[{"data":1,"prerenderedAt":558},["ShallowReactive",2],{"method-eckenhoff2019closedform":3},{"method":4,"reference":56,"equipment":76,"figures":98,"results":99},{"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":24,"limitations":29,"sensors":34,"platform":37,"estimator":40,"association":41,"timeModel":42,"deskew":43,"loopClosure":44,"globalOptimization":45,"mapRepresentation":46,"prior":47,"outputGeometry":48,"compute":49,"codeUrl":50,"codeLicense":43,"relatedVersions":51},"eckenhoff2019closedform","Eckenhoff et al., 2019","Closed-form preintegration","Closed-form preintegration methods for graph-based visual-inertial navigation",2019,"recent","C03","estimation_framework_or_library","本文推導 IMU 預積分方程的閉式解，而非以離散取樣近似量測動態，並提出兩種慣性模型：分段常數量測，以及分段常數的局部真實加速度。作者以 Monte Carlo 模擬分析模型選擇對估計的影響，並把此預積分分別用於緊耦合滑動視窗最佳化與鬆耦合直接影像對齊兩種視覺慣性系統。","Derives closed-form IMU preintegration under two inertial models and validates it in sliding-window and direct visual-inertial systems.","full_text_reviewed","peer_reviewed_published","supplementary","未在營建場域驗證；真實資料為 EuRoC 與 Delaware 大學 Gore Hall（228 m，跨三層樓）及 Smith Hall（230 m，跨兩層樓）的手持 VI-Sensor 資料。後兩者沒有獨立參考真值，以回到起點的終點誤差評估，並以樓層平面圖投影呈現軌跡，未評估點雲幾何。",[20,21,22,23],"simulation","public_benchmark","independent_reference","completed_building",[25,26,27,28],"Closed-form solutions improve estimation accuracy compared with discrete sampling (abstract)","In 50 Monte Carlo Gazebo MAV runs, Model 2 reached RMSE 0.093 m and 0.300 deg versus 0.107 m and 0.328 deg for discrete preintegration, without extra computational overhead (Sec. VI)","Gains over discrete preintegration are larger at lower IMU rates, relevant for low-cost MEMS sensors (Sec. VI; Table I)","On the 230 m UD Smith Hall run, Model 1 ending error was 0.632 m versus 1.699 m for OKVIS (Sec. VII-A2)",[30,31,32,33],"Proposed models improve on discrete preintegration in most but not all cases and are competitive with, not uniformly better than, OKVIS on EuRoC (Sec. VII-A; Tables II-III)","Direct VINS is sensitive to tuning parameters and drifts more when loop closures are unavailable; some V2 03 diff runs accepted incorrect loop closures (Sec. VII-B)","Improvement over discrete preintegration is small in the MAV simulation and shrinks at higher IMU rates (Sec. VI; Table I)","UD indoor runs have no ground truth; only return-to-start ending errors are reported (Sec. VII-A2)",[35,36],"IMU","stereo camera (both real-world systems)",[20,38,39],"UAV (EuRoC MAV dataset)","handheld (VI-Sensor in two University of Delaware buildings)","indirect system: tightly coupled sliding-window optimization with marginalization using closed-form preintegration; direct system: loosely coupled direct stereo image alignment whose relative-pose factors and preintegration factors are optimized with iSAM2 (GTSAM) without marginalization","indirect VIO: FAST features on a uniform grid tracked with KLT, stereo correspondences by KLT from left to right image, 8-point RANSAC outlier rejection and Cauchy loss (Sec. VII-A); direct VINS: photometric alignment of high-gradient pixels against keyframes with a Huber cost, keyframe depth from OpenCV StereoSGBM (Sec. V-B; Sec. VII-B)","discrete keyframes with analytically integrated IMU models","not_applicable","direct VINS keeps all states (no marginalization) to allow loop closures and outperforms the indirect VIO on loop-rich EuRoC sequences (Sec. VII-B)","indirect VIO: sliding-window bundle adjustment (inertial window 6 and pose window 8 on EuRoC, up to 300 features) solved with