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1、AnIntroductiontotheKalmanFilterGregWelch1andGaryBishop2TR95-041DepartmentofComputerScienceUniversityofNorthCarolinaatChapelHillChapelHill,NC27599-3175Updated:Monday,July24,2006AbstractIn1960,R.E.Kalmanpublishedhisfamouspaperdescribingarecursivesolutiontothediscrete-datalinearfilteringproblem
2、.Sincethattime,dueinlargeparttoad-vancesindigitalcomputing,theKalmanfilterhasbeenthesubjectofextensivere-searchandapplication,particularlyintheareaofautonomousorassistednavigation.TheKalmanfilterisasetofmathematicalequationsthatprovidesanefficientcom-putational(recursive)meanstoestimatethest
3、ateofaprocess,inawaythatmini-mizesthemeanofthesquarederror.Thefilterisverypowerfulinseveralaspects:itsupportsestimationsofpast,present,andevenfuturestates,anditcandosoevenwhentheprecisenatureofthemodeledsystemisunknown.ThepurposeofthispaperistoprovideapracticalintroductiontothediscreteKal-ma
4、nfilter.ThisintroductionincludesadescriptionandsomediscussionofthebasicdiscreteKalmanfilter,aderivation,descriptionandsomediscussionoftheextend-edKalmanfilter,andarelativelysimple(tangible)examplewithrealnumbers&results.1.welch@cs.unc.edu,http://www.cs.unc.edu/~welch2.gb@cs.unc.edu,http://ww
5、w.cs.unc.edu/~gbWelch&Bishop,AnIntroductiontotheKalmanFilter21TheDiscreteKalmanFilterIn1960,R.E.Kalmanpublishedhisfamouspaperdescribingarecursivesolutiontothediscrete-datalinearfilteringproblem[Kalman60].Sincethattime,dueinlargeparttoadvancesindigitalcomputing,theKalmanfilterhasbeenthesubjec
6、tofextensiveresearchandapplication,particularlyintheareaofautonomousorassistednavigation.Avery“friendly”introductiontothegeneralideaoftheKalmanfiltercanbefoundinChapter1of[Maybeck79],whileamorecompleteintroductorydiscussioncanbefoundin[Sorenson70],whichalsocontainssomeinterestinghistoricalna
7、rrative.Moreextensivereferencesinclude[Gelb74;Grewal93;Maybeck79;Lewis86;Brown92;Jacobs93].TheProcesstobeEstimatednTheKalmanfilteraddressesthegeneralproblemoftryingtoestimatethestatex∈ℜofadiscrete-timecontrolledprocessthatisgovernedbythelinearstoch
