filePARMATLABNeural Networks (Top)SOM Toolboxhttp://www.cis.hut.fi/projects/somtoolbox/Bayes Net Toolbox for Matlab/~murphyk/Software/BNT/bnt.htmlNetLab/netlab/Random Neural Networks/~ahossam/rnnsimv2/ftp: ftp:///pub/contrib/v5/nnet/rnnsimv2/NNSYSID Toolbox (tools for neural network based identification of nonlinear dynamic systems) http://www.iau.dtu.dk/research/control/nnsysid.htmlOceanography (Top)WAFO. Wave Analysis for Fatigue and Oceanographyhttp://www.maths.lth.se/matstat/wafo/ADCP toolbox for MATLAB (USGS, USA)Presented at the Hydroacoustics Workshop in Tampa and at ADCP's in Action in San Diego /operations/stg/pubs/ADCPtoolsSEA-MAT - Matlab Tools for Oceanographic AnalysisA collaborative effort to organize and distribute Matlab tools for the Oceanographic Community /Ocean Toolboxhttp://www.mar.dfo-mpo.gc.ca/science/ocean/epsonde/programming.htmlEUGENE D. GALLAGHER(Associate Professor, Environmental, Coastal & Ocean Sciences)/edgwebp.htmOptimization (Top)MODCONS - a MATLAB Toolbox for Multi-Objective Control System Design/mecheng/jfw/modcons.htmlLazy Learning Packagehttp://iridia.ulb.ac.be/~lazy/SDPT3 version 3.02 -- a MATLAB software for semidefinite-quadratic-linear programming .sg/~mattohkc/sdpt3.htmlMinimum Enclosing Balls: Matlab Code/meb/SOSTOOLS Sum of Squares Optimi zation Toolbox for MATLAB User’s guide/sostools/sostools.pdfPSOt - a Particle Swarm Optimization Toolbox for use with MatlabBy Brian Birge ... A Particle Swarm Optimization Toolbox (PSOt) for use with the Matlab scientific programming environment has been developed. PSO isintroduced briefly and then the use of the toolbox is explained with some examples. A link to downloadable code is provided.Plot/software/plotting/gbplot/Signal Processing (Top)Filter Design with Motorola DSP56Khttp://www.ee.ryerson.ca:8080/~mzeytin/dfp/index.htmlChange Detection and Adaptive Filtering Toolboxhttp://www.sigmoid.se/Signal Processing Toolbox/products/signal/ICA TU Toolboxhttp://mole.imm.dtu.dk/toolbox/menu.htmlTime-Frequency Toolbox for Matlabhttp://crttsn.univ-nantes.fr/~auger/tftb.htmlVoiceBox - Speech Processing Toolbox/hp/staff/dmb/voicebox/voicebox.htmlLeast Squared - Support Vector Machines (LS-SVM)http://www.esat.kuleuven.ac.be/sista/lssvmlab/WaveLab802 : the Wavelet ToolboxBy David Donoho, Mark Reynold Duncan, Xiaoming Huo, Ofer Levi /~wavelab/Time-series Matlab scriptshttp://wise-obs.tau.ac.il/~eran/MATLAB/TimeseriesCon.htmlUvi_Wave Wavelet Toolbox Home Pagehttp://www.gts.tsc.uvigo.es/~wavelets/index.htmlAnotherSupport Vector Machine (Top)MATLAB Support Vector Machine ToolboxDr Gavin CawleySchool of Information Systems, University of East Anglia/~gcc/svm/toolbox/LS-SVM - SISTASVM toolboxes/dmi/svm/LSVM Lagrangian Support Vector Machine/dmi/lsvm/Statistics (Top)Logistic regression/SAGA/software/saga/Multi-Parametric Toolbox (MPT) A tool (not only) for multi-parametric optimization. http://control.ee.ethz.ch/~mpt/ARfit: A Matlab package for the estimation of parameters and eigenmodes of multivariate autoregressive modelshttp://www.mat.univie.ac.at/~neum/software/arfit/The Dimensional Analysis Toolbox for MATLABHome: http://www.sbrs.de/Paper: http://www.isd.uni-stuttgart.de/~brueckner/Papers/similarity2002.pdfFATHOM for Matlab/personal/djones/PLS-toolbox/Multivariate analysis toolbox (N-way Toolbox - paper)http://www.models.kvl.dk/source/nwaytoolbox/index.aspClassification Toolbox for Matlabhttp://tiger.technion.ac.il/~eladyt/classification/index.htmMatlab toolbox for Robust Calibrationhttp://www.wis.kuleuven.ac.be/stat/robust/toolbox.htmlStatistical Parametric Mapping/spm/spm2.htmlEVIM: A Software Package for Extreme Value Analysis in Matlabby Ramazan Gençay, Faruk Selcuk and Abdurrahman Ulugulyagci, 2001.Manual (pdf file) evim.pdf - Software (zip file) evim.zipTime Series Analysishttp://www.dpmi.tu-graz.ac.at/~schloegl/matlab/tsa/Bayes Net Toolbox for MatlabWritten by Kevin Murphy/~murphyk/Software/BNT/bnt.htmlOther: /information/toolboxes.htmlARfit: A Matlab package for the estimation of parameters and eigenmodes of multivariate autoregressive models/~tapio/arfit/M-Fithttp://www.ill.fr/tas/matlab/doc/mfit4/mfit.htmlDimensional Analysis Toolbox for Matlab/The NaN-toolbox: A statistic-toolbox for Octave and Matlab®... handles data with and without MISSING VALUES.http://www-dpmi.tu-graz.ac.at/~schloegl/matlab/NaN/Iterative Methods for Optimization: Matlab Codes/~ctk/matlab_darts.htmlMultiscale Shape Analysis (MSA) Matlab Toolbox 2000p.br/~cesar/projects/multiscale/Multivariate Ecological & Oceanographic Data Analysis (FATHOM)From David Jones/personal/djones/glmlab (Generalized Linear Models in MATLA.au/staff/dunn/glmlab/glmlab.htmlSpacial and Geometric Analysis (SaGA) toolboxInteresting audio links with FAQ, VC++, on the topic机器学习网站北京大学视觉与听觉信息处理实验室北京邮电大学模式识别与智能系统学科复旦大学智能信息处理开放实验室IEEE Computer Society北京映象站点计算机科学论坛机器人足球赛模式识别国家重点实验室南京航空航天大学模式识别与神经计算实验室- PARNEC南京大学机器学习与数据挖掘研究所- LAMDA南京大学人工智能实验室南京大学软件新技术国家重点实验室人工生命之园数据挖掘研究院微软亚洲研究院中国科技大学人工智能中心中科院计算所中科院计算所生物信息学实验室中科院软件所中科院自动化所中科院自动化所人工智能实验室ACL Special Interest Group on Natural Language Learning (SIGNLL)ACMACM Digital LibraryACM SIGARTACM SIGIRACM SIGKDDACM SIGMODAdaptive Computation Group at University of New MexicoAI at Johns HopkinsAI BibliographiesAI Topics: A dynamic online library of introductory information about artificial intelligence Ant Colony OptimizationARIES Laboratory: Advanced Research in Intelligent Educational SystemsArtificial Intelligence Research in Environmental Sciences (AIRIES)Austrian Research Institute for AI (OFAI)Back Issues of Neuron DigestBibFinder: a computer science bibliography search engine integrating many other engines BioAPI ConsortiumBiological and Computational Learning Center at MITBiometrics ConsortiumBoosting siteBrain-Style Information Systems Research Group at RIKEN Brain Science Institute, Japan British Computer Society Specialist Group on Expert SystemsCanadian Society for Computational Studies of Intelligence (CSCSI)CI Collection of BibTex DatabasesCITE, the first-stop source for computational intelligence information and services on the web Classification Society of North AmericaCMU Advanced Multimedia Processing GroupCMU Web->KB ProjectCognitive and Neural Systems Department of Boston UniversityCognitive Sciences Eprint Archive (CogPrints)COLT: Computational Learning TheoryComputational Neural Engineering Laboratory at the University of FloridaComputational Neurobiology Lab at California, USAComputer Science Department of National University of SingaporeData Mining Server Online held by Rudjer Boskovic InstituteDatabase Group at Simon Frazer University, CanadaDBLP: Computer Science BibliographyDigital Biology: about creating artificial lifeDistributed AI Unit at Queen Mary & Westfield College, University of LondonDistributed Artificial Intelligence at HUJIDSI Neural Networks group at the Université di Firenze, ItalyEA-related literature at the EvALife research group at DAIMI, University of Aarhus, Denmark Electronic Research Group at Aberdeen UniversityElsevierComputerScienceEuropean Coordinating Committee for Artificial Intelligence (ECCAI)European Network of Excellence in ML (MLnet)European Neural Network Society (ENNS)Evolutionary Computing Group at University of the West of EnglandEvolutionary Multi-Objective Optimization RepositoryExplanation-Based Learning at University of Illinoise at Urbana-ChampaignFace Detection HomepageFace Recognition Vendor TestFace Recognition HomepageFace Recognition Research CommunityFingerpassftp of Jude Shavlik's Machine Learning Group (University of Wisconsin-Madison)GA-List Searchable DatabaseGenetic Algorithms Digest ArchiveGenetic Programming BibliographyGesture Recognition HomepageHCI Bibliography Project contain extended bibliographic information (abstract, key words, table of contents, section headings) for most publications Human-Computer Interaction dating back to 1980 and selected publications before 1980IBM ResearchIEEEIEEE Computer SocietyIEEE Neural Networks SocietyIllinois Genetic Algorithms Laboratory (IlliGAL)ILP Network of ExcellenceInductive Learning at University of Illinoise at Urbana-ChampaignIntelligent Agents RepositoryIntellimedia Project at North Carolina State UniversityInteractive Artificial Intelligence ResourcesInternational Association of Pattern RecognitionInternational Biometric Industry AssociationInternational Joint Conference on Artificial Intelligence (IJCAI)International Machine Learning Society (IMLS)International Neural Network Society (INNS)Internet Softbot Research at University of WashingtonJapanese Neural Network Society (JNNS)Java Agents for Meta-Learning Group (JAM) at Computer Science Department, Columbia University, for Fraud and Intrusion Detection Using Meta-Learning AgentsKernel MachinesKnowledge Discovery MineLaboratory for Natural and Simulated Cognition at McGill University, CanadaLearning Laboratory at Carnegie Mellon UniversityLearning Robots Laboratory at Carnegie Mellon UniversityLaboratoire d'Informatique et d'Intelligence Artificielle (IIA-ENSAIS)Machine Learning Group of Sydney University, AustraliaMammographic Image Analysis SocietyMDL Research on the WebMirek's Cellebration: 1D and 2D Cellular Automata explorerMIT Artificial Intelligence LaboratoryMIT Media LaboratoryMIT Media Laboratory Vision and Modeling GroupMLNET: a European network of excellence in Machine Learning, Case-based Reasoning and Knowledge AcquisitionMLnet Machine Learning Archive at GMD includes papers, software, and data sets MIRALab at University of Geneva: leading research on virtual human simulationNeural Adaptive Control Technology (NACT)Neural Computing Research Group at Aston University, UKNeural Information Processing Group at Technical University of BerlinNIPSNIPS OnlineNeural Network Benchmarks, Technical Reports,and Source Code maintained by Scott Fahlman at CMU; source code includes Quickprop, Cascade-Correlation, Aspirin/Migraines Neural Networks FAQ by Lutz PrecheltNeural Networks FAQ by Warren S. SarleNeural Networks: Freeware and Shareware ToolsNeural Network Group at Department of Medical Physics and Biophysics, University ofNeural Network Group at Université Catholique de LouvainNeural Network Group at Eindhoven University of TechnologyNeural Network Hyperplane Animator program that allows easy visualization of training data and weights in a back-propagation neural networkNeural Networks Research at TUT/ELENeural Networks Research Centre at Helsinki University of Technology, FinlandNeural Network Speech Group at Carnegie Mellon UniversityNeural Text Classification with Neural NetworksNonlinearity and Complexity HomepageOFAI and IMKAI library information system, provided by the Department of Medical Cybernetics and Artificial Intelligence at the University of Vienna (IMKAI) and the Austrian Research Institute for Artificial Intelligence (OFAI). It contains over 36,000 items (books, research papers, conference papers, journal articles) from many subareas of AI OntoWeb: Ontology-based information exchange for knowledge management and electronic commercePortal on Neural Network ForecastingPRAG: Pattern Recognition and Application Group at University of CagliariQuest Project at IBM Almaden Research Center: an academic website focusing on classification and regression trees. Maintained by Tjen-Sien LimReinforcement Learning at Carnegie Mellon UniversityResearchIndex: NECI Scientific Literature Digital Library, indexing over 200,000 computer science articlesReVision: Reviewing Vision in the Web!RIKEN: The Institute of Physical and Chemical Research, JapanSalford SystemsSANS Studies of Artificial Neural Systems, at the Royal Institute of Technology, Sweden Santa-Fe InstituteScirus: a search engine locating scientific information on the InternetSecond Moment: The News and Business Resource for Applied AnalyticsSEL-HPC Article Archive has sections for neural networks, distributed AI, theorem proving, and a variety of other computer science topicsSOAR Project at University of Southern CaliforniaSociety for AI and StatisticsSVM of ANU CanberraSVM of Bell LabsSVM of GMD-First BerlinSVM of MITSVM of Royal Holloway CollegeSVM of University of SouthamptonSVM-workshop at NIPS97TechOnLine: TechOnLine University offers free online courses and lecturesUCI Machine Learning GroupUMASS Distributed Artificial Intelligence LaboratoryUTCS Neural Networks Research Group of Artificial Intelligence Lab, Computer Science Department, University of Texas at AustinVivisimo Document Clustering: a powerful search engine which returns clustered results Worcester Polytechnic Institute Artificial Intelligence Research Group (AIRG)Xerion neural network simulator developed and used by the connectionist group at the University of TorontoYale's CTAN Advanced Technology Center for Theoretical and Applied Neuroscience ZooLand: Artificial Life Resource。

