[{"data":1,"prerenderedAt":99},["ShallowReactive",2],{"method-smith_cheeseman1986":3},{"method":4,"reference":45,"equipment":64,"figures":65,"results":66},{"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":21,"limitations":24,"sensors":29,"platform":30,"estimator":32,"association":33,"timeModel":34,"deskew":35,"loopClosure":36,"globalOptimization":37,"mapRepresentation":38,"prior":39,"outputGeometry":40,"compute":41,"codeUrl":42,"codeLicense":43,"relatedVersions":44},"smith_cheeseman1986","Smith & Cheeseman, 1986","Smith-Cheeseman spatial uncertainty","On the Representation and Estimation of Spatial Uncertainty",1986,"classic","C01","estimation_framework_or_library","本文以「近似轉換（approximate transformation, AT）」表示座標框架之間不確定的相對位姿，每個 AT 由平均關係與共變異數矩陣組成。作者定義兩個基本運算：串接（compounding）以一階泰勒展開與 3×6 雅可比矩陣傳遞共變異數，把一連串 AT 合成一個，不確定性隨之變大；合併（merging）以靜態卡爾曼濾波公式加權平均平行的 AT，使不確定性變小，並以電阻串並聯作類比。對惠斯登電橋這類無法以串並聯化簡的網路，作者提出刪除形成迴路的 AT（未用上全部資訊，並非最佳）或以 Delta-Y 轉換改寫網路（可用上全部資訊，但無法化簡所有網路），並表示以共同參考框架做遞迴狀態估計的通用方法仍在研究中。移動機器人範例與蒙地卡羅模擬顯示，平均值與共變異數的相對誤差通常小於 1%，但角度誤差大時分布呈新月形而非高斯分布。","Defines approximate transformations (mean plus covariance), first-order compounding and Kalman-based merging of parallel relations, and a network-reduction procedure validated against Monte Carlo simulation; the joint stochastic-map formulation is only announced here as work in progress.","full_text_reviewed","peer_reviewed_published","background","未在營建場域測試（僅有蒙地卡羅模擬）。其「串接使不確定性增加、平行量測合併使不確定性減少」的共變異數傳遞觀念，以及系統誤差須靠校正排除的前提，可作為討論 SLAM 點雲座標誤差累積、控制點與校正需求的理論背景（推論）。",[20],"simulation",[22,23],"[\"First-order estimates agreed with an independent Monte Carlo simulation","relative errors of the estimated means and covariances were typically below 1% unless angular errors were large (standard deviation above about 6 degrees) (Sec. 6.3, Sec. 7).\", \"Probabilistic estimates avoid the overly conservative worst-case max\u002Fmin error bounds of earlier work (Sec. 3).\", \"Lets a robot decide in advance whether a motion or sensing step will reach the accuracy a task needs, and judge when a sensor has glitched (Sec. 6.1, Sec. 7).\"]",[25,26,27,28],"[\"First-order approximation needs small errors and can underestimate or overestimate the covariance (Sec. 3.2).\", \"Errors are assumed independent and zero-mean","systematic errors are not modelled and must be removed by calibration (Sec. 3.2, Sec. 4.2).\", \"Series and parallel reduction cannot reduce every network (e.g., a Wheatstone bridge)","deleting ATs discards information and the Delta-Y method is not general (Sec. 5).\", \"Only two moments are estimated","with large angular errors the distribution becomes crescent-shaped rather than Gaussian (Sec. 6.3, Sec. 7, Fig. 5).\", \"Extension to six degrees of freedom introduces Jacobian singularities that can destroy the estimates (Sec. 7).\"]",[],[31],"[\"simulation\"]","first-order (linearized) mean and covariance propagation for compounding and reversal of ATs; merging of parallel ATs with static-state Kalman filter equations (optimal for Gaussian variables and linear mappings, optimal-linear otherwise); extended Kalman filter update named for nonlinear coordinate mappings","no data-association algorithm; the sensing procedure rejects an observation whose probability, given the prior AT estimate and the sensor error, is below a threshold (e.g., the camera viewed the wrong object), which the authors also describe as detecting sensor glitches","discrete moves; each relative motion and each sensing is a static AT in the network","not_applicable","implicit: when the robot observes its start frame from