[{"data":1,"prerenderedAt":377},["ShallowReactive",2],{"method-li2014onlinetemporal":3},{"method":4,"reference":55,"equipment":75,"figures":97,"results":98},{"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":30,"sensors":35,"platform":38,"estimator":41,"association":42,"timeModel":43,"deskew":44,"loopClosure":44,"globalOptimization":45,"mapRepresentation":44,"prior":45,"outputGeometry":46,"compute":47,"codeUrl":48,"codeLicense":49,"relatedVersions":50},"li2014onlinetemporal","Li & Mourikis, 2014","Online temporal calibration (camera-IMU)","Online temporal calibration for camera-IMU systems: Theory and algorithms",2014,"classic","C13","sensing_calibration_sync_preprocessing","本文把相機與 IMU 之間的時間偏移 td 納入 EKF 狀態，與 IMU 位姿、速度、偏差、相機對 IMU 外參及特徵位置一起線上估計，可用於已知地圖定位、EKF-SLAM 與 MSCKF 視覺慣性里程計，只增加一個純量狀態。作者證明除零角速度、等角速度或加速度計讀值固定等少數退化運動外，td 皆為局部可辨識，而這些運動即使已知 td 也會失去可觀性。實驗與模擬顯示線上估計的精度幾乎等同事先已知 td（Sec. 4 至 7）。","Estimates camera-IMU time offset online as a state variable and proves local identifiability except for a few degenerate motions.","full_text_reviewed","peer_reviewed_published","background","not_reported",[20,21,22,23],"simulation","controlled_experiment","completed_building","independent_reference",[25,26,27,28,29],"td estimate converged within seconds with a final standard deviation of 0.40 ms in the indoor map-based test, and maximum position error at known points was 4.6 cm (Sec. 7.1.1)","Map-based and EKF-SLAM td estimates agreed within 2.5 ms after the first 3 s and ended 0.7 ms apart (Sec. 7.1.2)","Outdoor MSCKF VIO over about 7.3 km kept errors below 0.5% of distance travelled, close to the known-td result and clearly better than nominal td = 0 with measured extrinsics (Sec. 7.1.3)","In 50-run VIO simulations, estimating both td and extrinsics gave pose RMSE close to perfectly known parameters (north 8.11 vs 7.93 m), while fixing either degraded accuracy and consistency (Table 3)","A simulated clock drift from 20 to 520 ms over 500 s was tracked consistently (Sec. 7.2.4)",[31,32,33,34],"td is not identifiable for zero or constant rotational velocity and for constant accelerometer readings, though these motions also break observability with known td (Sec. 6.4, 6.5)","If images lag the IMU (td \u003C 0) the EKF outputs estimates with latency unless a separate propagation thread is used (Sec. 4.4)","Indoor ground truth existed only at three time instants of the trajectory (Sec. 7.1.1)","Feature NEES in the EKF-SLAM simulation was 4.48 against an expected 3, attributed to measurement nonlinearity (Sec. 7.2.2)",[36,37],"monocular camera (one camera of a PointGrey Bumblebee2 stereo pair, 20 Hz)","IMU (Xsens MTI-G, 100 Hz)",[39,40,20],"sensor platform moved in two loops around a lab room (carrying mode not stated)","roof of a car driving about 7.3 km in 11 min in Riverside, CA","EKF with td (constant, or random walk when time-varying) and the camera-to-IMU transform in the state; demonstrated as map-based EKF localization, EKF-SLAM (inverse depth then xyz features, modified-Jacobian approach for consistency) and MSCKF 2.0 visual-inertial odometry, where only state augmentation at t + td changes","20 blue LEDs at known positions (map-based and persistent SLAM features); Shi-Tomasi corners tracked in images (about 65 temporary features per image in EKF-SLAM), matched by normalized cross-correlation in VIO","discrete-time IMU propagation; each image processed at t plus the current td estimate using a linearly interpolated IMU sample; td modeled as constant or as a random walk; optional timestamp jitter term in the residual covariance","not_applicable","none","time offset, poses","online, multi-threaded EKF (separate sensor queues and EKF thread); only one extra scalar state; runtime