Ceres using the Schur complement, with marginalization; direct VINS: iSAM2 incremental smoothing in GTSAM over all states without marginalization, allowing loop-closure relative-pose factors; simulation: GTSAM fixed-lag smoother (Sec. VI; Sec. VII)","no persistent map: sparse features in inverse-depth parameterization inside the sliding window (features marginalized after 3 s in simulation); the direct VINS keeps keyframes with stereo depth maps for alignment (Sec. V-A; Sec. VI; Sec. VII-B)","none","IMU trajectory (orientation, position, velocity, biases); IMU-camera extrinsics and camera intrinsics estimated online in the UD experiments; no dense map or point cloud (Sec. VII-A2)","real-time claimed; EuRoC window sizes chosen for real-time operation with minimal dropped frames; direct image alignment implemented as a CUDA kernel for GPU acceleration (GPU model not reported); no runtime values reported (Sec. VII)",null,[52],{"relation":53,"title":54,"doi_or_url":55},"preprint","arXiv:1805.02774 (v1 2018-05-07; v2 2019-03-20 final)","https:\u002F\u002Farxiv.org\u002Fabs\u002F1805.02774",{"id":5,"kind":57,"shortName":7,"title":58,"authors":59,"year":9,"venue":63,"venueType":64,"publisher":65,"volumeIssuePages":66,"doi":67,"arxivId":68,"url":55,"firstPublicDate":69,"publicationStatus":16,"metadataStatus":70,"fulltextStatus":15,"era":10,"classicReason":43,"codeUrl":50,"cluster":11,"topics":71,"mdpi":72,"verification":73,"label":6,"fulltextRoute":74,"versionRead":75,"addedByCensus":72},"method","Closed-form preintegration methods for graph-based visual–inertial navigation",[60,61,62],"Kevin Eckenhoff","Patrick Geneva","Guoquan Huang","The International Journal of Robotics Research","journal","SAGE","38(5):563-586","10.1177\u002F0278364919835021","1805.02774","2018-05-07","metadata_verified",[11],false,"corrected","arXiv","arXiv 1805.02774v2 (2019-03-20), labelled 'Final version ... accepted December 20, 2018' to IJRR; the SAGE version of record (38(5):563-586) was not opened",[77,84,88,93],{"category":78,"model":79,"canonical":79,"role":80,"dataset":81,"specs":82,"locator":83},"imu","ADIS16448","dataset sensor","EuRoC MAV","MEMS IMU, 200 Hz","Sec. VII-A1",{"category":85,"model":86,"canonical":50,"role":80,"dataset":81,"specs":87,"locator":83},"stereo_camera","not_reported","stereo pairs at 20 Hz",{"category":85,"model":89,"canonical":89,"role":90,"dataset":50,"specs":91,"locator":92},"VI-Sensor","method input","hand-held; IMU at 400 Hz; stereo images used by the stereo VIO; camera intrinsics and IMU-camera extrinsics estimated online","Sec. VII-A2",{"category":94,"model":95,"canonical":95,"role":96,"dataset":50,"specs":86,"locator":97},"compute","not_reported (GPU running the CUDA direct-alignment kernel)","compute for runtime","Sec. VII-B",[],{"totalRows":100,"groupCount":101,"groups":102,"others":557},92,4,[103,341,501,530],{"slug":104,"group":105,"sourceId":5,"sourceLabel":6,"table":106,"selfRows":107,"metrics":108,"seqs":116,"entrants":140,"cells":152,"outcomes":335,"locators":336,"hardware":337,"wordings":338,"notes":339},"eckenhoff2019closedform-table-ii","eckenhoff2019closedform:Table II","Table II",44,[109,113],{"label":110,"unit":111,"statistic":112,"alignment":47},"position RMSE","m","RMSE",{"label":114,"unit":115,"statistic":112,"alignment":47},"orientation RMSE","deg",[117,120,122,124,126,128,130,132,134,136,138],{"dataset":81,"sequence":118,"environment":119},"V1 01 easy","public benchmark (EuRoC MAV)",{"dataset":81,"sequence":121,"environment":119},"V1 