a later pose, the sensed AT is merged with the compounded chain as a parallel relation; no separate loop-closure module","none; the network is reduced by repeated compounding and merging; irreducible (Wheatstone-bridge) networks are handled approximately by deleting loop-forming ATs (nonoptimal) or by a Delta-Y transformation, and a general recursive state-estimation method is stated as under investigation","network of approximate transformations (relational map), each with a mean relation and covariance; the robot keeps the original ATs from motions and sensings and computes composite ATs on demand","none required; the robot's starting position is taken as the world frame","mean and covariance of the relative pose (x, y, theta) between any two frames; confidence ellipses derived from the covariance","no runtime or hardware reported; the authors state that the procedures need only simple matrix computations and are computationally simple and fast",null,"not_verified",[],{"id":5,"kind":46,"shortName":7,"title":8,"authors":47,"year":9,"venue":50,"venueType":51,"publisher":52,"volumeIssuePages":53,"doi":54,"arxivId":42,"url":55,"firstPublicDate":56,"publicationStatus":16,"metadataStatus":57,"fulltextStatus":15,"era":10,"classicReason":58,"codeUrl":42,"cluster":11,"topics":59,"mdpi":60,"verification":61,"label":6,"fulltextRoute":62,"versionRead":63,"addedByCensus":60},"method",[48,49],"Randall C. Smith","Peter Cheeseman","The International Journal of Robotics Research","journal","SAGE","5(4):56-68","10.1177\u002F027836498600500404","https:\u002F\u002Fapi.crossref.org\u002Fworks\u002F10.1177\u002F027836498600500404","1986-12","metadata_verified","evaluation-calibration-uncertainty method: defines approximate transformations with first-order covariance compounding and Kalman merging of parallel relations, validated against Monte Carlo simulation (Sec. 3, 4, 6.3); the joint stochastic-map (EKF) formulation that later works attribute to it is only announced here (Sec. 5) and is developed in smith_self_cheeseman1990; lu_milios1997 (Sec. 3.3) treats its compounding and merging as special cases of network estimation.",[11],false,"confirmed","NTU institutional (Chrome)","version of record, The International Journal of Robotics Research 5(4):56-68 (December 1986), SAGE PDF (13 pages, scanned pages with an OCR text layer); equation bodies and figure contents exist only as images and were not transcribed",[],[],{"totalRows":67,"groupCount":67,"groups":68,"others":98},1,[69],{"slug":70,"group":71,"sourceId":5,"sourceLabel":6,"table":72,"selfRows":67,"metrics":73,"seqs":79,"entrants":82,"cells":86,"outcomes":90,"locators":92,"hardware":94,"wordings":95,"notes":96},"smith-cheeseman1986-text-sec-6-3","smith_cheeseman1986:Text Sec.6.3","Text Sec.6.3",[74],{"label":75,"unit":76,"statistic":77,"alignment":78},"relative error in any component of the estimated means and covariances (compared to the simulated values)","%","not_reported","none",[80],{"dataset":81,"sequence":77,"environment":20},"Monte Carlo simulation (authors)",[83],{"name":84,"methodId":5,"linkable":85,"proposed":85,"self":85},"compounding of approximate transformations (first-order estimate)",true,[87],[88,88,88,67,88,88,89,89,88],0,-1,[91],"upper bound stated as typically less than 1%; does not hold when angular errors are large (standard deviation greater than 6 degrees)",[93],"Sec. 6.3",[],[],[97],"first-order AT estimates compared with an independent Monte Carlo simulation of a three-degree-of-freedom robot with Gaussian errors in the given relations",[],1790510664372]