not reported",null,"not_verified",[51],{"relation":52,"title":53,"doi_or_url":54},"conference_version","3-D motion estimation and online temporal calibration for camera-IMU systems (ICRA 2013)","https:\u002F\u002Fdoi.org\u002F10.1109\u002FICRA.2013.6631398",{"id":5,"kind":56,"shortName":7,"title":57,"authors":58,"year":9,"venue":61,"venueType":62,"publisher":63,"volumeIssuePages":64,"doi":65,"arxivId":48,"url":66,"firstPublicDate":67,"publicationStatus":16,"metadataStatus":68,"fulltextStatus":15,"era":10,"classicReason":69,"codeUrl":48,"cluster":11,"topics":70,"mdpi":71,"verification":72,"label":6,"fulltextRoute":73,"versionRead":74,"addedByCensus":71},"method","Online temporal calibration for camera–IMU systems: Theory and algorithms",[59,60],"Mingyang Li","Anastasios I. Mourikis","The International Journal of Robotics Research","journal","SAGE","33(7), pp. 947-964","10.1177\u002F0278364913515286","https:\u002F\u002Fdoi.org\u002F10.1177\u002F0278364913515286","2014-05-01","metadata_verified","principle reused: time offset treated as an estimated state with identifiability analysis; the same idea underlies online time-offset estimation in later LiDAR-inertial systems.",[11],false,"confirmed","NTU institutional (Chrome)","SAGE version of record, full-text HTML (IJRR 33(7):947-964), read on the NTU network",[76,82,86,92],{"category":77,"model":78,"canonical":78,"role":79,"dataset":48,"specs":80,"locator":81},"stereo_camera","PointGrey Bumblebee2 stereo pair (only one camera used)","method input","images at 20 Hz","Sec. 7.1",{"category":83,"model":84,"canonical":84,"role":79,"dataset":48,"specs":85,"locator":81},"imu","Xsens MTI-G","inertial measurements at 100 Hz",{"category":87,"model":88,"canonical":88,"role":89,"dataset":48,"specs":90,"locator":91},"gnss","GPS-INS system (model not stated)","reference or ground truth","ground truth for the outdoor driving experiment","Sec. 7.1.3",{"category":93,"model":94,"canonical":94,"role":89,"dataset":48,"specs":95,"locator":96},"other","20 blue LED lights at accurately known positions","mapped visual features and position reference in the lab","Sec. 7.1.1, 7.1.2",[],{"totalRows":99,"groupCount":100,"groups":101,"others":354},36,8,[102,236,283,320],{"slug":103,"group":104,"sourceId":5,"sourceLabel":6,"table":105,"selfRows":106,"metrics":107,"seqs":133,"entrants":138,"cells":148,"outcomes":228,"locators":229,"hardware":230,"wordings":231,"notes":232},"li2014onlinetemporal-table-3","li2014onlinetemporal:Table 3","Table 3",10,[108,112,114,116,119,121,123,126,128,130],{"label":109,"unit":110,"statistic":111,"alignment":18},"IMU position RMSE north","m","RMSE",{"label":113,"unit":110,"statistic":111,"alignment":18},"IMU position RMSE east",{"label":115,"unit":110,"statistic":111,"alignment":18},"IMU position RMSE down",{"label":117,"unit":118,"statistic":111,"alignment":18},"IMU orientation RMSE roll","deg",{"label":120,"unit":118,"statistic":111,"alignment":18},"IMU orientation RMSE pitch",{"label":122,"unit":118,"statistic":111,"alignment":18},"IMU orientation RMSE yaw",{"label":124,"unit":45,"statistic":125,"alignment":18},"IMU state NEES","mean",{"label":127,"unit":110,"statistic":111,"alignment":18},"calibration RMSE camera-to-IMU translation",{"label":129,"unit":118,"statistic":111,"alignment":18},"calibration RMSE camera-to-IMU rotation",{"label":131,"unit":132,"statistic":111,"alignment":18},"calibration RMSE td","ms",[134],{"dataset":135,"sequence":136,"environment":137},"simulation (from real trajectory)","VIO 5.5 km","simulated outdoor driving",[139,141,143,146],{"name":140,"methodId":48,"linkable":71,"proposed":71,"self":71},"imprecise: T_IC estimation on, td estimation off",{"name":142,"methodId":48,"linkable":71,"proposed":71,"self":71},"imprecise: T_IC estimation off, td estimation on",{"name":144,"methodId":5,"linkable":145,"proposed":145,"self":145},"proposed: T_IC and td estimation on",true,{"name":147,"methodId":48,"linkable":71,"proposed":71,"self":71},"precise: T_IC and td perfectly known",[149,153,156,159,162,164,166,168,170,172,174,176,178,180,182,184,185,188,189,191,192,194,196,198,200,203,205,207,209,212,213,215,216,218,219,220,221,223,225,227],[150,150,150,151,152,150,152,152,150],0,54.6,-1,[154,150,150,155,152,150,152,152,154],1,18.39,[157,150,150,158,152,150,152,152,154],2,8.11,[160,150,150,161,152,150,152,152,154],3,7.93,[150,154,150,163,152,150,152,152,154],81.82,[154,154,150,165,152,150,152,152,154],13.5,[157,154,150,167,152,150,152,152,154],5.18,[160,154,150,169,152,150,152,152,154],5,[150,157,150,171,152,150,152,152,154],14.53,[154,157,150,173,152,150,152,152,154],45.07,[157,157,150,175,152,150,152,152,154],0.64,[160,157,150,177,152,150,152,152,154],0.53,[150,160,150,179,152,150,152,152,154],0.39,[154,160,150,181,152,150,152,152,154],0.18,[157,160,150,183,152,150,152,152,154],0.06,[160,160,150,183,152,150,152,152,154],[150,186,150,187,152,150,152,152,154],4,0.33,[154,186,150,181,152,150,152,152,154],[157,186,150,190,152,150,152,152,154],0.05,[160,186,150,190,152,150,152,152,154],[150,169,150,193,152,150,152,152,154],1.19,[154,169,150,195,152,150,152,152,154],1.22,[157,169,150,197,152,150,152,152,154],0.7,[160,169,150,199,152,150,152,152,154],0.69,[150,201,150,202,152,150,152,152,157],6,85.4,[154,201,150,204,152,150,152,152,154],2046,[157,201,150,206,152,150,152,152,154],14.6,[160,201,150,208,152,150,152,152,154],14.5,[150,210,150,211,152,150,152,152,154],7,0.07,[154,210,150,48,150,150,152,152,154],[157,210,150,214,152,150,152,152,154],0.01,[160,210,150,48,150,150,152,152,154],[150,100,150,217,152,150,152,152,154],0.31,[154,100,150,48,150,150,152,152,154],[157,100,150,190,152,150,152,152,154],[160,100,150,48,150,150,152,152,154],[150,222,150,48,150,150,152,152,154],9,[154,222,150,224,152,150,152,152,154],0.28,[157,222,150,226,152,150,152,152,154],0.25,[160,222,150,48,150,150,152,152,154],[44],[105],[],[],[233,234,235],"MSCKF VIO simulation from a real 13 min, 5.5 km ground-truth trajectory; 50 Monte Carlo trials; average RMSE and NEES; imprecise cases start from nominal T_IC and td","MSCKF VIO simulation, 50 trials","MSCKF VIO simulation, 50 trials; expected NEES for a consistent 15-dim IMU error state is 15",{"slug":237,"group":238,"sourceId":5,"sourceLabel":6,"table":239,"selfRows":210,"metrics":240,"seqs":256,"entrants":260,"cells":263,"outcomes":276,"locators":277,"hardware":278,"wordings":279,"notes":280},"li2014onlinetemporal-table-2","li2014onlinetemporal:Table 2","Table 2",[241,243,245,248,250,252,254],{"label":242,"unit":110,"statistic":111,"alignment":18},"RMSE GpI (IMU position)",{"label":244,"unit":118,"statistic":111,"alignment":18},"RMSE IMU orientation",{"label":246,"unit":247,"statistic":111,"alignment":18},"RMSE GvI (IMU velocity)","m\u002Fs",{"label":249,"unit":110,"statistic":111,"alignment":18},"RMSE CpI (camera-to-IMU translation)",{"label":251,"unit":118,"statistic":111,"alignment":18},"RMSE camera-to-IMU rotation",{"label":253,"unit":110,"statistic":111,"alignment":18},"RMSE Gpf (feature position)",{"label":255,"unit":132,"statistic":111,"alignment":18},"RMSE td",[257],{"dataset":20,"sequence":258,"environment":259},"EKF-SLAM","simulated room",[261],{"name":262,"methodId":5,"linkable":145,"proposed":145,"self":145},"proposed EKF-SLAM with online td and T_IC",[264,266,268,270,271,272,274],[150,150,150,265,152,150,152,152,150],0.078,[150,154,150,267,152,150,152,152,154],0.26,[150,157,150,269,152,150,152,152,154],0.017,[150,160,150,214,152,150,152,152,154],[150,186,150,211,152,150,152,152,154],[150,169,150,273,152,150,152,152,154],0.094,[150,201,150,275,152,150,152,152,154],0.1,[],[239],[],[],[281,282],"EKF-SLAM