[{"data":1,"prerenderedAt":477},["ShallowReactive",2],{"method-zhang2016degeneracy":3},{"method":4,"reference":49,"equipment":70,"figures":95,"results":96},{"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":27,"sensors":32,"platform":35,"estimator":37,"association":38,"timeModel":39,"deskew":40,"loopClosure":41,"globalOptimization":42,"mapRepresentation":43,"prior":44,"outputGeometry":43,"compute":45,"codeUrl":46,"codeLicense":47,"relatedVersions":48},"zhang2016degeneracy","Zhang et al., 2016","Degeneracy factor \u002F solution remapping","On degeneracy of optimization-based state estimation problems",2016,"classic","C02","registration_component","本文把退化定義為解對約束擾動的剛度，並證明線性化系統的退化因子 D 等於 AᵀA 最小特徵值加一，對應的特徵向量即為最退化的方向。方法以門檻判定退化方向（門檻取自一組同時含良好與退化場景的樣本資料，設在兩群間隔的中點），再以解重映射（solution remapping）在退化方向保留預測值、只在條件良好方向更新，可作為 Levenberg-Marquardt 等求解器的外掛步驟，額外複雜度為 O(kn² + n³)。作者以 uEye 相機與馬達旋轉的 Hokuyo UTM-30LX 組成的手持視覺光達系統，在走廊、平坦地面以及 538 m 室內外路線測試，終點位置誤差為行進距離的 0.71%。","Defines a degeneracy factor D = lambda_min + 1 of A^T A (stiffness of the solution under a constraint disturbance), thresholds eigenvalues to find degenerate directions, and applies solution remapping that keeps the prediction in degenerate directions and updates only well-conditioned ones; demonstrated on a handheld camera and rotating-lidar system with 0.71% end error over 538 m.","full_text_reviewed","peer_reviewed_published","main_body","原文未在工地驗證；後續 X-ICP 在瑞士 Rümlang 工地的比較中以本法為基線並指出其單一門檻的問題（見 tuna2024xicp）。",[],[21,22,23,24,25,26],"improves estimation in environmentally degenerate cases (abstract)","In the corridor test the D\u002FICN ratio drops at the two feature-poor corners, which the authors read as D being more effective than ICN; IMCE is noisy because it also depends on the residual sum and constraint count (Sec. VI Test 1, Fig. 7)","On flat ground, the compared ICN and D curves show an obvious drop between 35 and 70 s and D\u002FICN decreases slightly, while IMCE is noisy or barely decreases because it also depends on R and the number of constraints (Sec. VI Test 2, Fig. 8)","Identified the physically expected degenerate directions: lateral or vertical translation for visual odometry (Test 1); forward and lateral translation plus yaw on flat ground (Test 2)","Test 3 (538 m indoor and outdoor loop): 0.71% end position error, whereas a constant motion prior gave about three times larger end drift (Sec. VI, Fig. 10)","Negligible add-in cost as a plug-in to common solvers (Sec. I, Theorem 1)",[28,29,30,31],"Threshold is set empirically at the midpoint between well-conditioned and degenerate lambda_min groups from one sample dataset (Sec. IV-B, Fig. 4)","Assumes A is appropriately noise-weighted and the problem is full rank (Sec. III)","Relies on the prediction in degenerate directions, which the authors treat as the only usable estimate there (Sec. IV-B, Sec. VII; dependency, not an author-stated limitation)","single eigenvalue threshold needs heuristic tuning because rotation and translation eigenvalue scales differ (tuna2024xicp Sec. VII-D\u002FE, secondary)",[33,34],"monocular camera (uEye monochrome, 60 Hz, 752 x 480, 76 deg horizontal FOV)","custom 3D lidar (Hokuyo UTM-30LX rotated by a motor, 0.25 deg encoder)",[36],"handheld (sensor pack carried by a person walking at 0.5 m\u002Fs)","Plug-in to linear or nonlinear least-squares solvers: eigen-decomposition of A^T A at the first nonlinear iteration, eigenvalues below an empirical threshold mark degenerate directions, and solution remapping updates only well-conditioned directions (Algorithm 1); demonstrated inside three Levenberg-Marquardt modules (frame-to-frame visual odometry, sweep-to-sweep refinement, sweep-to-map registration)","not_applicable (generic to optimization-based estimation; demonstrated with scan matching and visual