统计学英语词汇

统计学专业词汇英语翻译Abbe-Helmert criterion Abbe-Helmert准则美、英、加标准(美军标准105D) ABC standard (MIL-STD-105D) 非常态曲线abnormal curve非常态性abnormality简易生命表abridged life table突出分布；突出分配abrupt distribution绝对连续性absolute continuity绝对离差absolute deviation绝对离势absolute dispersion绝对有效性absolute efficiency估计量的绝对有效性absolute efficiency of estimator绝对误差absolute error在线英语学习绝对次数absolute frequency绝对测度absolute measure绝对动差absolute moment绝对常态计分检定absolute normal score test绝对临界absolute threshold绝对变异absolute variation绝对不偏估计量absolutely unbiased estimator吸收界限absorbing barrier吸收状态absorbing state吸收系数absorption coefficient吸收分布absorption distributions吸收律absorption law加速因子accelerated factor加速寿命试验accelerated life test加速随机逼近accelerated stochastic approximation 加速试验accelerated test乘幂加速近似acceleration by powering允收制程水准acceptable process level允收品质acceptable quality允收品质水准acceptable quality level (AQL)允收可靠度水准acceptable reliability level (ARL)允收；验收acceptance接受界限；允收界线acceptance boundary允收系数acceptance coefficient允收管制图acceptance control chart允收管制界限acceptance control limit接受准则；允收准则acceptance criterion允收误差acceptance error允收检验acceptance inspection允收界限acceptance limit允收界线acceptance line允收数acceptance number接受域；允收域acceptance region允收抽样acceptance sampling属性允收抽样；计数值允收抽样acceptance sampling by attributes 属量允收抽样；计量值允收抽样acceptance sampling by variables 允收抽样计画acceptance sampling plan允收抽样方案；允收抽样计画acceptance sampling scheme允收检定；验收检定acceptance testing允收值acceptance value接受区；允收区acceptance zone接近时间；故障诊断时间access time在线英语学习接近性；故障诊断性accessibility可达界限点accessible boundary point可达点accessible point事故统计accident statistics偶然误差accidental error偶然波动accidental fluctuation偶然移动accidental movement偶然变异accidental variation国民所得帐accounts of national income 累积离差accumulated deviation累积次数accumulated frequency累积过程accumulated process准确度；准确性accuracy估计准确度accuracy of estimation取得成本acquisition cost行动action行动空间action space主动备便active standby实际次数actual frequency实际数actual number实际值actual value保险精算师actuary适应性adaptability适应控制adaptive control适应估计adaptive estimation适应估计量adaptive estimator适应推论adaptive inference适应的M型估计量adaptive M-estimator 适应最适性adaptive optimization适应品质管制adaptive quality control适应的R型估计量adaptive R-estimator适应值adaptive value适应的截尾平均数adaptively trimmed mean累积寿命期addition of life length机率加法法则addition rule of probability加法(随机漫步)过程；可加(随机漫步)过程additive (random walk) process 加法函数additive function加法模型additive model加法运算additive operation可加性additive property加法定理additive theorem可加性双向配置；可加性双因子配置additive two-way lay-out在线英语学习可加性additivity平均数可加性additivity of means可加性检定additivity test附着机率adherent probabilities伴随矩阵adjoint matrix调整平均数adjusted average调整判定系数adjusted coefficient of determination调整平均数adjusted mean调整值adjusted value调整因子；调整系数adjustment factor链比的修正adjustment of chain relatives行政时间administrative time可容性admissibility贝氏估计量的可容性admissibility of Bayes estimator可容决策函数admissible decision function可容决策规则admissible decision rule可容设计admissible design可容估计量admissible estimator可容假设admissible hypothesis可容数admissible number可容区域admissible region可容策略admissible strategy可容检定admissible test采用值adopted value仿射α可分解性affine α-resolvability仿射性affinity年龄构成age composition年龄相依生死过程age dependent birth and death process 年龄分布age distribution年龄组age group老年幼年比aged-child ratio年龄相依生死过程age-dependent birth and death process年龄相依分支过程age-dependent branching process年龄别性别死亡率age-sex specific death rate年龄别死亡率age-specific death rate年龄别生育率age-specific fertility rate综合指数aggregate index number总市值aggregate market value总面值aggregate par value综合值加权法aggregate-value method of weighting总合aggregation综合指数aggregative index在线英语学习总合模型aggregative model老化指数aging index老化过程aging process农业灾害统计agricultural damage statistics农业劳动生产力指数agricultural labor productivity index农业土地生产力指数agricultural land productivity index农产品产地价格agricultural prices at farm gate农业生产指数agricultural production indices农、林、渔、牧、狩猎工作人员agricultural;forestry and fishery workers;animal producers;hunters and trappers农业普查agriculture census农业人口agriculture population农业生产统计agriculture production statistics农、林、渔、牧业普查agriculture;forestry;fishing;livestock censuses 标的精度aimed precisionAitken estimator Aitken估计量Ajne‘s An test Ajne的An检定随机变数aleatory variable演算法algorithm假名；别名alias假次数aliased frequencies余相关alienation余相关系数alienation coefficient列线图alignment chart所有可能回归法all possible regression配置allocation样本配置allocation of a sample可靠度配置allocation of reliability异峰度的allokurtic异峰度曲线allokurtic curre可允许缺点allowable defects几乎可容决策函数almost admissible decision function几乎到处收敛almost certain convergence几乎必然地almost certainly几乎等变异数almost equivariance几乎到处almost everywhere几乎到处收敛almost everywhere convergence几乎到处收敛almost sure convergence几乎必然地almost surely欧特(Alter)周期图Alter periodiagram交替更新过程alternating renewal process对立假设alternative hypothesis组间变异among class variation在线英语学习资讯量amount of information检验量amount of inspection幅度amplitude幅比amplitude ratio娱乐指数amusement index娱乐统计amusement statistics类比计算机analogue computer类比analogy分析图analysis chart属性资料分析；计数资料分析analysis of attribute data相关分析analysis of correlation互变异分析analysis of covariance (ANCOVA) 互变异分析模型analysis of covariance model 互变异分析表analysis of covariance table离势分析analysis of dispersion平均数分析analysis of means回归分析analysis of regression允差分析analysis of tolerance不确定性分析analysis of uncertainty变异性分析analysis of variability变异数分析模型analysis of variance model 变异数分析analysis of variance (ANOVA)变异数分析表analysis of variance table分析回归；解析回归analytic regression解析调查analytic survey分析趋势analytic trend分析误差analytical error分析表analytical table辅助ancillarity辅助概度ancillarity likelihood辅助估计量ancillary estimator辅助讯息ancillary information辅助统计量ancillary statisticAnderson-Darling statistic Anderson-Darling统计量Anderson‘s classification statistic Anderson分类统计量Andrews‘Fourier-type plot Andrews的Fourier型描点图角变换angular transformation角变数angular variables异类分布anisotropic distribution年减量annual decrement年增量annual increment年总增加率annual rate of total increase在线英语学习岁入与岁出annual receipts arid outlays不等偏态的anomicAnosov‘s theorem Anosov定理Ansari-Bradley dispersion test Ansari-Bradley离势检定反众数antimode反秩anti-rank反数列antiseries对立变换antithetic transforms对立变量antithetic variates反向回归函数；逆序回归函数antitonic regression function 非周期状态aperiodic state应用统计学applied statistics鉴定成本；评估成本appraisal cost品质评估appraisal of quality评估制度appraisal system近似误差approximate error近似F分布；近似F分配approximate F-distribution近似常态性approximate normality实验设计的近似理论approximate theory of experimental designs 近似变异数approximate variance近似；逼近approximation近似误差approximation error逼近理论approximation theory水产养殖统计aquaculture statistics随意性arbitrariness暂定平均数arbitrary average暂定平均数arbitrary mean暂定原点arbitrary origin暂定尺度arbitrary scale反正弦分布；反正弦分配arc sine distribution反正弦变换arc sine transformation地区长条图area bar chart地区图area chart地区比较因子area comparability factor地区图解area diagram地区图area graph地区样本area sample地区抽样area samplingArfwedson distribution Arfwedson分布；Arfwedson分配算术平均数arithmetic average算术交叉arithmetic cross算术图arithmetic graph在线英语学习算术线图arithmetic line chart算术平均数arithmetic mean算术机率纸arithmetic probability paper算术尺度arithmetic scaleArmitage‘s restricted procedure Armitage受制程序Arnold distribution Arnold分布；Arnold分配序列；阵array序列分布；序列分配array distribution到达分布；到达分配arrival distribution人工智慧artificial intelligence (AI)拟变数artificial variable递增因素ascending factor递增次序ascending order确定误差ascertainment error试验；分析assay装配检验assembly inspection评估可靠度assessed reliability评估值assessed value可寻原因assignable cause可寻变异assignable variation指派模型assignment model指派问题assignment problem可相联设计associable design相联组associate class相联二元随机变数associated binary random variables 相联元件associated components相联因变数associated dependent variable相联因子组associated factor sets时间相联的associated in time相联随机变数associated random variables相联变量associated variate相联处理associates相联association相联分析association analysis相联系数association coefficient属性相联association of attributes相联方案association scheme相联表association table假定平均数assumed average假定平均数assumed mean假定中位数assumed median假定原点assumed origin在线英语学习假设；前提assumption品质保证assurance quality显著性的星标asterisk for significance天文统计astronomical statistics不对称分布；不对称分配asymmetrical distribution 不对称因子设计asymmetrical factorial design不对称检定asymmetrical test不对称截尾平均数asymmetrically trimmed mean 不对称性asymmetry渐近线asymptote渐近贝氏程序asymptotic Bayes procedure渐近偏误asymptotic bias渐近分布；渐近分配asymptotic distribution概度比率的渐近分布；概度比率的渐近分配asymptotic distribution of likelihood ratio最大概度估计量渐近分布；最大概度估计量渐近分配asymptotic distribution of maximum likelihood estimator渐近效率asymptotic efficiency贝式估计量渐近效率asymptotic efficiency of Bayes estimators渐近展开式asymptotic expansion动差渐近展开式asymptotic expansion of moments渐近推论asymptotic inference渐近平均值asymptotic mean渐近大中取小性质asymptotic minimax property渐近常态性asymptotic normality顺序统计量的渐近常态性asymptotic normality of order statistics最大概度估计量的渐近最适性asymptotic optimality of maximum likelihood estimator渐近检力asymptotic power尼曼－皮逊检定的渐近检力asymptotic power of Neyman-Pearson (N-P)test均匀最强力检定的渐近检力asymptotic power of uniformly most powerful test渐近相对效率asymptotic relative efficiency渐近标准误差asymptotic standard error渐近理论asymptotic theory渐近变异数asymptotic variance渐近有效估计量asymptotically efficient estimator渐近局部最适设计asymptotically locally optimal design渐近最强力检定asymptotically most powerful test渐近最短不偏信赖区间asymptotically shortest unbiased confidence interval 渐近平稳的asymptotically stationary渐近次大中取小的asymptotically subminimax渐近不偏估计量asymptotically unbiased estimator渐近不偏最强力检定asymptotically unbiased most powerful test渐近弱辅助的asymptotically weakly ancillary按固定价格at constant prices在线英语学习按当期价格at current prices按要素成本at factor cost按市价at market prices疾病侵袭率attack rate减弱；衰减attenuation减弱相关法attenuation correlation method属性；计数值attribute属性分类attribute classification属性资料attribute data属性检验attribute inspection属性量测值attribute measurement属性抽样attribute sampling属性统计attribute statistics属性检定attribute testing属性值；计数值attribute value稽核检验audit inspection自我频谱auto spectrum自触曲线；自身成长曲线auto-catalytic curve自身相关母体autocorrelated population自身相关autocorrelation自身相关系数autocorrelation coefficient自身相关函数autocorrelation function自我互变异数autocovariance自我互变异函数autocovariance