[{"data":1,"prerenderedAt":405},["ShallowReactive",2],{"method-censi2007covariance":3},{"method":4,"reference":45,"equipment":64,"figures":71,"results":72},{"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":25,"sensors":32,"platform":34,"estimator":35,"association":36,"timeModel":37,"deskew":37,"loopClosure":38,"globalOptimization":38,"mapRepresentation":37,"prior":39,"outputGeometry":40,"compute":41,"codeUrl":42,"codeLicense":43,"relatedVersions":44},"censi2007covariance","Censi, 2007","ICP covariance (Censi)","An accurate closed-form estimate of ICP's covariance",2007,"classic","C02","evaluation_method_or_metric","作者以 ICP 最小化的誤差函數為對象，利用隱函數定理推導估計值對量測的一階敏感度，得到封閉形式共變異數，並考慮同一量測被多個對應重複使用與量測彼此相關的情形。論文只處理二維平面（x、y、θ）的定位與掃描匹配，分析對象為點對線段 ICP；以 52 條射線、雜訊標準差 0.03 m 的模擬測距儀，在正方形、走廊與圓形環境各做 300 次蒙地卡羅模擬；在走廊與圓形等約束不足情形，改以 Fisher 資訊矩陣找出不可觀測方向，只比較可觀測子空間上的誤差。","Closed-form first-order ICP covariance via the implicit function theorem (uses d2J\u002Fdz dx, not only the Hessian), derived and tested for 2D (x, y, theta) localization and point-to-segment scan matching in Monte Carlo simulation, with Fisher-information analysis for corridor and circular under-constrained cases.","full_text_reviewed","peer_reviewed_published","background","not_reported；論文指出走廊是實務上最常見的約束不足情形（Sec. V），與長廊、隧道等營建場景的關聯及對工程點雲不確定性傳遞的意義均屬推論",[20],"simulation",[22,23,24],"square environment, scan matching: predicted std 7.7 mm, 7.7 mm, 0.060 deg vs Monte Carlo 7.6 mm, 7.8 mm, 0.058 deg, while the Hessian method gives 20.0 mm, 20.3 mm, 0.171 deg (Fig. 4 table)","localization: prediction close to the Cramer-Rao bound and to the sample covariance (Fig. 4 table)","accounts for measurements shared by several correspondences and for correlated measurement noise (Sec. IV)",[26,27,28,29,30,31],"only planar 2D localization and scan matching (x, y, theta) are derived and tested; no 3D formulation is given (Sec. I, IV, V)","validation limited to Monte Carlo simulation of three synthetic environments; no real sensor data (Sec. V)","assumes ICP converged inside the basin of the true solution; wrong convergence is not modelled (Sec. I-B)","models only the error due to sensor noise; the Cramer-Rao bound approximates localization well but is optimistic for scan matching (Sec. I-B)","moderately optimistic in the circular environment on the observable manifold (Fig. 4 summary table)","closed-form derivatives are not given in the paper (Sec. IV)",[33],"simulated 2D range finder: 52 rays over 360 deg, zero-mean Gaussian range noise with 0.03 m standard deviation",[20],"first-order covariance of the minimizer via the implicit function theorem: cov(x_hat) = (d2J\u002Fdx2)^-1 (d2J\u002Fdz dx) cov(z) (d2J\u002Fdz dx)^T (d2J\u002Fdx2)^-1 evaluated at the estimate; uses only the error function J, not the ICP algorithm internals; requires matrix products and a 3x3 inversion","analysed ICP variant is 2D point-to-segment ('vanilla' ICP): each correspondence uses one point of the current scan and the two reference-scan points that form the closest polyline segment","not_applicable","none","measurement covariance cov(z), which may be a full (correlated) matrix; for localization the map is treated as noise-free (z = y_t); an optional odometry term in a MAP cost (Eq. 10) bounds the covariance by cov(u)","covariance of the ICP pose estimate","evaluating Eq. 6 needs matrix multiplications and inversion of a 3x3 matrix; described as negligible relative to ICP itself; no timing figures or hardware reported",null,"not_verified",[],{"id":5,"kind":46,"shortName":7,"title":8,"authors":47,"year":9,"venue":49,"venueType":50,"publisher":51,"volumeIssuePages":52,"doi":53,"arxivId":42,"url":54,"firstPublicDate":55,"publicationStatus":16,"metadataStatus":56,"fulltextStatus":15,"era":10,"classicReason":57,"codeUrl":42,"cluster":11,"topics":58,"mdpi":60,"verification":61,"label":6,"fulltextRoute":62,"versionRead":63,"addedByCensus":60},"component",[48],"Andrea Censi","Proceedings 2007 IEEE International Conference