constraints)","not_applicable to the degeneracy method itself; the host vision-lidar system models visual odometry drift with constant velocity within each 1 s lidar sweep","not_applicable to the degeneracy method itself; the host system removes lidar distortion caused by visual odometry drift with a linear motion model within a sweep","not_reported","none","not_applicable","A prediction x_p is required and kept in the degenerate directions; in Test 1 it came from a constant velocity model","Adds O(kn^2 + n^3) time to the original solver (Theorem 1), which reduces to O(k) for small fixed n such as 6-DOF; directions are computed at the first nonlinear iteration only; host system runs visual odometry at 60 Hz and scan matching at 1 Hz; processor not reported",null,"not_verified",[],{"id":5,"kind":50,"shortName":7,"title":8,"authors":51,"year":9,"venue":55,"venueType":56,"publisher":57,"volumeIssuePages":58,"doi":59,"arxivId":46,"url":60,"firstPublicDate":61,"publicationStatus":16,"metadataStatus":62,"fulltextStatus":15,"era":10,"classicReason":63,"codeUrl":46,"cluster":11,"topics":64,"mdpi":66,"verification":67,"label":6,"fulltextRoute":68,"versionRead":69,"addedByCensus":66},"component",[52,53,54],"Ji Zhang","Michael Kaess","Sanjiv Singh","2016 IEEE International Conference on Robotics and Automation (ICRA)","conference","IEEE","pp. 809-816","10.1109\u002Ficra.2016.7487211","https:\u002F\u002Fwww.cs.cmu.edu\u002F~kaess\u002Fpub\u002FZhang16icra.pdf","2016-05","metadata_verified","principle reused: defines a degeneracy factor from the eigen-structure of the linearized problem and solution remapping that only updates well-conditioned directions; later LiDAR degeneracy work (X-ICP, Hinduja 2019, Tuna 2025, Hatleskog 2024) uses it as the reference baseline.",[11,65],"C13",false,"corrected","author copy","Author-posted copy on the CMU (Kaess) publication page carrying the published IEEE ICRA 2016 layout (pp. 809-816, 978-1-4673-8025-6\u002F16, © 2016 IEEE); pagination matches the version of record. IEEE Xplore copy not opened.",[71,77,81,86,90],{"category":72,"model":73,"canonical":73,"role":74,"dataset":46,"specs":75,"locator":76},"camera","uEye monochrome camera","method input","60 Hz frame rate, 752 x 480 pixels, 76 deg horizontal field of view","Sec. V-A; Fig. 5",{"category":78,"model":79,"canonical":79,"role":74,"dataset":46,"specs":80,"locator":76},"lidar","Hokuyo UTM-30LX","180 deg field of view, 0.25 deg resolution, 40 lines\u002Fs; rotated by a motor to form a custom 3D lidar",{"category":82,"model":83,"canonical":83,"role":74,"dataset":46,"specs":84,"locator":85},"other","motor (model not reported)","rotates the laser scanner back and forth between -90 and 90 deg at 180 deg\u002Fs average; one 180 deg sweep lasts 1 s","Sec. V-A; Sec. V-B2",{"category":82,"model":87,"canonical":87,"role":74,"dataset":46,"specs":88,"locator":89},"encoder (model not reported)","measures motor rotation angle with 0.25 deg resolution","Sec. V-A",{"category":91,"model":92,"canonical":92,"role":74,"dataset":46,"specs":93,"locator":94},"platform","handheld custom-built camera and lidar sensor pack","carried by a person walking at 0.5 m\u002Fs","Sec. VI; Fig. 5",[],{"totalRows":97,"groupCount":98,"groups":99,"others":424},45,13,[100,215,286,368],{"slug":101,"group":102,"sourceId":103,"sourceLabel":104,"table":105,"selfRows":106,"metrics":107,"seqs":125,"entrants":134,"cells":143,"outcomes":208,"locators":209,"hardware":210,"wordings":211,"notes":212},"tuna2024xicp-table-i","tuna2024xicp:Table I","tuna2024xicp","Tuna et al., 2024","Table I",9,[108,112,114,117,118,120,121,122,123],{"label":109,"unit":110,"statistic":111,"alignment":41},"APE Translation mu(sigma) [m]","m","mean",{"label":109,"unit":110,"statistic":113,"alignment":41},"std",{"label":115,"unit":116,"statistic":111,"alignment":41},"APE