function自我互变异生成函数autocovariance generating function自动交互作用侦测automatic interaction detection(AID)自动切换复联automatic switch-over redundancy自主方程式autonomous equation自身回归；自回归autoregression自身回归整合移动平均模型(ARIMA模型) autoregressive integrated moving average model (ARIMA model)自身回归模型(AR模型) autoregressive model (AR model)自身回归移动平均模型(ARMA模型) autoregressive moving average model (ARMA model) 自身回归算子autoregressive operator自身回归过程autoregressive process自身回归方案autoregressive scheme自身回归数列autoregressive series自身回归变换autoregressive transformation辅助资讯auxiliary information辅助动差auxiliary moment辅助统计量auxiliary statistic可用度availability可用特性available characteristic在线英语学习平均数average平均检验量average amount of inspection平均数及全距管制图average and range chart年平均每日交通量average annual daily traffic平均项目连串长度average article run length平均可用度average availability分组平均校正average correction for grouping平均临界值法average critical value method平均离差average deviation对平均数的平均离差average deviation about the mean 平均发散度average divergence平均误差average error平均额外不良品界限average extra defectives limit平均不准确度average inaccuracy平均组间相关average intercorrelation平均组内相关average intracorrelation平均连接average linkage平均不良数average number of defects平均不良数管制图average number of defects chart比值平均average of relatives平均出厂水准average outgoing level平均出厂品质average outgoing quality (AOQ)平均出厂品质曲线average outgoing quality curve平均出厂品质水准average outgoing quality level平均出厂品质界限average outgoing quality limit (AOQL) 平均消费倾向average propensity to consume平均储蓄倾向average propensity to save平均品质水准average quality level平均品质水准线average quality level line平均品质线average quality line平均品质保护average quality protection平均全距average range平均连串长度average run length平均样本数average sample number (ASN)平均样本数曲线average sample number curve平均样本数函数average sample number function平均样本连串长度average sample run length平均样本大小average sample size (ASS)平均样本大小曲线average sample size curve平均抽样average sampling平均斜率average slope平均总检验数average total inspection (ATI)在线英语学习平均总检验数曲线average total inspection curve平均值average value国民平均教育年数average years for formal education 可避原因avoidable cause可避免的品质成本avoidable quality cost轴分布axial distribution轴向量axial vector机率公设axioms of probability横轴axis of abscissa纵轴axis of ordinate轴测图axonometric chart轴测法；轴量法axonometrytype A OC curve A型OC曲线unbiased critical region of type A A型不偏临界域type A distirubtion A型分布；A型分配type A series A型级数type A region A型区域A-optimal discrete design A型最适离散设计加快折旧Accelerated Depreciation意外与健康福利Accident and Health Benefits应收账款Accounts Receivable (AR)具增值作用的收购项目Accretive Acquisition酸性测试比率Acid Test收购Acquisition收购溢价Acquisition Premium天灾债券Act of God Bond活跃债券投资者Active Bond Crowd活动收入Active Income积极投资Active Investing积极管理Active Management。

Adaptive OFDM Modulation for Underwater Acoustic Communications_ Design Considerations

Adaptive OFDM Modulation for Underwater Acoustic Communications:Design Considerations andExperimental ResultsAndreja Radosevic,Student Member,IEEE,Rameez Ahmed,Tolga M.Duman,Fellow,IEEE,John G.Proakis,Life Fellow,IEEE,and Milica Stojanovic,Fellow,IEEEAbstract—In this paper,we explore design aspects of adaptive modulation based on orthogonal frequency-division multiplexing (OFDM)for underwater acoustic(UWA)communications,and study its performance using real-time at-sea experiments.Our design criterion is to maximize the system throughput under a target average bit error rate(BER).We consider two different schemes based on the level of adaptivity:in theﬁrst scheme,only the modulation levels are adjusted while the power is allocated uniformly across the subcarriers,whereas in the second scheme, both the modulation levels and the power are adjusted adaptively. For both schemes we linearly predict the channel one travel time ahead so as to improve the performance in the presence of a long propagation delay.The system design assumes a feedback link from the receiver that is exploited in two forms:one that conveys the modulation alphabet and quantized power levels to be used for each subcarrier,and the other that conveys a quantized estimate of the sparse channel impulse response.The second approach is shown to be advantageous,as it requires signiﬁcantly fewer feedback bits for the same system throughput.The effectiveness of the proposed adaptive schemes is demonstrated using computer simulations,real channel measurements recorded in shallow water off the western coast of Kauai,HI,USA,in June2008, and real-time at-sea experiments conducted at the same location in July2011.We note that this is theﬁrst paper that presents adaptive modulation results for UWA links with real-time at-sea experiments.Index Terms—Adaptive modulation,feedback,orthogonal frequency-division multiplexing(OFDM),underwater acoustic (UWA)communication.Manuscript received February26,2012;revised October17,2012and Feb-ruary12,2013;accepted March12,2013.Date of publication May24,2013; date of current version April10,2014.This work was supported by the Multidis-ciplinary University Research Initiative(MURI)of the U.S.Ofﬁce of Naval Re-search(ONR)under Grants N00014-07-1-0738/0739,N00014-10-1-0576,and N00014-09-1-0700.Associate Editor:S.Zhou.A.Radosevic is with Qualcomm Technologies Inc.,San Diego,CA92122 USA(e-mail:radosevica@).R.Ahmed and M.Stojanovic are with the Department of Electrical and Com-puter Engineering,Northeastern University,Boston,MA02115USA(e-mail: rarameez@;millitsa@).T.M.Duman is with the Department of Electrical and Electronics En-gineering,Bilkent University,Bilkent,Ankara06800,Turkey(e-mail: duman@.tr).J.G.Proakis is with the Department of Electrical and Computer Engi-neering,University of California at San Diego,La Jolla,CA92093USA (e-mail:jproakis@).Color versions of one or more of theﬁgures in this paper are available online at .Digital Object Identiﬁer10.1109/JOE.2013.2253212I.I NTRODUCTIONU NDERWATER ACOUSTIC(UWA)channels are con-sidered as some of the most challenging communication media,generally characterized by low propagation speed of sound in water(nominally1500m/s),limited bandwidth,and randomly time-varying multipath propagation which results in frequency-selective fading[1].Delay spreading in an UWA channel can occur over tens of milliseconds;however,the channel impulse response often has a sparse structure,with only a few propagation paths carrying most of the channel energy.Orthogonal frequency-division multiplexing(OFDM)has re-cently emerged as a promising alternative to single-carrier sys-tems for UWA communications because of its robustness to channels that exhibit long delay spreads and frequency selec-tivity[2]–[14].However,applying OFDM to UWA channels is a challenging task because of its sensitivity to frequency offset that arises due to motion.In particular,because of the low speed of sound and the fact that acoustic communication signals oc-cupy a bandwidth that is not negligible with respect to the center frequency,motion-induced Doppler effects result in major prob-lems such as nonuniform frequency shift across the signal band-width and intercarrier interference(ICI)[15],[16].Time-varying multipath propagation and limited bandwidth place signiﬁcant constraints on the achievable throughput of UWA communication systems.To support high spectral efﬁciencies over long intervals of time in a nonstationary environment such as the UWA channel,we consider commu-nication systems employing adaptive modulation schemes. While adaptive signaling techniques have been extensively studied for radio channels[17]–[21],only preliminary results for UWA channels are reported in[22]–[26],where simulations and recorded data are used to demonstrate the effectiveness of the proposed adaptation metrics.The performance of an adaptive system depends on the trans-mitter’s knowledge of the channel which is provided via feed-back from the receiver.Since sound propagates at a very low speed,the design and implementation of an adaptive system es-sentially relies on the ability to predict the channel at least one travel time ahead.This is a very challenging task for communi-cations in the range of several kilometers which imposes signiﬁ-cant limitations on the use of feedback.However,our prior work has shown that channel prediction is possible over such intervals of time using a low-order predictor[27].Crucial to successful0364-9059©2013IEEE.Personal use is permitted,but republication/redistribution requires IEEE permission.See /publications_standards/publications/rights/index.html for more information.Fig.1.The adaptive system with the important functional blocks.channel prediction is motion compensation that stabilizes the nonuniform Doppler shift and enables (sparse)channel estima-tion.The so-obtained channel estimates contain only a few sig-ni ﬁcant coef ﬁcients that are shown to be stable enough to sup-port prediction several seconds into the future.In this paper,we design an adaptive OFDM system and study its performance using recorded test channels and real-time at-sea experiments.Our approach and contributions are the following.•We estimate small Doppler rates (less than 10)that cor-respond either to drifting of the instruments,or residuals after initial resampling in mobile systems (e.g.,systems using autonomous underwater vehicles).Proper Doppler compensation ensures stability over intervals of time that are long enough to support channel prediction several sec-onds ahead.•We exploit the sparse multipath structure of the channel impulse response to estimate the most signi ﬁcant channel paths and simplify the prediction problem.Speci ﬁcally,we estimate only a few signi ﬁcant paths of the channel within a possibly large overall delay spread.We treat the statistical properties of the underlying random process of the channel fading as unknown,and compute the parameters of a linear predictor adaptively,by applying a recursive least squares (RLS)algorithm [28].•We develop two modulation schemes,distinguished by the level of adaptivity:Scheme 1adjusts only the modula-tion level and assumes a uniform power allocation,while scheme 2adjusts both the modulation level and the power allotted to each subcarrier.Both schemes are based on a greedy algorithm whose optimality was discussed in [20].•We propose a new design criterion for an adaptive OFDM system based on the information that is fed back to the transmitter.Speci ﬁcally,we consider two cases.In the ﬁrst case,the information about the modulation alphabet and the quantized power level for each subcarrier is computed at the receiver and fed back to the transmitter.In the second case,the quantized channel estimates are fed back,and the adaptive algorithm for bit loading and power allocation is implemented at the transmitter.