02 med",{"dataset":81,"sequence":123,"environment":119},"V1 03 diff",{"dataset":81,"sequence":125,"environment":119},"V2 01 easy",{"dataset":81,"sequence":127,"environment":119},"V2 02 med",{"dataset":81,"sequence":129,"environment":119},"V2 03 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stereo VIO; absolute RMSE averaged over 10 runs; ground-truth initialisation",{"slug":342,"group":343,"sourceId":5,"sourceLabel":6,"table":344,"selfRows":107,"metrics":345,"seqs":348,"entrants":360,"cells":364,"outcomes":495,"locators":496,"hardware":497,"wordings":498,"notes":499},"eckenhoff2019closedform-table-iv","eckenhoff2019closedform:Table IV","Table IV",[346,347],{"label":110,"unit":111,"statistic":112,"alignment":47},{"label":114,"unit":115,"statistic":112,"alignment":47},[349,350,351,352,353,354,355,356,357,358,359],{"dataset":81,"sequence":118,"environment":119},{"dataset":81,"sequence":121,"environment":119},{"dataset":81,"sequence":123,"environment":119},{"dataset":81,"sequence":125,"environment":119},{"dataset":81,"sequence":127,"environment":119},{"dataset":81,"sequence":129,"environment":119},{"dataset":81,"sequence":131,"environment":119},{"dataset":81,"sequence":133,"environment":119},{"dataset":81,"sequence":135,"environment":119},{"dataset":81,"sequence":137,"environment":119},{"dataset":81,"sequence":139,"environment":119},[361,362,363],{"name":142,"methodId":5,"linkable":143,"proposed":143,"self":143},{"name":145,"methodId":5,"linkable":143,"proposed":143,"self":143},{"name":147,"methodId":148,"linkable":143,"proposed":72,"self":72},[365,367,369,371,373,375,377,379,381,383,385,387,389,391,393,395,397,398,400,402,404,406,408,410,412,414,416,418,420,422,424,426,428,430,432,434,436,438,440,442,444,446,448,450,452,454,456,458,459,461,463,465,467,469,471,473,475,477,479,481,483,485,487,489,491,493],[154,154,154,366,156,154,156,156,154],0.2445,[154,158,154,368,156,154,156,156,154],2.218,[158,154,154,370,156,154,156,156,154],0.2482,[158,158,154,372,156,154,156,156,154],2.246,[165,154,154,374,156,154,156,156,154],0.253,[165,158,154,376,156,154,156,156,154],2.223,[154,154,158,378,156,154,156,156,154],0.1598,[154,158,158,380,156,154,156,156,154],1.767,[158,154,158,382,156,154,156,156,154],0.1309,[158,158,158,384,156,154,156,156,154],1.483,[165,154,158,386,156,154,156,156,154],0.1763,[165,158,158,388,156,154,156,156,154],1.899,[154,154,165,390,156,154,156,156,154],0.099,[154,158,165,392,156,154,156,156,154],1.18,[158,154,165,394,156,154,156,156,154],0.103,[158,158,165,396,156,154,156,156,154],1.279,[165,154,165,394,156,154,156,156,154],[165,158,165,399,156,154,156,156,154],1.234,[154,154,170,401,156,154,156,156,154],0.1627,[154,158,170,403,156,154,156,156,154],2.089,[158,154,170,405,156,154,156,156,154],0.194,[158,158,170,407,156,154,156,156,154],1.956,[165,154,170,409,156,154,156,156,154],0.1664,[165,158,170,411,156,154,156,156,154],1.533,[154,154,101,413,156,154,156,156,154],0.1809,[154,158,101,415,156,154,156,156,154],2.53,[158,154,101,417,156,154,156,156,154],0.1665,[158,158,101,419,156,154,156,156,154],2.527,[165,154,101,421,156,154,156,156,154],0.1688,[165,158,101,423,156,154,156,156,154],2.309,[154,154,238,425,156,154,156,156,154],0.9337,[154,158,238,427,156,154,156,156,154],6.187,[158,154,238,429,156,154,156,156,154],0.8927,[158,158,238,431,156,154,156,156,154],5.425,[165,154,238,433,156,154,156,156,154],1.0137,[165,158,238,435,156,154,156,156,154],4.998,[154,154,255,437,156,154,156,156,154],0.2947,[154,158,255,439,156,154,156,156,154],2.27,[