Rotation mu(sigma) [deg]","deg",{"label":115,"unit":116,"statistic":113,"alignment":41},{"label":109,"unit":110,"statistic":111,"alignment":119},"first-pose",{"label":109,"unit":110,"statistic":113,"alignment":119},{"label":115,"unit":116,"statistic":111,"alignment":119},{"label":115,"unit":116,"statistic":113,"alignment":119},{"label":124,"unit":110,"statistic":41,"alignment":41},"Last Position Error [m]",[126,130,132],{"dataset":127,"sequence":128,"environment":129},"Seemuhle underground mine (authors' data)","VLP-16 run; first 15 m alignment","underground mine tunnel",{"dataset":127,"sequence":131,"environment":129},"VLP-16 run; origin alignment",{"dataset":127,"sequence":133,"environment":129},"VLP-16 run; full 521.8 m traverse",[135,138,140],{"name":136,"methodId":103,"linkable":137,"proposed":137,"self":66},"X-ICP (Proposed)",true,{"name":139,"methodId":5,"linkable":137,"proposed":66,"self":137},"Zhang et al. [12]",{"name":141,"methodId":142,"linkable":137,"proposed":66,"self":66},"Hinduja et al. [17]","hinduja2019degeneracy",[144,148,151,154,157,160,163,166,169,172,174,176,178,180,182,184,186,188,190,192,194,196,198,200,202,204,206],[145,145,145,146,147,145,147,147,145],0,2.05,-1,[145,149,145,150,147,145,147,147,149],1,1.23,[145,152,145,153,147,145,147,147,149],2,2.55,[145,155,145,156,147,145,147,147,149],3,0.76,[145,158,149,159,147,145,147,147,149],4,2.45,[145,161,149,162,147,145,147,147,149],5,1.35,[145,164,149,165,147,145,147,147,149],6,2.5,[145,167,149,168,147,145,147,147,149],7,1.03,[145,170,152,171,147,145,147,147,149],8,0.27,[149,145,145,173,147,145,147,147,149],3.36,[149,149,145,175,147,145,147,147,149],1.74,[149,152,145,177,147,145,147,147,149],4.06,[149,155,145,179,147,145,147,147,149],1.37,[149,158,149,181,147,145,147,147,149],3.73,[149,161,149,183,147,145,147,147,149],1.8,[149,164,149,185,147,145,147,147,149],4.11,[149,167,149,187,147,145,147,147,149],1.52,[149,170,152,189,147,145,147,147,149],6.37,[152,145,145,191,147,145,147,147,149],5.79,[152,149,145,193,147,145,147,147,149],5.26,[152,152,145,195,147,145,147,147,149],7.67,[152,155,145,197,147,145,147,147,149],4.72,[152,158,149,199,147,145,147,147,149],8.16,[152,161,149,201,147,145,147,147,149],4.83,[152,164,149,203,147,145,147,147,149],8.03,[152,167,149,205,147,145,147,147,149],4.73,[152,170,152,207,147,145,147,147,149],24.17,[],[105],[],[],[213,214],"Seemuhle underground mine, ANYmal with VLP-16, 521.8 m; APE via EVO against Leica RTC 360 ground truth, mu (sigma); 'first 15 m' = trajectory aligned on the first 15 m (about 200 poses), 'origin' = aligned at the first pose; plus last-position error","Same setting as other Table I rows",{"slug":216,"group":217,"sourceId":218,"sourceLabel":219,"table":220,"selfRows":170,"metrics":221,"seqs":238,"entrants":246,"cells":255,"outcomes":280,"locators":281,"hardware":282,"wordings":283,"notes":284},"hatleskog2024probdegen-table-ii","hatleskog2024probdegen:Table II","hatleskog2024probdegen","Hatleskog & Alexis, 2024","Table II",[222,224,226,228,230,232,234,236],{"label":223,"unit":110,"statistic":111,"alignment":41},"APE [m], mean (SD 0.13)",{"label":225,"unit":116,"statistic":111,"alignment":41},"APE [deg], mean (SD 0.52)",{"label":227,"unit":110,"statistic":111,"alignment":41},"RPE [m], mean (SD 0.01)",{"label":229,"unit":116,"statistic":111,"alignment":41},"RPE [deg], mean (SD 0.21)",{"label":231,"unit":110,"statistic":111,"alignment":41},"APE [m], mean (SD 0.12)",{"label":233,"unit":116,"statistic":111,"alignment":41},"APE [deg], mean (SD 0.17)",{"label":235,"unit":110,"statistic":111,"alignment":41},"RPE [m], mean (SD 0.03)",{"label":237,"unit":116,"statistic":111,"alignment":41},"RPE [deg], mean (SD 0.19)",[239,243],{"dataset":240,"sequence":241,"environment":242},"Seemühle Mine","full trajectory","abandoned underground mine, self-similar