•We demonstrate the effectiveness of the proposed adap-tive schemes using computer simulations,test channels recorded during the Kauai Acoustic Communications Mul-tidisciplinary University Research Initiative (MURI)2008(KAM08)experiment in shallow water off the westerncoast of Kauai,HI,USA,in June 2008,and real-time at-sea experiments conducted during the Kauai Acoustic Com-munications MURI 2011(KAM11)experiment at the same location in July 2011.The numerical and experimental re-sults show that the adaptive modulation scheme can pro-vide signi ﬁcant throughput improvements as compared to conventional,nonadaptive modulation for the same power and target bit error rate (BER).The paper is organized as follows.In Section II,we describe the system and the channel model that characterizes an UWA channel.In Section III,we introduce a linear RLS predictor for the channel tap coef ﬁcients.In Section IV,we introduce the rules for selection of the modulation levels,the information that is fed back to the transmitter,and the adaptive OFDM schemes.In Section V,we demonstrate the performance of the proposed adaptive schemes using numerical and experimental results that are based on recorded test channels and real-time at-sea trials,respectively.In Section VI,we provide concluding remarks.II.S YSTEM AND C HANNEL M ODELLet us consider an OFDM system with subcarriers,where the th block of the input data symbols ,,is modulated using the inverse fast Fourier transform (IFFT).The block of input data consists of information-bearing sym-bols and pilots,with corresponding sets denoted as and ,respectively.We assume that the information symbols are inde-pendent,while candidate modulation schemes are binary phase-shift keying (BPSK),quadrature phase-shift keying (QPSK),8phase-shift keying (8PSK),and 16-quadrature amplitude mod-ulation (16QAM)with 2-D Gray mapping.In other words,for the th subcarrier,where ,and the th block,the modu-lation level ,and if no data are transmitted.It is assumed that the pilot symbols takevalues from the QPSK modulation alphabet.For each modula-tion alphabet,we assume a uniform distribution of the constel-lation points with a normalized average power.The transmitter sends frames of OFDM blocks,such that one OFDM block oc-cupies an interval ,where and are the symbol duration and the guard time interval,respectively.We denote by the total bandwidth of the system,by the fre-quency of the ﬁrst subcarrier,by the central frequency,and by the subcarrier separation.In this paper,we consider an adaptive system illustrated in Fig.1.The different functional blocks of the system,such as channel and Doppler estimation,channel prediction,adaptiveRADOSEVIC et al.:ADAPTIVE OFDM MODULATION FOR UNDERWATER ACOUSTIC COMMUNICATIONS359allocation,and feedback information,are discussed in the rest of the paper.A.Channel ModelLet us now deﬁne the impulse response of the overall channel(1) where is the number of distinct propagation paths,is the delay variable,and is the time at which the channel is ob-served.Coefﬁcient represents the real-valued gain of the th path,and represents the corresponding delay.Here, we emphasize that the channel model(1)includes the initial re-sampling operation at the receiver by a common Doppler factor. Assuming a high bandwidth(sufﬁcient resolution in the delay variable),the set of coefﬁcients offers a good representation of the actual propagation paths.The re-ceived signal is given as(2) where is the transmitted signal and represents the ad-ditive white Gaussian noise(AWGN)process with zero mean and power spectral density normalized to unity.1If we also de-ﬁne the equivalent baseband signals and with respect to the frequency,such that(3) we then obtain(4)where(5) and is the equivalent baseband noise.Equation(4)implies the equivalent baseband channel response(6)B.Modeling of the Time-Varying Path DelayFollowing the approach from our previous work[27],we model the time-varying path delays as(7)1The AWGN assumption incurs no loss of generality of the proposed adaptive scheme even though acoustic noise is not white.where is the Doppler scaling factor,which is some func-tion of time.This model includes theﬁxed term,which describes the nominal propagation delay corresponding to the system geometry at the time of transmission,and an additional term that describes the effect of motion at the time of either due to drifting of the instruments(Doppler rates less than10)in stationary systems,or residuals after initial resampling in mobile systems(e.g.,systems using au-tonomous underwater vehicles).The system motion during a period of time corresponding to a few seconds(or several data packets)is modeled by velocity and acceleration terms which lead to a linear Doppler rate.A more accurate model could include higher order terms;however,experimental results con-ﬁrm that this is not necessary.Speciﬁcally,we model as a piecewise linear function(8) where,and are the Doppler scaling factors evaluated at time instances.This channel model is deemed suitable for the time scales of interest to an adaptive UWA communication system,since pro-viding a reliable predicted channel state information(CSI)de-pends on the availability of a stable signal reference that can be obtained through accurate motion compensation.For example, for a2-km link and the center frequency20kHz,a small Doppler rate can cause the phase of in (5)to change up to radians during a time interval of1.33s that corresponds to the propagation delay of one travel time.2 Such a phase shift can considerably degrade the performance of channel prediction and the reliability of the corresponding CSI. In other words,proper Doppler compensation ensures stability over intervals of time that are long enough to support channel prediction several seconds ahead.Model(7)allows one to decouple phase into two terms:one that is not related to motion,and another that is re-lated to motion.While theﬁrst term may not be predictable with sufﬁcient accuracy because frequency may be several orders of magnitude larger than the inverse of the path delay,the second term can be predicted using the estimates of the Doppler scaling factors.With this fact in mind,we proceed to develop a channel prediction method that focuses on two general terms:a complex-valued coefﬁcient and a mo-tion-induced phase.In other words, we model the baseband channel as(9) where we treat each as an unknown complex-valued channel coefﬁcient,which is assumed to be stable over a prolonged period of time(tens of seconds),and as an unknown motion-induced phase,which is modeled as a second-order polynomial based on expressions(7)and(8).We 2Here we should make a distinction between making the prediction for one travel time ahead,and for the round-trip time(two travel times ahead),since the two cases correspond to different feedback implementation strategies,i.e., different functions performed by the two ends of a link.360IEEE JOURNAL OF OCEANIC ENGINEERING,VOL.39,NO.2,APRIL2014Fig.2.Channel estimates obtained by the RLS and the MP algorithm. emphasize that this model is valid for some interval of time,but its parameters may change from one such interval to another. Our goal is to develop a two-step procedure in which weﬁrst estimate the channel coefﬁcients at the receiver from a probe signal,and then use the so-obtained estimates to form predic-tions,which areﬁnally fed back to the transmitter.This CSI will be used at the receiver(or the transmitter)to perform adaptive allocation of the modulation levels and power for each subcar-rier in the current OFDM block transmission.C.Channel EstimationChannel estimation consists of two steps.In theﬁrst step, initial phase compensation is performed to produce a stable reference signal.This step includes resampling by a nominal (average)Doppler factor and removal of the phase offset. Here,we should emphasize that the process relies on the esti-mates of the Doppler scaling factors,which are assumed to be available with a certain precision(e.g.,from a dedicated synchronization preamble).In the second step,the so-obtained signal is used to estimate the path coefﬁcients.The Doppler factors are not needed thereafter,as we conjecture that the channel coefﬁcients after motion compensation exhibit sufﬁcient stability to allow prediction several seconds into the future.Fig.2illustrates the channel estimates obtained from real data collected during the KAM08experiment.Speciﬁcally, in this section,we will focus on channel estimates obtained from a short probe signal described in[29].After the initial phase compensation where a phase-locked loop(PLL)was used,we perform channel estimation from the received signal using the matching pursuit(MP)algorithm[30].Note from Fig.2that the MP algorithm produces eight coefﬁcients,where neighboring coefﬁcients belong to the same propagation path due to the path dispersion[1].For further analysis,we weigh the adjacent coefﬁcients based on the channel tap power and merge them,so as to represent the channel via four propagation paths,,,and.Therefore,the MP algorithm provides estimates of the channel coefﬁcients,assuming that channel coefﬁcients are sufﬁcient for the description of the sparse multipath structure.These estimates are denotedby Fig.3.(a)Magnitudes and(b)phases of the channel path coefﬁcients.,and computed at time instances separated by155ms.For comparison purposes,we also provide the channel estimate obtained using the RLS algorithm.Different peaks in the channel estimates can be associated with multiple surface and bottom reﬂections calculated from the geometry of the experiment.As can be seen from theﬁgure,the MP algorithm successfully estimates the signiﬁcant channel coefﬁcients,and reduces the estimation error with respect to that incurred by the RLS algorithm.We emphasize that positions of the signiﬁcant paths may drift on a larger time scale(tens of seconds),and,therefore,have to be updated accordingly.In Fig.3,we show the magnitudes and phases of the signiﬁcant paths over a time period of8s.As we initially conjectured,the phases of remain relatively stable for more than a few seconds(a propagation delay over several kilometers).III.C HANNEL P REDICTIONAs we previously reported in[27],the future values of are predicted from the estimates.In particular, if the OFDM blocks are periodically transmitted at time instances,we use observations made at timesto predict the channel at time.To account for possible correlation between the path coefﬁcients, we allow for their joint prediction.In other words,we use all channel coefﬁcients to predict each new coefﬁcient.The prediction is thus made as(10) where(11)(12) Matrix contains prediction coefﬁcients that are to be determined.RADOSEVIC et al.:ADAPTIVE OFDM MODULATION FOR UNDERWATER ACOUSTIC COMMUNICATIONS 361Table IP REDICTION RLS ALGORITHMBecause the second-order statistics are not available for the random process ,we compute adaptively,by ap-plying the RLS algorithm as speci ﬁed in Table I.In (14),is an matrix,which represents an estimate of the in-verse joint autocorrelation matrix and is a small constant,typically a fraction of the minimum among vari-ances of the channel coef ﬁcients jointly predicted by the RLS algorithm.As discussed earlier,UWA systems suffer from inherently long propagation delays,which pose additional challenges in the design of a predictor.To counteract this problem,channel prediction one travel time ahead is achieved by using an RLS predictor of a low-order (e.g.,or )and a small forgetting factor [e.g.,,which corresponds toan effective window of length].Note that the forgetting factor is uniquely speci ﬁed for all channel coef ﬁcients.With a small order and only a few sig-ni ﬁcant paths,i.e.,a small ,computational complexity of joint channel prediction is suf ﬁciently low to allow for a practical im-plementation.The structure of matrix is primarily driven by the ge-ometry of the propagation environment,i.e.,not all of the prop-agation paths are mutually correlated.In the present data set,the strongest arrival often exhibits more stability,and the con-tribution from the