158,154,255,441,156,154,156,156,154],0.3277,[158,158,255,443,156,154,156,156,154],2.148,[165,154,255,445,156,154,156,156,154],0.3217,[165,158,255,447,156,154,156,156,154],2.226,[154,154,272,449,156,154,156,156,154],0.1882,[154,158,272,451,156,154,156,156,154],1.65,[158,154,272,453,156,154,156,156,154],0.2136,[158,158,272,455,156,154,156,156,154],1.582,[165,154,272,457,156,154,156,156,154],0.2008,[165,158,272,384,156,154,156,156,154],[154,154,287,460,156,154,156,156,154],0.233,[154,158,287,462,156,154,156,156,154],2.096,[158,154,287,464,156,154,156,156,154],0.2295,[158,158,287,466,156,154,156,156,154],2.121,[165,154,287,468,156,154,156,156,154],0.2288,[165,158,287,470,156,154,156,156,154],2.092,[154,154,303,472,156,154,156,156,154],0.4792,[154,158,303,474,156,154,156,156,154],2.513,[158,154,303,476,156,154,156,156,154],0.4867,[158,158,303,478,156,154,156,156,154],2.627,[165,154,303,480,156,154,156,156,154],0.4724,[165,158,303,482,156,154,156,156,154],2.562,[154,154,320,484,156,154,156,156,154],0.2884,[154,158,320,486,156,154,156,156,154],1.664,[158,154,320,488,156,154,156,156,154],0.3014,[158,158,320,490,156,154,156,156,154],1.722,[165,154,320,492,156,154,156,156,154],0.2946,[165,158,320,494,156,154,156,156,154],1.7,[],[344],[],[],[500],"Direct stereo VINS (iSAM2, loop closures); absolute RMSE averaged over 10 runs; ground-truth initialisation",{"slug":502,"group":503,"sourceId":5,"sourceLabel":6,"table":504,"selfRows":165,"metrics":505,"seqs":509,"entrants":514,"cells":519,"outcomes":524,"locators":525,"hardware":526,"wordings":527,"notes":528},"eckenhoff2019closedform-text-sec-vii-a2-gore-hall","eckenhoff2019closedform:Text Sec.VII-A2 (Gore Hall)","Text Sec.VII-A2 (Gore Hall)",[506],{"label":507,"unit":111,"statistic":508,"alignment":47},"ending error (0.33% of the path)","mean",[510],{"dataset":511,"sequence":512,"environment":513},"UD Gore Hall","","completed building (indoor, three floors)",[515,517],{"name":516,"methodId":5,"linkable":143,"proposed":143,"self":143},"Model 1",{"name":518,"methodId":5,"linkable":143,"proposed":143,"self":143},"Model 2",[520,522],[154,154,154,521,156,154,156,156,154],0.763,[158,154,154,523,156,154,156,156,154],0.747,[],[92],[],[],[529],"228 m hand-held loop from the first floor up the staircase to the third floor and back, one loop per level; ending error at the return to the start; each preintegration model run ten times and averaged",{"slug":531,"group":532,"sourceId":5,"sourceLabel":6,"table":533,"selfRows":165,"metrics":534,"seqs":539,"entrants":543,"cells":546,"outcomes":551,"locators":552,"hardware":553,"wordings":554,"notes":555},"eckenhoff2019closedform-text-sec-vii-a2-smith-hall","eckenhoff2019closedform:Text Sec.VII-A2 (Smith Hall)","Text Sec.VII-A2 (Smith Hall)",[535,537],{"label":536,"unit":111,"statistic":86,"alignment":47},"ending error (0.28% of the path)",{"label":538,"unit":111,"statistic":86,"alignment":47},"ending error (0.35% of the path)",[540],{"dataset":541,"sequence":512,"environment":542},"UD Smith Hall","completed building (indoor, two floors)",[544,545],{"name":516,"methodId":5,"linkable":143,"proposed":143,"self":143},{"name":518,"methodId":5,"linkable":143,"proposed":143,"self":143},[547,549],[154,154,154,548,156,154,156,156,154],0.632,[158,158,154,550,156,154,156,156,154],0.788,[],[92],[],[],[556],"230 m hand-held run over the second and first floors returning to the start, with people walking, varying lighting and feature-poor areas; ending error at the return to the start",[],1790510657718]