tunnel",{"dataset":240,"sequence":244,"environment":245},"non-tunnel segments","underground mine, segments before and after the tunnel",[247,249,251,253],{"name":248,"methodId":5,"linkable":137,"proposed":66,"self":137},"Zhang [14]",{"name":250,"methodId":142,"linkable":137,"proposed":66,"self":66},"Hinduja [15]",{"name":252,"methodId":218,"linkable":137,"proposed":137,"self":66},"Ours",{"name":254,"methodId":46,"linkable":66,"proposed":66,"self":66},"Lee [19] (Switch-SLAM)",[256,258,260,262,264,265,266,267,269,270,272,274,275,277,278,279],[145,145,145,257,147,145,147,147,145],0.57,[149,145,145,259,147,145,147,147,145],0.18,[145,149,145,261,147,145,147,147,145],0.6,[152,152,145,263,147,145,147,147,145],0.01,[145,152,145,263,147,145,147,147,145],[149,152,145,263,147,145,147,147,145],[155,152,145,263,147,145,147,147,145],[145,155,145,268,147,145,147,147,145],0.17,[155,155,145,268,147,145,147,147,145],[145,158,149,271,147,145,147,147,145],0.53,[145,161,149,273,147,145,147,147,145],0.7,[145,164,149,263,147,145,147,147,145],[152,167,149,276,147,145,147,147,145],0.12,[145,167,149,276,147,145,147,147,145],[149,167,149,276,147,145,147,147,145],[155,167,149,276,147,145,147,147,145],[],[220],[],[],[285],"Seemühle mine, mean (SD) APE and RPE",{"slug":287,"group":288,"sourceId":289,"sourceLabel":290,"table":291,"selfRows":158,"metrics":292,"seqs":298,"entrants":305,"cells":321,"outcomes":362,"locators":363,"hardware":364,"wordings":365,"notes":366},"genzicp2025-table-v","genzicp2025:Table V","genzicp2025","Lee et al., 2025a","Table V",[293,296],{"label":294,"unit":110,"statistic":295,"alignment":41},"absolute pose error, translation, RMSE [m]","RMSE",{"label":297,"unit":110,"statistic":295,"alignment":41},"relative pose error, translation, RMSE [m]",[299,303],{"dataset":300,"sequence":301,"environment":302},"Ground-Challenge","Corridor1 (zigzag)","indoor corridor (degenerate)",{"dataset":300,"sequence":304,"environment":302},"Corridor2 (straight forward)",[306,309,312,315,317,319],{"name":307,"methodId":308,"linkable":137,"proposed":66,"self":66},"KISS-ICP [5]","kissicp2023",{"name":310,"methodId":311,"linkable":137,"proposed":66,"self":66},"CT-ICP [6]","cticp2022",{"name":313,"methodId":314,"linkable":137,"proposed":66,"self":66},"DLO [14]","dlo2022",{"name":316,"methodId":5,"linkable":137,"proposed":66,"self":137},"Zhang et al. [18]",{"name":318,"methodId":103,"linkable":137,"proposed":66,"self":66},"X-ICP [24]",{"name":320,"methodId":289,"linkable":137,"proposed":137,"self":66},"Ours (GenZ-ICP)",[322,324,326,328,330,332,334,336,337,338,340,342,343,345,347,349,351,353,354,355,356,358,359,361],[145,145,145,323,147,145,147,147,145],2.17,[145,149,145,325,147,145,147,147,145],0.15,[149,145,145,327,147,145,147,147,145],0.54,[149,149,145,329,147,145,147,147,145],0.06,[152,145,145,331,147,145,147,147,145],0.45,[152,149,145,333,147,145,147,147,145],0.08,[155,145,145,335,147,145,147,147,145],0.28,[155,149,145,329,147,145,147,147,145],[158,145,145,146,147,145,147,147,145],[158,149,145,339,147,145,147,147,145],0.07,[161,145,145,341,147,145,147,147,145],0.24,[161,149,145,329,147,145,147,147,145],[145,145,149,344,147,145,147,147,145],0.68,[145,149,149,346,147,145,147,147,145],0.16,[149,145,149,348,147,145,147,147,145],1.3,[149,149,149,350,147,145,147,147,145],0.14,[152,145,149,352,147,145,147,147,145],0.93,[152,149,149,350,147,145,147,147,145],[155,145,149,335,147,145,147,147,145],[155,149,149,350,147,145,147,147,145],[158,145,149,357,147,145,147,147,145],6.92,[158,149,149,325,147,145,147,147,145],[161,145,149,360,147,145,147,147,145],0.2,[161,149,149,350,147,145,147,147,145],[],[291],[],[],[367],"Ground-Challenge corridors; translation APE and RPE via EVO; only RMSE columns kept (mean, max, std omitted); Zhang et al. and X-ICP reimplemented by the authors on the same