simulation in a 7 x 12 x 5 m room for 90 s at 0.37 m\u002Fs average, 50 persistent and 100 temporary features per image; RMSE averaged over Monte Carlo trials and second half","EKF-SLAM simulation",{"slug":284,"group":285,"sourceId":5,"sourceLabel":6,"table":286,"selfRows":201,"metrics":287,"seqs":294,"entrants":298,"cells":301,"outcomes":313,"locators":314,"hardware":315,"wordings":316,"notes":317},"li2014onlinetemporal-table-1","li2014onlinetemporal:Table 1","Table 1",[288,289,290,291,292,293],{"label":242,"unit":110,"statistic":111,"alignment":18},{"label":244,"unit":118,"statistic":111,"alignment":18},{"label":246,"unit":247,"statistic":111,"alignment":18},{"label":249,"unit":110,"statistic":111,"alignment":18},{"label":251,"unit":118,"statistic":111,"alignment":18},{"label":255,"unit":132,"statistic":111,"alignment":18},[295],{"dataset":20,"sequence":296,"environment":297},"map-based","simulated landmarks",[299],{"name":300,"methodId":5,"linkable":145,"proposed":145,"self":145},"proposed map-based EKF with online td",[302,304,305,307,309,311],[150,150,150,303,152,150,152,152,150],0.096,[150,154,150,275,152,150,152,152,154],[150,157,150,306,152,150,152,152,154],0.021,[150,160,150,308,152,150,152,152,154],0.088,[150,186,150,310,152,150,152,152,154],0.036,[150,169,150,312,152,150,152,152,154],1.519,[],[286],[],[],[318,319],"Map-based EKF simulation, 50 Monte Carlo trials, sinusoidal trajectory, 6 known landmarks per image (5 to 20 m), IMU 100 Hz, images 10 Hz, td drawn from N(0, 50 ms); RMSE averaged over trials and second half of trajectory","Map-based EKF simulation, 50 trials",{"slug":321,"group":322,"sourceId":5,"sourceLabel":6,"table":323,"selfRows":186,"metrics":324,"seqs":333,"entrants":335,"cells":337,"outcomes":346,"locators":347,"hardware":349,"wordings":350,"notes":351},"li2014onlinetemporal-text-sec-7-2-2","li2014onlinetemporal:Text Sec. 7.2.2","Text Sec. 7.2.2",[325,327,329,331],{"label":326,"unit":45,"statistic":125,"alignment":45},"average NEES IMU state (expected 15)",{"label":328,"unit":45,"statistic":125,"alignment":45},"average NEES T_IC (expected 6)",{"label":330,"unit":45,"statistic":125,"alignment":45},"average NEES td (expected 1)",{"label":332,"unit":45,"statistic":125,"alignment":45},"average NEES feature position (expected 3)",[334],{"dataset":20,"sequence":258,"environment":259},[336],{"name":262,"methodId":5,"linkable":145,"proposed":145,"self":145},[338,340,342,344],[150,150,150,339,152,150,152,152,150],17,[150,154,150,341,152,150,152,152,154],6.66,[150,157,150,343,152,150,152,152,154],0.87,[150,160,150,345,152,150,152,152,154],4.48,[],[348],"Sec. 7.2.2",[],[],[352,353],"EKF-SLAM simulation consistency; expected values 15, 6, 1 and 3","EKF-SLAM simulation consistency",[355,361,366,371],{"group":356,"slug":357,"sourceLabel":6,"table":358,"selfRows":160,"datasets":359},"li2014onlinetemporal:Text Sec. 7.1.2","li2014onlinetemporal-text-sec-7-1-2","Text Sec. 7.1.2",[360],"own indoor lab dataset",{"group":362,"slug":363,"sourceLabel":6,"table":364,"selfRows":160,"datasets":365},"li2014onlinetemporal:Text Sec. 7.2.1","li2014onlinetemporal-text-sec-7-2-1","Text Sec. 7.2.1",[20],{"group":367,"slug":368,"sourceLabel":6,"table":369,"selfRows":157,"datasets":370},"li2014onlinetemporal:Text Sec. 7.1.1","li2014onlinetemporal-text-sec-7-1-1","Text Sec. 7.1.1",[360],{"group":372,"slug":373,"sourceLabel":6,"table":374,"selfRows":154,"datasets":375},"li2014onlinetemporal:Text Sec. 7.1.3","li2014onlinetemporal-text-sec-7-1-3","Text Sec. 7.1.3",[376],"own Riverside driving dataset",1790510663312]