[{"data":1,"prerenderedAt":56},["ShallowReactive",2],{"method-bell1993ikf":3},{"method":4,"reference":35,"equipment":54,"figures":55,"results":33},{"id":5,"label":6,"shortName":7,"title":8,"year":9,"era":10,"cluster":11,"scope":12,"keyIdeaZh":13,"keyIdeaEn":14,"fulltextStatus":15,"publicationStatus":16,"recommendation":17,"constructionRelevance":18,"validationEnvironment":19,"strengths":20,"limitations":24,"sensors":29,"platform":30,"estimator":31,"association":18,"timeModel":32,"deskew":18,"loopClosure":18,"globalOptimization":18,"mapRepresentation":18,"prior":18,"outputGeometry":18,"compute":18,"codeUrl":33,"codeLicense":18,"relatedVersions":34},"bell1993ikf","Bell & Cathey, 1993","IKF as Gauss-Newton","The iterated Kalman filter update as a Gauss-Newton method",1993,"classic","C03","estimation_framework_or_library","本文證明迭代卡爾曼濾波（iterated Kalman filter, IKF）的量測更新步驟，就是以 Gauss-Newton 法近似最大概似估計；只迭代一次時即為 EKF 更新，量測函數為仿射時兩者都退化為一般卡爾曼更新。作者以二維雙站測距的解析例子說明，當觀測越來越精確時，IKF 更新與最大概似估計都會正確收斂，而 EKF 更新會收斂到有偏的值，同時其誤差共變異數卻趨近於零。這提供了把迭代濾波理解為單步最佳化的理論基礎。","Shows that the iterated Kalman filter update is a Gauss-Newton method for a maximum-likelihood estimate, with an example where the EKF update fails to converge correctly.","full_text_reviewed","peer_reviewed_published","background","not_applicable",[],[21,22,23],"Formal equivalence between IKF update and Gauss-Newton (abstract)","In the closed-form bistatic ranging example the IKF and ML updates converge to the true state as the observation becomes exact, whereas the EKF converges to a biased value while its covariance goes to zero (Sec. VII)","The authors state this convergence and false-convergence behaviour holds generally when an exact measurement completely determines the state (Sec. I)",[25,26,27,28],"Equivalence concerns the measurement update step; Barfoot notes the IEKF-MAP correspondence holds only for the correction step at a single timestep (barfoot2017ser, Sec. 4.2.6)","The update problem is static: system dynamics do not enter the analysis (Sec. II)","The IKF generally performs better than the EKF at the expense of more computation (Sec. I)","The covariance expression assumes the measurement function is affine near the estimate and the true state (Sec. IV)",[],[],"iterated Kalman filter measurement update shown to generate the same iterates as Gauss-Newton applied to the maximum-likelihood (weighted least-squares) update problem that stacks the predicted state and the observation; a single iterate gives the EKF update","discrete time",null,[],{"id":5,"kind":36,"shortName":7,"title":8,"authors":37,"year":9,"venue":40,"venueType":41,"publisher":42,"volumeIssuePages":43,"doi":44,"arxivId":33,"url":45,"firstPublicDate":46,"publicationStatus":16,"metadataStatus":47,"fulltextStatus":15,"era":10,"classicReason":48,"codeUrl":33,"cluster":11,"topics":49,"mdpi":50,"verification":51,"label":6,"fulltextRoute":52,"versionRead":53,"addedByCensus":50},"method",[38,39],"B. M. Bell","F. W. Cathey","IEEE Transactions on Automatic Control","journal","IEEE","38(2):294-297","10.1109\u002F9.250476","https:\u002F\u002Fapi.crossref.org\u002Fworks\u002F10.1109\u002F9.250476","1993","metadata_verified","principle reused: establishes the iterated Kalman filter update as Gauss-Newton, the link between iterated filters used in LiDAR-inertial odometry and optimization-based estimation.",[11],false,"confirmed","NTU institutional (curl)","Version of record: IEEE Transactions on Automatic Control 38(2):294-297, February 1993 (IEEE Xplore PDF, arnumber 250476)",[],[],1790510665122]