on Robotics and Automation","conference","IEEE","pp. 3167-3172","10.1109\u002Frobot.2007.363961","https:\u002F\u002Fapi.crossref.org\u002Fworks\u002F10.1109\u002Frobot.2007.363961","2007-04","metadata_verified","evaluation-calibration-uncertainty method: closed-form ICP covariance used to propagate registration uncertainty into SLAM back-ends and map quality statements.",[11,59],"C13",false,"confirmed","NTU institutional (Chrome)","IEEE Xplore version of record (Proc. ICRA 2007, pp. 3167-3172, 6 pages), PDF fetched inside the IEEE Xplore page in Chrome under NTU access and parsed with pdf.js in the page; nothing stored locally",[65],{"category":66,"model":67,"canonical":67,"role":68,"dataset":42,"specs":69,"locator":70},"other","simulated 2D range finder (52 rays distributed on 360 deg)","method input","52 rays distributed on 360 deg; zero-mean Gaussian range noise with 0.03 m standard deviation","Sec. V",[],{"totalRows":73,"groupCount":74,"groups":75,"others":394},31,6,[76,170,256,331],{"slug":77,"group":78,"sourceId":79,"sourceLabel":80,"table":81,"selfRows":82,"metrics":83,"seqs":102,"entrants":107,"cells":115,"outcomes":160,"locators":165,"hardware":166,"wordings":167,"notes":168},"brossard2020icpcov-table-1","brossard2020icpcov:Table 1","brossard2020icpcov","Brossard et al., 2020","Table 1",8,[84,88,90,92,94,96,98,100],{"label":85,"unit":86,"statistic":87,"alignment":38},"NNE trans.","unitless","mean",{"label":89,"unit":86,"statistic":87,"alignment":38},"NNE rot.",{"label":91,"unit":86,"statistic":87,"alignment":38},"KL div. trans.",{"label":93,"unit":86,"statistic":87,"alignment":38},"KL div. rot.",{"label":95,"unit":86,"statistic":87,"alignment":38},"NNE* trans. (robust)",{"label":97,"unit":86,"statistic":87,"alignment":38},"NNE* rot. (robust)",{"label":99,"unit":86,"statistic":87,"alignment":38},"KL div.* trans. (robust)",{"label":101,"unit":86,"statistic":87,"alignment":38},"KL div.* rot. (robust)",[103],{"dataset":104,"sequence":105,"environment":106},"Challenging data sets for point cloud registration (Pomerleau et al. 2012)","average of 8 sequences","structured to unstructured, indoor to outdoor",[108,111,113],{"name":109,"methodId":5,"linkable":110,"proposed":60,"self":110},"Q_censi (closed-form, Censi 2007)",true,{"name":112,"methodId":42,"linkable":60,"proposed":60,"self":60},"Q_monte carlo (65 Monte Carlo ICP samples)",{"name":114,"methodId":79,"linkable":110,"proposed":110,"self":60},"proposed",[116,120,122,125,128,131,134,135,137,138,139,140,141,143,145,146,147,149,151,152,153,155,157,158],[117,117,117,118,117,117,119,119,117],0,1000,-1,[117,121,117,118,117,117,119,119,117],1,[117,123,117,124,121,117,119,119,117],2,10000,[117,126,117,127,123,117,119,119,117],3,100000,[117,129,117,130,119,117,119,119,117],4,38,[117,132,117,133,126,117,119,119,117],5,100,[117,74,117,118,117,117,119,119,117],[117,136,117,127,123,117,119,119,117],7,[121,117,117,118,117,117,119,119,117],[121,121,117,133,126,117,119,119,117],[121,123,117,124,121,117,119,119,117],[121,126,117,124,121,117,119,119,117],[121,129,117,142,119,117,119,119,117],22,[121,132,117,144,119,117,119,119,117],20,[121,74,117,118,117,117,119,119,117],[121,136,117,118,117,117,119,119,117],[123,117,117,148,119,117,119,119,117],4.2,[123,121,117,150,119,117,119,119,117],34,[123,123,117,133,126,117,119,119,117],[123,126,117,133,126,117,119,119,117],[123,129,117,154,119,117,119,119,117],0.8,[123,132,117,156,119,117,119,119,117],3.8,[123,74,117,73,119,117,119,119,117],[123,136,117,159,119,117,119,119,117],98,[161,162,163,164],"printed only as order of magnitude 10^3","printed only as order of magnitude 10^4","printed only as order of magnitude 10^5","printed only as order of magnitude 10^2",[81],[],[],[169],"ICP covariance consistency averaged over 8 sequences, 1020 registrations x 1000 initializations; Q_ini 0.1 m and 10 deg; noise and bias SD 5 cm; NNE target 1; starred = robust statistics after removing extreme quantiles; baselines printed as orders of