other,weaker paths in its prediction appears to be negligible.Therefore,the strongest path can be predicted independently,without loss in performance.In other words,if channel coef ﬁcient corresponds to the strongest path,(18)can be modi ﬁed as follows:the th column of is recursively updated only for those elements that correspond to the prior ob-servations of the th coef ﬁcient.In addition,exploiting the correlation among the re-maining paths may lead to a performance improvement,whose exact amount is determined by the environmental pro ﬁle,and accuracy of the channel and Doppler estimates.After performing channel prediction at the receiver,the so-obtained CSI is used to initialize adaptive allocation of the modulation levels and power across the OFDM subcarriers.As we will discuss later,depending on which end of the com-munication link performs adaptive allocation,different types of information are fed back over a low-rate feedback channel.In the following,we describe the design framework,initiallyproposed in [26],under which we developed two practical adaptive modulation schemes,and we also discuss the design of bandlimited feedback.IV .A DAPTIVE M ODULATION AND P OWER A LLOCATION The system model assumes that residual Doppler effects are negligible after proper initial motion compensation [resampling by a nominal Doppler factor and removal of the phase offset].After this initial step,it is also assumed that the channel is constant at least over the transmission interval of one OFDM block.Therefore,the received signal can be expressed as(20)where(21)and ,,and are,respectively,the received signal after fast Fourier transform (FFT)demodulation,the transmitted power,and zero-mean circularly symmetric complex AWGNwith varianceper dimension.The noise term includes the effects of ambient noise and residual ICI on the th subcarrier and the th OFDM block,which is approximated as a Gaussian random variable.For the transmission of each OFDM block,we adaptivelycompute the size of the modulation alphabetand the transmission power .The objective of our adaptive OFDM system is to maximize the throughput by maintaining a target average BER.To maintain the BER at a ﬁxed value,we propose the following optimization criterion:maximize subject to(22)where is the overall average power allocated to the th OFDM block,is the average BER for the th subcarrier,and is the target average BER.The average power can beexpressed aswhere is a constant and is the residual power from the previous block which was not allocated (i.e.,is less than the minimum power increment required by the algorithm for a one-bit increase of the overall throughput).Here,we should emphasize the difference be-tween total power allocation and distribution of this total power among the subcarriers.In the former case,one can designan adaptive scheme where the total poweris adaptively allocated (and uniformly distributed among the subcarriers)to achieve the prespeci ﬁed performance [e.g.,the target average BER or signal-to-noise (SNR)at the receiver]for the ﬁxed system throughput,whereas in the latter case,the ﬁxed total362IEEE JOURNAL OF OCEANIC ENGINEERING,VOL.39,NO.2,APRIL2014power is nonuniformly distributed among the subcarriers to achieve the prespeciﬁed performance,and to maximize the system throughput.For the purpose of experimental sea trials, the total power allocation is initially set to a value which is able to support the target error rate,and avoid the outage scenario(no data transmission).To reduce the computational complexity of the adaptive algo-rithm,the subcarriers of the th OFDM block can be grouped into clusters.If we assume,we group consecutive sub-carriers into clusters,where is the size of each cluster.We denote by and,respectively,the allocated power and the level to the th cluster,.The optimal power level for each cluster depends on the transfer function of the channel.If the channel does not change much within a cluster,computation of and is performed based on the average channel gain cluster that if a cluster is affected by a deep fade, it will be dominated by the subcarrier with the lowest channel gain.Clustering reduces the computational load(see[26]for more details),but implies possible error penalization and/or a decrease in throughput as compared to the full computation of modulation levels and powers for all subcarriers.A.Thresholds for Modulation LevelsDue to the large propagation delays,the proposed adaptive OFDM transmission relies on channel prediction.We obtain predictions of the channel gains one travel time ahead based on the time-domain predictions of the most signiﬁcant channel coefﬁcients(10).We model the prediction error on the th channel path as a complex zero-mean circularly symmetric Gaussian random variable with variance per dimension. Furthermore,based on the a priori obtained from the channel prediction,we model as a complex Gaussian random variable with mean(23) and variance,where is the number of sig-niﬁcant time-domain channel coefﬁcients.Assuming that the current channel gain is perfectly known,we apply max-imum likelihood symbol detection for the AWGN channel at the output of the matchedﬁlter.Thus,the probability of bit error for the th subcarrier for M-ary phase-shift keying(MPSK)/mul-tiple quadrature amplitude modulation(MQAM)is well approx-imated by[18](24) where coefﬁcients are determined numerically for each modulation alphabet,as accurately as desired for the BER approximation and take values for,respectively.For transmission of the th OFDM block,the adaptive system has knowledge of the predicted values,but not of the full channel.Therefore,from(24),the average BER on the th subcarrier is obtained as[18](25) For a given target,we now compute the thresholds for the available modulation levels.The solution for is given by(26) where is the principal branch of the Lambert -function,the inverse function of.Note that if,the threshold goes to zero,i.e.,.This case corresponds either to high SNR regimes with reliable CSI,or to very high target BERs of the system.Reasonably accurate approximations for,which can be computed efﬁciently,are provided in[31].We should emphasize that different thresholds correspond to different av-erage values of,since all of the subcarriers are affected by the prediction error of the same variance.The optimization problem(22)is hard to solve from the standpoint of a practical implementation,because it is com-putationally too intensive to be run at the receiver(or the transmitter)for every OFDM block.Therefore,we pursue suboptimal solutions which are obtained by relaxing one of the problem constraints.Speciﬁcally,we focus on two adaptive schemes in the rest of this section.B.Adaptive Scheme1The optimal solution for(22)includes a nonuniform power allocation for a maximum attainable throughput,such that the target average BER is.This causes that each subcarrier con-tributes to the average BER differently,due to the frequency se-lectivity of the channel.However,the problem can be simpliﬁed if we consider adaptive allocation of the modulation levels while distributing the power uniformly among the subcarriers.Since we adaptively allocate only the modulation levels,the so-ob-tained solution for(22)will be suboptimal.Speciﬁcally,we apply a greedy algorithm that computes the modulation levels in a given block using the allocations from the previous block for initialization.The proposed algorithm is given inRADOSEVIC et al.:ADAPTIVE OFDM MODULATION FOR UNDERWATER ACOUSTIC COMMUNICATIONS 363Table IIM ODULATION L EVEL ALLOCATIONTable II.Similar greedy algorithms have already been consid-ered in [32]and [33].After initialization of the algorithm for each subcarrier,as given by (27)–(30),we successively increase the modulation levels for those subcarriers that require the smallest power in-crement (31)–(43),while maintaining the average BER below the target .If the set of modulation levels from the previous transmission interval is not a greedy-based solution for the cur-rently available CSI ,the algorithm greedily searches for the closest solution which is used as a new initialization point of the algorithm.Also,if the algorithm does not support the throughput from the previous transmission interval (i.e.,it fails during the initialization step),it searches for the subcarrier with the largest power decrement that is required to decrease the modulation level .The algorithm is terminated when theprespeci ﬁedis achieved.C.Adaptive Scheme 2In the second scheme,we consider adaptive allocation of themodulation levels and the subcarrier powers such that for each subcarrier.Once the thresholds are computed from (26),we apply the adaptive algorithm of Table III to generate the signal of the thOFDM block.The algorithm is terminated when the available power is exhausted,or when all subcarriers achieve the max-imum modulation level (16QAM).Here,we emphasize that for those subcarriers that are in a deep fade no data are transmitted (zero power is allocated).In other words,the subcarrier with index is in deep fade if threshold is high enough to violate the power constraint in (22).Because of the additional freedom to adjust the power,this scheme will achieve a higher overall throughput as compared to scheme 1.D.Limited Feedback for Adaptive UWA SystemsWe assume that a limited-feedback channel is available for conveying information from the receiver back to the transmitter.The receiver has knowledge of the channel frequency response at subcarrier frequencies and the corresponding channel im-pulse response.The transmitter needs to know the modulation levels and the power levels at the frequencies.To accomplish this,there are different feedback options.Here we consider three different alternatives.A ﬁrst option is to feed back the frequency response at the subcarriers,where is typically of the order of 1000.If the channel frequency response changes slowly across frequencies,neighboring subcarriers would be allocated the same modula-tion and power levels.In such a case,it is not necessary to feed back the channel frequency response in amplitude and phase for each subcarrier.Hence,the total number of bits fed back can be reduced from a factor of to some factor,say ,where is the number of subcarriers contained in the coher-ence bandwidth of the channel.A second option is to transmit the actual modulation levels and the power levels directly to the transmitter at the subcar-rier frequencies.bits may be used to represent the available modulation levels.For example,in our case,we usedbits.The power levels can be uniformly quantized,such that bits are used to represent each quantization level.A third option is to feed back the values of the quantized channel impulse response.Since the impulse response is sparse,the total number of bits required to convey this information to the transmitter is ,where is the number of sig-ni ﬁcant coef ﬁcients in the channel impulse response (typically,or less for the shallow-water channels considered),is the number of bits required to represent the quantized com-plex-valued channel coef ﬁcients,and is the number of bits required to represent the time delay of each dominant channel coef ﬁcient.To further reduce the number of bits fed back to the trans-mitter,we applied a lossless data compression technique.In par-ticular,we employed run length encoding (RLE)[34],which is a simple coding scheme that provides good compression of data that contains many runs of zeros or ones,together with the well-known Lempel–Ziv–Welch (LZW)algorithm (used as an inner code)[35],to ef ﬁciently compress the feedback informa-tion.As we will see in the following section,assuming perfect CSI at the receiver,feeding back the sparse channel impulse re-sponse and computing the modulation levels and power levels at the transmitter requires signi ﬁcantly fewer bits.。