LiDAR-only framework",{"slug":369,"group":370,"sourceId":218,"sourceLabel":219,"table":105,"selfRows":158,"metrics":371,"seqs":374,"entrants":389,"cells":394,"outcomes":411,"locators":414,"hardware":419,"wordings":420,"notes":421},"hatleskog2024probdegen-table-i","hatleskog2024probdegen:Table I",[372],{"label":373,"unit":42,"statistic":41,"alignment":42},"degeneracy-induced drift (qualitative)",[375,379,381,385],{"dataset":376,"sequence":377,"environment":378},"Rümlang Construction Site","exp. 1 (VLP-16, FOV cut to 180 deg)","large open area of a construction site",{"dataset":240,"sequence":380,"environment":129},"exp. 2 (VLP-16, full FOV)",{"dataset":382,"sequence":383,"environment":384},"RelyOn Nutec","exp. 3 (OS0-64, FOV cut to 180 deg)","cylindrical tank, radius 8 m, height 16 m",{"dataset":386,"sequence":387,"environment":388},"Fyllingsdalen Bicycle Tunnel","exp. 4 (OS0-128, full FOV)","500 m straight bicycle tunnel section",[390,391,392,393],{"name":252,"methodId":218,"linkable":137,"proposed":137,"self":66},{"name":248,"methodId":5,"linkable":137,"proposed":66,"self":137},{"name":250,"methodId":142,"linkable":137,"proposed":66,"self":66},{"name":254,"methodId":46,"linkable":66,"proposed":66,"self":66},[395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410],[145,145,145,46,145,145,147,147,145],[149,145,145,46,149,145,147,147,149],[152,145,145,46,149,145,147,147,149],[155,145,145,46,149,145,147,147,149],[145,145,149,46,145,149,147,147,149],[149,145,149,46,149,149,147,147,149],[152,145,149,46,145,149,147,147,149],[155,145,149,46,149,149,147,147,149],[145,145,152,46,145,152,147,147,149],[149,145,152,46,149,152,147,147,149],[152,145,152,46,149,152,147,147,149],[155,145,152,46,149,152,147,147,149],[145,145,155,46,145,155,147,147,149],[149,145,155,46,149,155,147,147,149],[152,145,155,46,145,155,147,147,149],[155,145,155,46,149,155,147,147,149],[412,413],"no degeneracy-induced drift","degeneracy-induced drift",[415,416,417,418],"Table I, Fig. 2","Table I, Fig. 3","Table I, Fig. 4","Table I, Fig. 5",[],[],[422,423],"Qualitative presence or absence of degeneracy-induced drift in partial maps; no numeric values","Qualitative drift check",[425,429,436,442,448,454,460,465,471],{"group":426,"slug":427,"sourceLabel":104,"table":220,"selfRows":158,"datasets":428},"tuna2024xicp:Table II","tuna2024xicp-table-ii",[127],{"group":430,"slug":431,"sourceLabel":432,"table":433,"selfRows":158,"datasets":434},"tuna2025informed:Table 3","tuna2025informed-table-3","Tuna et al., 2025","Table 3",[435],"ANYmal simulation",{"group":437,"slug":438,"sourceLabel":432,"table":439,"selfRows":155,"datasets":440},"tuna2025informed:Table 4","tuna2025informed-table-4","Table 4",[441],"ANYmal forest experiment",{"group":443,"slug":444,"sourceLabel":432,"table":445,"selfRows":155,"datasets":446},"tuna2025informed:Table 5","tuna2025informed-table-5","Table 5",[447],"ENWIDE (Ulmberg bicycle tunnel)",{"group":449,"slug":450,"sourceLabel":290,"table":451,"selfRows":152,"datasets":452},"genzicp2025:Table VI","genzicp2025-table-vi","Table VI",[453],"SubT-MRS",{"group":455,"slug":456,"sourceLabel":290,"table":457,"selfRows":149,"datasets":458},"genzicp2025:Table IV","genzicp2025-table-iv","Table IV",[459],"HILTI-Oxford 2022",{"group":461,"slug":462,"sourceLabel":219,"table":463,"selfRows":149,"datasets":464},"hatleskog2024probdegen:Text Sec. IV-E","hatleskog2024probdegen-text-sec-iv-e","Text Sec. IV-E",[386],{"group":466,"slug":467,"sourceLabel":432,"table":468,"selfRows":149,"datasets":469},"tuna2025informed:Table 6","tuna2025informed-table-6","Table 6",[470],"HEAP excavator experiment",{"group":472,"slug":473,"sourceLabel":6,"table":474,"selfRows":149,"datasets":475},"zhang2016degeneracy:Text Sec.VI","zhang2016degeneracy-text-sec-vi","Text Sec.VI",[476],"authors' own data (Test 3)",1790510657825]