magnitude",{"slug":171,"group":172,"sourceId":173,"sourceLabel":174,"table":175,"selfRows":136,"metrics":176,"seqs":179,"entrants":200,"cells":207,"outcomes":249,"locators":250,"hardware":251,"wordings":252,"notes":253},"landry2019cello3d-table-ii","landry2019cello3d:Table II","landry2019cello3d","Landry et al., 2019","Table II",[177],{"label":178,"unit":38,"statistic":87,"alignment":38},"Avg. KL divergence",[180,184,187,190,193,195,198],{"dataset":181,"sequence":182,"environment":183},"Challenging data sets (ETH)","Apartment (trained on Haupt. and Stairs; 1190 pairs)","indoor apartment",{"dataset":181,"sequence":185,"environment":186},"Hauptgebaude (trained on Apt and Stairs; 938 pairs)","indoor, structured (Hauptgebaude)",{"dataset":181,"sequence":188,"environment":189},"Stairs (trained on Apt and Haupt.; 798 pairs)","indoor, structured (Stairs)",{"dataset":181,"sequence":191,"environment":192},"Gazebo Summer (trained on Gzb. Winter; 826 pairs)","semi-structured outdoor (Gazebo)",{"dataset":181,"sequence":194,"environment":192},"Gazebo Winter (trained on Gzb. Summer; 798 pairs)",{"dataset":181,"sequence":196,"environment":197},"Wood Autumn (trained on Wd Summer; 812 pairs)","unstructured forest",{"dataset":181,"sequence":199,"environment":197},"Wood Summer (trained on Wd Autumn; 966 pairs)",[201,203,205],{"name":202,"methodId":42,"linkable":60,"proposed":60,"self":60},"Baseline (mean training covariance)",{"name":204,"methodId":173,"linkable":110,"proposed":110,"self":60},"Ours (CELLO-3D)",{"name":206,"methodId":5,"linkable":110,"proposed":60,"self":110},"Censi",[208,210,212,214,215,217,219,221,223,225,227,229,231,233,235,237,239,241,243,245,247],[117,117,117,209,119,117,119,119,117],34.1,[121,117,117,211,119,117,119,119,121],26.6,[123,117,117,213,119,117,119,119,121],91900000,[117,117,121,150,119,117,119,119,121],[121,117,121,216,119,117,119,119,121],26.7,[123,117,121,218,119,117,119,119,121],206000000,[117,117,123,220,119,117,119,119,121],33.7,[121,117,123,222,119,117,119,119,121],27,[123,117,123,224,119,117,119,119,121],76500000,[117,117,126,226,119,117,119,119,121],20.8,[121,117,126,228,119,117,119,119,121],19.8,[123,117,126,230,119,117,119,119,121],2550000,[117,117,129,232,119,117,119,119,121],20.3,[121,117,129,234,119,117,119,119,121],18.9,[123,117,129,236,119,117,119,119,121],2250000,[117,117,132,238,119,117,119,119,121],13.2,[121,117,132,240,119,117,119,119,121],11.5,[123,117,132,242,119,117,119,119,121],4940000,[117,117,74,244,119,117,119,119,121],13.6,[121,117,74,246,119,117,119,119,121],11.3,[123,117,74,248,119,117,119,119,121],35200000,[],[175],[],[],[254,255],"Average KL divergence between sampled and predicted ICP covariance per test group; trained on the named other group","Average KL divergence per test group",{"slug":257,"group":258,"sourceId":5,"sourceLabel":6,"table":259,"selfRows":132,"metrics":260,"seqs":275,"entrants":280,"cells":288,"outcomes":324,"locators":325,"hardware":327,"wordings":328,"notes":329},"censi2007covariance-fig-4-table-circle-scan-matching","censi2007covariance:Fig. 4 table (circle, scan matching)","Fig. 4 table (circle, scan matching)",[261,265,267,270,273],{"label":262,"unit":263,"statistic":264,"alignment":38},"sigma(x) of ICP error","mm","std",{"label":266,"unit":263,"statistic":264,"alignment":38},"sigma(y) of ICP error",{"label":268,"unit":269,"statistic":264,"alignment":38},"sigma(theta) of ICP error","deg",{"label":271,"unit":272,"statistic":264,"alignment":38},"sigma(w1) projected on O of ICP error","not_reported (projected coordinate)",{"label":274,"unit":272,"statistic":264,"alignment":38},"sigma(w2) projected on O of ICP error",[276],{"dataset":277,"sequence":278,"environment":279},"simulation (Monte Carlo, 300 runs)","circular environment, scan matching","circular environment, scan matching; circle of 5 m radius, first pose (0,2 m,0 deg), displacement (0.1,0,2 deg)",[281,283,285,287],{"name":282,"methodId":42,"linkable":60,"proposed":60,"self":60},"true (Monte