数字信号处理论文 Adaptivefrequencyestimationofthree-phase powersystems

Adaptive frequency estimation of three-phasepower systems$Reza Arablouei a,n,1,Kutluyıl Doğançay a,1,Stefan Werner b,1a School of Engineering,University of South Australia,Mawson Lakes,SA5095,Australiab Department of Signal Processing and Acoustics,School of Electrical Engineering,Aalto University,Espoo,Finlanda r t i c l e i n f oArticle history:Received14April2014Received in revised form18October2014Accepted25November2014Available online4December2014Keywords:Adaptive signal processingFrequency estimationInverse power methodLinear predictive modelingTotal least-squaresa b s t r a c tThe frequency of a three-phase power system can be estimated by identifying theparameter of a second-order autoregressive(AR2)linear predictive model for thecomplex-valuedαβsignal of the system.Since,in practice,both input and output ofthe AR2model are observed with noise,the recursive least-squares(RLS)estimate of thesystem frequency using this model is biased.We show that the estimation bias can beevaluated and subtracted from the RLS estimate to yield a bias-compensated RLS(BCRLS)estimate if the variance of the noise is known a priori.Moreover,in order to simulta-neously compensate for the noise on both input and output of the AR2model,we utilizethe concept of total least-square(TLS)estimation and calculate a recursive TLS(RTLS)estimate of the system frequency by employing the inverse power method.Unlike theBCRLS algorithm,the RTLS algorithm does not require the prior knowledge of the noisevariance.We prove mean convergence and asymptotic unbiasedness of the BCRLS andRTLS algorithms.Simulation results show that the RTLS algorithm outperforms the RLSand BCRLS algorithms as well as a recently-proposed widely-linear TLS-based algorithm inestimating the frequency of both balanced and unbalanced three-phase power systems.&2014Elsevier B.V.All rights reserved.1.IntroductionIn electric power grids,the system frequency nor-mally fluctuates around its nominal value within anacceptable range.Deviation of the system frequencyfrom its nominal range represents an imbalancebetween load and generation,which is a critical event.Therefore,it is imperative to closely watch the possiblevariations in the frequency.Most protection-and-control applications in electric power systems requireaccurate and fast estimation of the system frequency.An erroneous estimate of the frequency may cause acatastrophic grid failure due to inadequate or delayedload shedding[2–7].In three-phase systems,none of the single phases canfaithfully characterize the whole system and its properties.Therefore,a robust frequency estimator should take intoaccount the information of all three phases[8–12].Clarke'stransform applied to the voltages of a three-phase powersystem produces a complex-valued signal(known as theαβsignal)that incorporates the information of the three phases.In many applications,theαβsignal can be considered as afaithful representative for a three-phase system[13].Thephase voltages are digitized at the measurement points byquantizing the samples taken at uniform intervals.Therefore,in practice,the observed voltage data and consequently theαβsignal are contaminated with noise/error.From a signal-processing point of view,the noisy samplesof theαβsignal and the sampling rate comprise the availabledata while the amplitudes of the three phase voltages,Contents lists available at ScienceDirectjournal homepage:/locate/sigproSignal Processing/10.1016/j.sigpro.2014.11.0180165-1684/&2014Elsevier B.V.All rights reserved.☆This work was partially presented in the European Signal ProcessingConference,Lisbon,Portugal,September2014[1].n Corresponding author.Tel.:þ61883023316.E-mail address:arary003@.au(R.Arablouei).1EURASIP member.Signal Processing109(2015)290–300the initial phase angle,and the system frequency are the unknown parameters.A plethora of techniques have been developed to extract these parameters,particularly the system frequency,from the observable data.Some of the most well-known frequency estimation techniques are based on zero-crossing[14],phase-locked loop[15–17],discrete Fourier transform[18],Viterbi algorithm[19],extended Kalman filter [20],Newton's method[21],data(auto)correlation[22–24], demodulation[25],least-error-squares curve fitting[26],least mean-square(LMS)[27],least mean-phase[28],adaptive notch filters[29,30],and minimum-variance distortionless response(MVDR)spectrum[31].In order to estimate the system frequency within the realm of linear adaptive signal processing,time evolution of the noiselessαβsignal can be modeled by either a first-order autoregressive(AR1)[27]or a second-order autoregressive (AR2)linear predictive model[32–36].The AR1is suitable for balanced three-phase systems,i.e.,when the voltage magni-tudes of the three phases are identical.It relates two con-secutive noiseless samples of theαβsignal of a balanced system via a single complex-valued parameter.The modulus of this parameter is equal to unity and its phase angle is equal to the system angular frequency multiplied by the sampling interval.Therefore,the system frequency can be estimated by identifying the parameter of the AR1model from the noisy voltage observations using any linear estimation technique, e.g.,the LMS algorithm as proposed in[27].The AR1-based frequency estimators lose their accuracy when the system is unbalanced,since in such systems,the strictly-linear AR1model becomes inexact.Augmenting the AR1model using the notion of widely-linear modeling[37]can provide a remedy for this weakness in handling the unba-lanced three-phase power systems[38–40].The frequency estimation techniques based on the widely-linear AR1model can estimate the system frequency by identifying the para-meters of the widely-linear model even when the system in unbalanced.However,despite introducing an extra complex-valued model parameter,the widely-linear-AR1-based meth-ods cannot cope with the cases of severe unbalancedness,e.g., when the readings of two phases drop to zero.This is mainly due to the inherent limitation of the widely-linear AR1model for such events caused by its approximate nature.On the other hand,the AR2model linearly relates three consecutive noiseless samples of theαβsignal via a single real-valued parameter that is equal to the cosine of the product of the system angular frequency and the sampling interval.Thus, the system frequency can be estimated by identifying the parameter of the AR2model from the noisy observations of theαβsignal while being harmlessly oblivious to the values of the phase voltage magnitudes and the initial phase angle.In other words,since the parameter of the AR2model depends only on the system frequency and the sampling interval,any frequency estimator built on this model is virtually insensitive to the balance state of the three-phase power system.As theαβsignal is observed with noise,a reliable frequency estimation technique based on the AR2model should minimize the effect of noise.In[34,35],the least-squares(LS)method has been used for this purpose.A recursive LS(RLS)frequency estimator has also been pro-posed in[41].The LS-based approaches are best suited to counter the effect of the noise at the output of a linear model.However,since in the AR2model,the input of the model is also subject to observational noise,the LS-based frequency estimators are biased.Such bias can falsely indicate a shift in the system frequency and invoke unne-cessary corrective actions,which may have harmful fallouts. Thus,any bias in frequency estimation can seriously com-promise the stability and reliability of a power system.One way to eliminate the estimation bias is to evaluate the bias separately and subtract it from the biased estimate [42–44].The evaluation of the bias usually requires prior knowledge of the noise variance or an extra procedure for estimating the noise variance.Alternatively,the total least-squares(TLS)estimation technique can be utilized to compen-sate for the noise on both input and output of the AR2model. TLS is a fitting method that improves accuracy of the LS estimation techniques when both the input and output data of a linear system are subject to observational error.It finds an estimate for the system parameters that fits the input to the output with minimum perturbation in the data.A TLS estima-tor can eliminate the estimation bias induced by the input noise without performing any explicit bias calculation[45–47]. Two efficient recursive TLS algorithms have been developed in [48,49]utilizing the line-search optimization.The latter mini-mize a Rayleigh-quotient cost function and the former employs the inverse power method[50].The TLS technique has recently been utilized to estimate the frequency of three-phase power systems based on the widely-linear AR1model[51,52].In this paper,we show that the RLS algorithm based on the AR2model for the noiselessαβsignal is biased when applied to adaptive frequency estimation of three-phase power systems at the presence of noise.In order to obtain unbiased estimates while employing the AR2model,we develop a bias-com-pensated RLS(BCRLS)algorithm as well as a recursive TLS (RTLS)algorithm.We derive the BCRLS algorithm by evaluating the estimation bias and subtracting it from the biased RLS estimate.To derive the RTLS algorithm,we calculate the TLS estimate of the AR2model parameter by implementing a single iteration of the inverse power method at each time instant. Unlike the algorithms proposed in[48,49],our RTLS algorithm does not implement any line-search optimization.We show that the BCRLS and RTLS algorithms are convergent in the mean and asymptotically unbiased.We verify the effectiveness of the proposed algorithms in estimating the frequency of both balanced and unbalanced three-phase power systems through simulated experiments.2.Signal and system modelThe phase-to-neutral voltages of a three-phase power system,sampled at the rate of1=τ,are represented byv a;n¼V a cos2πfτnþθðÞ;v b;n¼V b cos2πfτnþθÀ2π3andv c;n¼V c cos2πfτnþθþ2π3where f is the system frequency,V a,V b,and V c are the peak voltage values,θis an initial phase angle,and n is the integer time index.In practice,these voltages areR.Arablouei et al./Signal Processing109(2015)290–300291measured with noise.We express the noisy measurements as~va ;n ¼v a ;n þηa ;n ;~vb ;n ¼v b ;n þηb ;n ;and~vc ;n ¼v c ;n þηc ;n where ηa ;n ,ηb ;n ,and ηc ;n denote the additive noise of the respective phases.We assume that the noises are zero-mean i.i.d.Thus,we have E ηa ;n ÂÃ¼E ηb ;n ÂÃ¼E ηc ;n ÂÃ¼0;E η2a ;n h i ¼σ2a ;E η2b ;n h i¼σ2b ;and E η2c ;n h i¼σ2c :Application of the Clarke's transform to the noisy three-phase voltages results in v α;n v β;n "#þηα;n ηβ;n "#¼ﬃﬃﬃ23r 1À1=2À1=20ﬃﬃﬃ3p =2Àﬃﬃﬃ3p =2"#v a ;nv b ;n v c ;n264375þηa ;n ηb ;n ηc ;n 2643750B @1C A :This transformation yields a complex-valued voltage signal (known as the αβsignal)that can represent the three-phase power system.The noiseless αβsignal is calculated as v n ¼v α;n þjv β;n¼A þjB ðÞcos 2πf τn þθðÞþB þjC ðÞsin 2πf τn þθðÞ;ð1ÞwhereA ¼ﬃﬃﬃ23r V a þ12ﬃﬃﬃ6p V b þV c ðÞ;B ¼À12ﬃﬃﬃ2p V b ÀV c ðÞ;and C ¼1ﬃﬃﬃ3r V bþV c ðÞ:Writing the noisy αβsignal as ~vn ¼v n þηn ;ð2Þthe additive complex noise,ηn ,is related to the noise at the individual phases viaηn ¼ηα;n þj ηβ;n¼ﬃﬃﬃ2r ηa ;n Àηb ;n Àηc ;n þj ﬃﬃﬃ2p ηb ;n Àηc ;n ÀÁ:In Appendix A ,we show that the time evolution of thenoiseless αβsignal,v n ,can be described via a second-order autoregressive (AR2)linear predictive model expressed as12v n À2þv n ðÞ¼hv n À1ð3Þwhere h ¼cos 2πf τðÞð4ÞThis model relates the system frequency to three conse-cutive noiseless voltage samples of the three phases through its real-valued parameter h .Using (3)and (4),the system frequency can be extracted from any three consecutive noiseless samples of the αβsignal provided that 0o 2πf τo πor τo12f:However,since the measured samples are noisy,the identification of the model parameter h should be per-formed via a linear estimation technique.Given an esti-mate of h at time instant n ,denoted by ^hn ,the system frequency estimate is calculated by ^f n ¼1cos À1^h n :3.Recursive least squaresBased on the model (3),an exponentially-weighted LS estimate of h at time instant n from the noisy αβsignal is given by [53]w n ¼argmin wjj y n Àw x n jj 2ð5Þwherex n ¼Λ~v n À1~v n À2…~v 1~v02666666437777775andy n ¼Λ2~v n À2þ~v n ~v n À3þ~vn À1…~v 0þ~v 2~v À1þ~v 12666666437777775are the exponentially-weighted input and output datavectors,respectively,Λ¼diag 1;ﬃﬃﬃλp ;…;ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃλn À2p ;ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃλn À1p n ois an exponential weighting matrix and 0{λo 1is the forgetting factor.A recursive solution for the optimization problem of (5),called the RLS estimate,is given as [53]w n ¼p n r nð6Þwhere p n is the exponentially-weighted time-averaged covariance of the input and output computed as p n ¼x H n y n¼12∑n i ¼1λn Ài ~vni À1~v i À2þ~v i ðÞ¼λp n À1þ1~v n n À1~v n À2þ~v n ðÞð7ÞR.Arablouei et al./Signal Processing 109(2015)290–300292and r n is the exponentially-weighted time-averaged var-iance of the input computed as r n ¼x H n x n¼∑ni ¼1λn Ài ~v n i À1~v i À1¼λr n À1þ~vn À12:ð8ÞNote that we consider w n a recursive estimate because p n and r n can be updated recursively.3.1.Estimation biasAs n -1,the RLS estimate w n converges in the mean [53].Thus,we have w 1¼lim n -1E w n ½¼lim n -1E pn n!:ð9ÞApplying Slutsky's theorem [54]to (9)yields w 1¼p 1r 1ð10Þwherep 1¼lim n -1E p nÂÃð11Þandr 1¼lim n -1E r n ½ :ð12ÞIn Appendix B ,we show that p 1¼hD 1Àλð13Þand r 1¼D þσ2ð14ÞwhereD ¼B 2þA 2þC 2and σ2¼23σ2a þσ2b þσ2c ÀÁ:Substituting (13)and (14)into (10)gives w 1¼hD:ð15ÞIt is seen from (15)that,when the noise is present,i.e.,σ2a 0,the LS estimate is biased.This is due to the fact that the LS estimation techniques only compensate for the effect of the noise at the output of the underlying linear model and neglect the effect of the noise at the input.The estimation bias of the LS approach is b ¼w 1Àh ¼Àh σ2D þσ2:4.Bias-compensated recursive least squaresA bias-compensated RLS (BCRLS)estimate can bedevised by subtracting the LS estimation bias from the RLS estimate as ωn ¼w n Àb¼p n r n þh σ2D þσ2:ð16ÞSince h and D in (16)are not known a priori ,they need to be substituted by some known quantities.The parameter h can be replaced with its most recent estimate ωn À1.Considering (14)and taking r n as an instantaneous approx-imation for r 1,D can also be replaced with 1ÀλðÞr n Àσ2.Consequently,the BCRLS estimate is stated as ωn ¼p n r n þσ21ÀλðÞr nωn À1:ð17ÞNote that this estimate still requires the prior knowledge of the noise variance σ2.We list the BCRLS algorithm in Table 1.4.1.Convergence in the meanWhen the forgetting factor,λ,is close to unity (λ-1),after a sufficiently large number of iterations,p n and r n converge to p 1and r 1,respectively.Subsequently,taking the expectation of both sides of (17)results in ωn p 1r σ1ÀλðÞr ωn À1ð18Þwhere ωn ¼E ωn ½ :Using (13),(14)and (18)is written as ωn ¼hD D þσ2σωn À1:ð19ÞSince we have 0oσ2o 1;the recursion (19)is stable hence convergent.As a result,at the steady state,(19)turns into ω1¼hD D þσ2þσ2D þσ2ω1ð20Þwhere ω1¼lim n -1ωn :Table 1Frequency estimation using the BCRLS algorithm.initialization r 0¼0p 0¼0ω0¼0for n ¼1;2;…r n ¼λr n À1þ~vn À1 2p n ¼λp n À1þ~v n n À1~v n À2þ~v n ðÞ=2ωn ¼p nr n þσ21ÀλðÞr n ωn À1^f n ¼1cos À1ωn ðÞR.Arablouei et al./Signal Processing 109(2015)290–300293We conclude from (20)that the BCRLS algorithm is asymptotically unbiased as ω1¼h :5.Recursive total least squaresIn view of the fact that both input and output of the model (3)are observed with noise,in this section,we utilize the TLS estimation technique to identify h .The TLS estimate of h at time instant n ,denoted by w n ,is computed such that it fits the input data vector,x n ,to the output data vector,y n ,by incurring minimum perturbation in the data,i.e.,it holds that x n þεn ðÞw n ¼y n þδnwhere ½εn ;δn is the minimum Frobenius-norm perturbation.According to the analysis of [47],using the singular value decomposition of the augmented and weighted datamatrix x n ;y n ÂÃT ,the TLS estimate is given by w n ¼Àz 1;n γz 2;nwhere z n ¼z 1;n ;z 2;n ÂÃTis the right singular vector corre-sponding to the smallest singular value of x n ;y n ÂÃT .The weighting matrix T accounts for the disparity in the variance of the noise on the input and output,denotedby ς2i and ς2o ,respectively,and is defined asT ¼100γ"#whereγ¼ﬃﬃﬃﬃﬃς2iς2o s ¼ﬃﬃﬃﬃﬃﬃﬃσ21σ2s ¼ﬃﬃﬃ2p :The vector z n is also the eigenvector corresponding to the smallest eigenvalue of the augmented and weighted data covariance matrixΨn ¼T x H n y H n "#x n ;y n ÂÃT ;which can be written asΨn ¼r nﬃﬃﬃ2p p n ﬃﬃﬃ2p p nn2s n "#where p n and r n are given by (7)and (8),respectively,ands n is the exponentially-weighted time-averaged variance of the output computed as s n ¼y H n y n¼14∑ni ¼1λn Ài ~v n i À2þ~v n i ÀÁ~v i À2þ~v i ðÞ¼λs n À1þ14~v n À2þ~v n2:ð21ÞThe eigen-decomposition of Ψn gives z n .However,as a computationally more efficient alternative,we propose toupdate z n adaptively by executing a single iteration of the inverse power method at each time instant.In numerical analysis,the inverse power method is used to find an approximate eigenvector when an approximation to a corre-sponding eigenvalue is known [50].We are interested in finding the eigenvector that belongs to the smallest eigenva-lue.Therefore,we may take zero as an approximation to this eigenvalue.Consequently,estimating z n using the inverse power method is realized by the following recursion:z n ¼ΨÀ1nz n À1:ð22ÞMultiplying both sides of (22)by Ψn =ﬃﬃﬃ2p z 2;n À1z 2;ngives Ψnw n À1=ﬃﬃﬃ2p "#¼z 2;n À12;nw n À1À1=ﬃﬃﬃ2p "#or equivalently r n w n Àp n ¼z 2;n À1z 2;nw n À1ð23Þandp n n w n Às n ¼Àz 2;n À12z 2;n:ð24ÞSolving (23)for w n after substituting (24)into it yields a recursive TLS (RTLS)estimate of h as w n ¼p n þ2s n w n À1r n n w n À1:ð25ÞWe summarize the RTLS algorithm in Table 2.5.1.Convergence in the meanAs λ-1and after a sufficiently large number of itera-tions,p n ,r n ,and s n converge to p 1,r 1,and s 1¼lim n -1E s n ½ ;ð26Þrespectively.Subsequently,taking the expectation of both sides of (25)gives w n ¼p 1þ2s 1w n À1r 1þ2p n 1w n À1ð27Þwhere w n ¼E w n ½ :Table 2Frequency estimation using the RTLS algorithm.initialization r 0¼0s 0¼0p 0¼0w 0¼0for n ¼1;2;…r n ¼λr n À1þ~vn À1 2p n ¼λp n À1þ~v n n À1~v n À2þ~v n ðÞ=2s n ¼λs n À1þ~vn À2þ~v n 2=4w n ¼p n þ2s n w n À1n nn À1^f n ¼1cos À1w n ðÞR.Arablouei et al./Signal Processing 109(2015)290–300294In Appendix B ,we show that s 1¼2h 2D þσ221ÀλðÞ:ð28ÞSubstitution of (13),(14)and (28)into (27)leads tow n hD þ2h 2D þσ2w n À1D þσ2þ2hDw:ð29ÞIntroducing a change of variable as u n w and using (29),we can show that u n ¼σ2σ2þ2h 2þ1 Du n À1:Since we have 0oσ2σ2þ2h 2þ1Do 1;it holds thatu 1¼lim n -1u n¼0and consequently w 1¼lim n -1w n¼h :In other words,the RTLS algorithm is convergent in the mean and asymptotically unbiased.5.2.Relation to BCRLSThe recursion (25)can be rearranged as w n ¼p n r n þ2s n Àp n n w nr nw n À1ð30ÞIf we make the following approximation at the steady state:s n Àp n n w n %s 1Àp n1h%σ2and substitute it into (30),we obtain the following approximate recursion:w n %p n n þσ2nw n À1:ð31ÞResemblance of (31)and (17)indicates that,at the steady state,the update equation of the RTLS algorithm becomes very similar to that of the BCRLS algorithm.However,unlike the BCRLS algorithm,the RTLS algorithm does not require the prior knowledge of the noise variance.6.SimulationsWe compare the frequency estimation performance of the RLS,BCRLS,and RTLS algorithms as well as the widely-linear RLS (WLRLS)algorithm [55,56]and the augmented inverse power iterations (AIPI)algorithm [52]for a three-phase power system where f ¼50Hz,τ¼2ms,and σ2a¼σ2b¼σ2c¼σ2:The WLRLS and AIPI algorithms are based on a first-order autoregressive (AR1)widely-linear predictive model for the noiseless αβsignal,i.e.,v n ¼hv n À1þgv n n À1:We set λ¼0:999in all the experiments and σ2¼0:01in the experiments of Figs.1–3.In Fig.1a,we depict the estimated frequency using different algorithms when the system undergoes several voltage sags making it progressively more unbalanced as shown in Fig.1b.The system is balanced during the initial 0:25seconds.Then,the voltage of phase c drops by 50%.After 0:25seconds,the voltage of phase a ,and after further 0:25seconds,the voltage of phase b reduce to zero.Zero or almost zero phase voltages can occur in the aftermath of short-circuit to ground or combined asymmetric sags.In Fig.2a,we compare the frequency estimation per-formance of different algorithms when the voltages of a444546474849505152time (s)f r e q u e n c y (H z )-101p h a s eb-101time (s)p h a s e c-101p h a s e aFig.1.(a)Estimated frequency of and (b)a three-phase power systemthat undergoes several voltage sags.R.Arablouei et al./Signal Processing 109(2015)290–300295balanced system are distorted by third,fifth,seventh,and ninth harmonics.The magnitudes of the harmonic distor-tions,relative to the voltage signal with fundamentalfrequency,are 20%,15%,10%,and 10%,respectively.The distorted samples of the voltages of the three phases are shown in Fig.2b.In Fig.3,we plot the estimated frequency using di-fferent algorithms when a sinusoidal oscillation occurs in the frequency of a balanced system after 0:33seconds.The peak and the maximum change rate for the oscillation are 1Hz and 2Hz =s,respectively.In Figs.4–6,we plot the steady-state bias and root-mean-square error (RMSE)of different algorithms against the signal-to-noise ratio,which is considered to be 1=σ2.The steady-state bias and RMSE are defined aslim n -1E ^f nh i Àf and lim n -1ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃE ^f nÀf 2 !s ;respectively.We run the algorithms for 4seconds to reach the steady state.We evaluate the expectations by taking the ensemble average over 104independent trials and the steady-state values by averaging over the last 0.1s.In Fig.4,the system is balanced.In Fig.5,a short-circuit between phase a and ground has made the system unbalanced.404550556065time (s)f r e q u e n c y (H z )time (s)p h a s e cp h a s e ap h a s ebFig. 