Carlo sample)",{"name":284,"methodId":42,"linkable":60,"proposed":60,"self":60},"Hessian [1]",{"name":286,"methodId":42,"linkable":60,"proposed":60,"self":60},"Offline [1]",{"name":114,"methodId":5,"linkable":110,"proposed":110,"self":110},[289,291,292,294,296,298,300,301,303,305,307,309,311,313,315,317,318,320,321,323],[117,117,117,290,119,117,119,119,117],284,[117,121,117,73,119,117,119,119,117],[117,123,117,293,119,117,119,119,117],8.2,[117,126,117,295,119,117,119,119,117],1.5,[117,129,117,297,119,117,119,119,117],0.39,[121,117,117,299,119,117,119,119,117],13,[121,121,117,136,119,117,119,119,117],[121,123,117,302,119,117,119,119,117],0.3,[121,126,117,304,119,117,119,119,117],0.78,[121,129,117,306,119,117,119,119,117],0.36,[123,117,117,308,119,117,119,119,117],378,[123,121,117,310,119,117,119,119,117],43,[123,123,117,312,119,117,119,119,117],5.6,[123,126,117,314,119,117,119,119,117],3.27,[123,129,117,316,119,117,119,119,117],8.37,[126,117,117,299,119,117,119,119,117],[126,121,117,319,119,117,119,119,117],9,[126,123,117,302,119,117,119,119,117],[126,126,117,322,119,117,119,119,117],0.84,[126,129,117,306,119,117,119,119,117],[],[326],"Fig. 4 (embedded table, circle)",[],[],[330],"Std of scan-matching error: Monte Carlo sample (true) vs predicted; sigma(w1), sigma(w2) are errors projected on the observable manifold O",{"slug":332,"group":333,"sourceId":5,"sourceLabel":6,"table":334,"selfRows":132,"metrics":335,"seqs":341,"entrants":345,"cells":350,"outcomes":388,"locators":389,"hardware":391,"wordings":392,"notes":393},"censi2007covariance-fig-4-table-corridor-scan-matching","censi2007covariance:Fig. 4 table (corridor, scan matching)","Fig. 4 table (corridor, scan matching)",[336,337,338,339,340],{"label":262,"unit":263,"statistic":264,"alignment":38},{"label":266,"unit":263,"statistic":264,"alignment":38},{"label":268,"unit":269,"statistic":264,"alignment":38},{"label":271,"unit":272,"statistic":264,"alignment":38},{"label":274,"unit":272,"statistic":264,"alignment":38},[342],{"dataset":277,"sequence":343,"environment":344},"corridor environment, scan matching","corridor environment, scan matching; 10 m square with two sides removed, first pose (0,0,10 deg), displacement (0.1 m,0,2 deg)",[346,347,348,349],{"name":282,"methodId":42,"linkable":60,"proposed":60,"self":60},{"name":284,"methodId":42,"linkable":60,"proposed":60,"self":60},{"name":286,"methodId":42,"linkable":60,"proposed":60,"self":60},{"name":114,"methodId":5,"linkable":110,"proposed":110,"self":110},[351,352,354,356,357,359,361,363,365,367,369,371,373,375,377,379,381,383,385,386],[117,117,117,130,119,117,119,119,117],[117,121,117,353,119,117,119,119,117],219,[117,123,117,355,119,117,119,119,117],0.22,[117,126,117,322,119,117,119,119,117],[117,129,117,358,119,117,119,119,117],0.38,[121,117,117,360,119,117,119,119,117],33,[121,121,117,362,119,117,119,119,117],186,[121,123,117,364,119,117,119,119,117],0.24,[121,126,117,366,119,117,119,119,117],0.94,[121,129,117,368,119,117,119,119,117],0.42,[123,117,117,370,119,117,119,119,117],50,[123,121,117,372,119,117,119,119,117],273,[123,123,117,374,119,117,119,119,117],0.14,[123,126,117,376,119,117,119,119,117],0.63,[123,129,117,378,119,117,119,119,117],0.26,[126,117,117,380,119,117,119,119,117],40,[126,121,117,382,119,117,119,119,117],257,[126,123,117,384,119,117,119,119,117],0.19,[126,126,117,322,119,117,119,119,117],[126,129,117,387,119,117,119,119,117],0.33,[],[390],"Fig. 4 (embedded table, corridor)",[],[],[330],[395,400],{"group":396,"slug":397,"sourceLabel":6,"table":398,"selfRows":126,"datasets":399},"censi2007covariance:Fig. 4 table (square, localization)","censi2007covariance-fig-4-table-square-localization","Fig. 4 table (square, localization)",[277],{"group":401,"slug":402,"sourceLabel":6,"table":403,"selfRows":126,"datasets":404},"censi2007covariance:Fig. 4 table (square, scan matching)","censi2007covariance-fig-4-table-square-scan-matching","Fig. 4 table (square, scan matching)",[277],1790510664055]