2.(a)Estimated frequency of (b)a balanced three-phase powersystem that is contaminated with noise and harmonics.47484950515253time (s)f r e q u e n c y (H z )Fig.3.Estimated and tracked frequency of a balanced three-phase power system that experiences a sinusoidal oscillation in the system frequency.-70-60-50-40-30-20-1001020signal-to-noise ratio (dB)s t e a d y -s t a t e b i a s (d B)-40-30-20-1001020signal-to-noise ratio (dB)s t e a d y -s t a t e r o o t -m e a n -s q u a r e e r r o r (d B )Fig.4.(a)Steady-state bias and (b)steady-state root-mean-square error for estimating frequency of a balanced three-phase power system.R.Arablouei et al./Signal Processing 109(2015)290–300296In Fig.6,the voltage readings of both phases a and b are zero.From the above simulation results,we observe that the BCRLS algorithmconverges fast,similar to all the other algorithms considered;offers great improvement over the RLS and WLRLS algorithms in frequency estimation performance; outperforms the AIPI algorithm when the three-phasesystem is highly unbalanced.Moreover,we observe that the RTLS algorithm exhibits good performance at the presence of harmo-nics due to its ability to separate the signal subspace from the noise subspace,which would ideally include the measurement noise and the harmonics as repre-sented by the smallest eigenvalue of the augmented and weighted data covariance matrix;has a good capability to track the changes in the system frequency;successfully removes the estimation bias,as it is evi-dent from the considerable gap between the estimation bias of the RTLS and RLS/WLRLS algorithms;is more efficacious than the BCRLS algorithm in elim-inating the estimation bias while not requiring the prior knowledge of the noise variance;outperforms the AIPI algorithm in all the considered cases.We notice that the AR1-model-based AIPI algorithm performs relatively well when the system is balanced or moderately unbalanced.However,its performance degrades dramatically when the system is highly unbalanced,such as when the voltage readings of two out of three phases are near-zero.On the other hand,the BCRLS and RTLS algorithms are almost insensitive to the balance state of the system.Note that the AIPI algorithm,similar to any other frequency estimator developed upon the notion of widely-linear AR1modeling,identifies two complex-valued parameters while the BCRLS and RTLS algorithms identify only one real-valued parameter.This makes the BCRLS and RTLS algorithms less-70-60-50-40-30-20-1001020signal-to-noise ratio (dB)s t e a d y -s t a t e b i a s (d B )-40-30-20-1001020signal-to-noise ratio (dB)s t e a d y -s t a t e r o o t -m e a n -s q u a r e e r r o r (d B )Fig.5.(a)Steady-state bias and (b)steady-state root-mean-square error for estimating frequency of an unbalanced three-phase power system suffering from a phase-to-groundfault.-70-60-50-40-30-20-1001020signal-to-noise ratio (dB)s t e a d y -s t a t e b i a s (d B )-40-30-20-1001020signal-to-noise ratio (dB)s t e a d y -s t a t e r o o t -m e a n -s q u a r e e r r o r (d B )Fig.6.(a)Steady-state bias and (b)steady-state root-mean-square error for estimating frequency of an unbalanced three-phase power system suffering from two phase-to-ground faults.R.Arablouei et al./Signal Processing 109(2015)290–300297。

遨控180度矢量变频

低频（30Hz）扭矩补偿电流波形图 Low Frq.(30Hz) With T.C.
不同压缩机参数适应能力
Different Compressor Parameter Adaptive Capability
测试方法：用同一控制系统，无需更改任何参数，分别启动和运行美芝压缩机： Test method: Use the same control system and control parameter to boot and
压缩机在使用了一段时间以后，其部分参数会发生较大的变化，在这种情况下，RSA技术可以保证控制系统稳定运行，并且保持良好的性能； The compressor’s parameter will be changed when it is used for some time, but RSA technology can make the system stable and acquire good performance. 针对不同的压缩机，控制参数的调整非常简单方便，对大多压缩机而言，甚至无需调整控制参数即可获得良好的控制性能，大大缩短开发调试周期。 For different compressor, control parameter is easy to be regulated, shorten the developing-time.
低频（20Hz）扭矩补偿电流波形图 Low Frq.(20Hz) With T.C.
扭矩补偿
Torque Compensation 本控制系统包含扭矩控制技术，可有效补偿单转子压缩机旋转过程中的周期性扭矩波动，使得压缩机在低频运行时更加平稳、安静。 The high efficient torque control (torque compensation) technology can reduce the speed fluctuation in low frequency, so the compressor run more stable and quiet.

基于RMSprop的粒子群优化算法

2021年$月计算机工程与设计Mar.2021第42卷第$期COMPUTER ENGINEERING AND DESIGN Vol.42No.$基于RMSprop的粒子群优化算法张天泽，李元香+,项正龙，李梦莹（武汉大学计算机学院，湖北武汉430072）摘要：粒子群算法对所有粒子采用相同的惯性权重，忽视了单个粒子的特性，导致收敛精度偏低且易陷入局部最优。

结合RMSprop算法中对每一个维度进行自适应设置的策略，提出一种自适应惯性权重粒子群优化算法RMSPSO。

考虑粒子每一个维度的速度变化及动量，进行自适应动态惯性权重设置，使算法在全局寻优和局部寻优之间达到良好平衡。

选取10个典型测试函数，将改进后的粒子群算法（RMSPSO）与4个主流粒子群算法进行实验对比分析，实验结果表明，在单峰、多峰和组合函数上，RMSPSO算法在收敛速度和收敛精度上取得了明显进步&关键词：粒子群算法；RMSprop算法；自适应；梯度下降；惯性权重中图法分类号：TP301文献标识号：A文章编号：1000-7024（2021）03-0642-07doi：10.16208/j.issnl000-7024.2021.0$.007Particle swarm optimization algorithm based on RMSprop method ZHANG Tian-ze,LI Yuan-xiang+&XIANG Zheng-long,LI Meng-ying(School of Computer Science&Wuhan University&Wuhan430072&China)Abstract：For the particle swarm optimization(PSO)algorithm&the same inertia weight is adopted for all particles and the cha-racteristicsofsingleparticleareignored,resultinginlowconvergenceaccuracyandeasinesstofa l intolocaloptimum6Combined with the strategy of setting each dimension adaptively in RMSprop algorithm&an adaptive inertia weight particle swarm optimization algorithm RMSPSO was proposed6Considering the velocity and momentum of each dimension of particles,the adaptive dynamicinertiaweightwasset,whichmadethealgorithmachieveagoodbalancebetweenglobaloptimizationandlocaloptimiza-tion6Ten typical test functions were selected and the improved particle swarm optimization(RMSPSO)wascomparedwithfour mainstream particle swarm optimization algorithms.The results show that the RMSPSO algorithm makes progress in convergence speed and accuracy in unimodal&multimodal and combined functions.Key words：particle swarm optimization；RMSprop algorithm；adaptive#gradient descent；inertia weighto引言粒子群算法（particle swarm optimization,PSO）1*是由Kennedy和Eberhart提出的一种结构简单、收敛速度快的进化算法。

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2
School of Media, Soongsil University, Seoul, South Korea
Abstract
In this paper, we propose a model parameter estimation algorithm from block motion vectors for extracting accurate motion information with the assumption that the undergoing motion can be characterized by an affine model. The motion may be caused either by a moving camera or a moving object. The proposed method first extracts motion vectors from a sequence of images by using sizevariable block matching, and then processes them by adaptive robust estimation to estimate model parameters. Typically, a robust estimation filters out outliers (velocity vectors that do not fit into the model) by fitting velocity vectors to a predefined model. To filter out potential outliers, our adaptive robust estimation defines a continuous weight function based on a sigmoid function. During the estimation process, we tune the sigmoid function gradually to its hard-limit as the errors between the model and input data are decreased, so that we can effectively separate non-outliers from outliers with the help of the finally tuned hard-limit form of the weight function. Experimental results show that the suggested approach is very effective in estimating model parameters reliably. Keywords: model parameters, adaptive robust estimation, outlier rejection, weight tuning
Adaptive Robust Estimation of Model Parameters from Block Motion Vectors
Seok-Woo Jang1, Marc Pomplun1, and Hyung-Il Choi2
1
Department of Computer Science, University of Massachusetts at Boston, Boston, USA
model with a particular choice of parameters. The merit function is conventionally arranged so that small values represent close agreement. The parameters of the model are then adjusted to achieve the minimum in the merit function. The adjustment process is thus a problem of minimizing the residual error with respect to model parameters by filtering out suspected outliers in input data. A common approach to multi-dimensional minimization problems is the Levenberg-Marquardt method [7]. This method works well in practice and has become the standard of nonlinear least-square data fitting. This is a continuous optimization method that offers a powerful compromise between the steepest gradient method and the inverse-Hessian method. It uses the latter method when the process is far from the minimum. It switches continuously to the former as the minimum is approached. However, the Levenberg-Marquardt method does not improve global convergence capabilities if it is not controlled effectively [8]. In a practical environment, we also noticed that the existing robust estimation method uses a binary weight function called a threshold even in the initial steps of the minimization process. In those steps, it is very difficult to separate non-outliers (velocity vectors of concern) from outliers (velocity vectors out of concern) based on a threshold since model parameters have not been fitted yet. Thus, the parameters could be updated incorrectly. In addition, the estimation method generates a new binary weight function for every iteration, discarding the previous one. This can cause oscillations of weights because the method discards the correlation of the two weight functions. In this paper, to deal with these limitations, we propose a model parameter estimation method using adaptive robust estimation. The proposed method first extracts motion vectors from a sequence of images by using size-variable block matching, and then processes them by adaptive robust estimation to estimate model parameters. Typically, a robust estimation filters out outliers by fitting velocity vectors to a predefined model. To filter out potential outliers, our adaptive robust estimation defines a continuous weight function based on a sigmoid function. During the estimation process, we tune the sigmoid function gradually to its hard-limit as the errors between the model and input data are decreased, so that we can effectively separate non-outliers from outliers with the help of the finally tuned hard-limit form of the weight function. Fig. 1 shows the overall procedure of our method.
1.with the progress of image processing and multimedia technologies, there has been much interest in the area of analyzing dynamic images and estimating motion information over the last few years. Especially, estimating model parameters from block motion vectors is a fundamental and important research topic since we may presume that a camera motion or moving target can be represented as a parametric model [1]. Such an approach is often used in many applications like image panorama composition, model-based video coding, moving object tracking, and camera calibration [2-5]. We can find various types of methods for this topic in related literature. Among these, the robust estimation approach based on the outlier rejection scheme seems to provide very promising results [1]. In general, the robust estimation method is well-known for a good statistical estimator that is insensitive to small departures from the idealized assumptions for which the estimation is optimized [6]. It requires a merit function that measures the agreement between the input data (velocity vectors) and the