[{"data":1,"prerenderedAt":210},["ShallowReactive",2],{"method-furgale2013unifiedcalib":3},{"method":4,"reference":56,"equipment":77,"figures":103,"results":104},{"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":22,"limitations":26,"sensors":32,"platform":35,"estimator":38,"association":39,"timeModel":40,"deskew":41,"loopClosure":41,"globalOptimization":42,"mapRepresentation":41,"prior":43,"outputGeometry":44,"compute":45,"codeUrl":46,"codeLicense":47,"relatedVersions":48},"furgale2013unifiedcalib","Furgale et al., 2013","Kalibr (unified temporal-spatial calibration)","Unified temporal and spatial calibration for multi-sensor systems",2013,"classic","C13","sensing_calibration_sync_preprocessing","本文以連續時間 B-spline 表示 IMU 位姿與偏差，把相機與 IMU 之間的固定時間偏移 d 直接寫入影像量測模型，與外參、重力方向及 IMU 偏差一起以 Levenberg-Marquardt 做最大概似批次估計，取代先估時間、再估空間的兩階段作法。以 FPGA 打時間戳的自製視覺慣性感測器在棋盤格前揮動，四種曝光時間各十組資料的時間偏移對曝光時間斜率為 0.498（理論值 0.5），與擬合線的差異都在 ±0.2 ms 內，約為 IMU 5 ms 取樣週期的 4%。只用陀螺儀、只用加速度計或分離估計的 RMS 誤差分別為 0.165、0.572、0.344 ms，本法為 0.054 ms。","Joint continuous-time maximum-likelihood estimation of temporal offset and spatial transformation between sensors.","full_text_reviewed","peer_reviewed_published","background","not_reported",[20,21],"controlled_experiment","simulation",[23,24,25],"Estimated offset versus exposure time has slope 0.498 (theory 0.5) over 40 real datasets; all deviations from the fit within 0.2 ms, about 4% of the 5 ms IMU period (Sec. V-B, Fig. 5)","Joint use of camera, gyroscopes and accelerometers gave RMS error 0.054 ms versus 0.165 ms (gyroscopes only), 0.572 ms (accelerometer only) and 0.344 ms (separated estimation of Mair et al.) (Sec. V-B, Fig. 7)","Simulation over 500 trials returned consistent marginal uncertainty for the time offset (Sec. V-A, Fig. 4)",[27,28,29,30,31],"Demonstrated for camera-IMU only; LiDAR not covered (inference from scope)","Requires a known calibration target, camera intrinsics and IMU noise models (Sec. IV)","Assumes a constant offset; start-up changes and drift without a common clock need online estimation without a target (Sec. VI)","True delays were unavailable, so accuracy is judged against the expected slope of 0.5 (Sec. V-B)","Temporal padding must be chosen: too small breaks the optimization, too large raises runtime (Sec. IV)",[33,34],"global-shutter cameras (Aptina MT9V034 image sensors in a custom visual-inertial sensor)","IMU (Analog Devices ADIS16488, tactical grade)",[36,37],"custom visual-inertial sensor head waved in front of a static checkerboard calibration pattern (40 real datasets of about 90 s; the paper does not state that it was hand-held)","simulation (500 trials)","continuous-time batch maximum-likelihood estimation: IMU pose as a sixth-order B-spline and biases as cubic B-splines (50 basis functions per second), jointly estimating gravity direction, camera-IMU transform, time offset, pose and biases with Levenberg-Marquardt and the CHOLMOD sparse solver","checkerboard corner detections with known correspondence to calibration-pattern points (assumed known)","continuous-time B-spline states with a single constant time offset d between camera and IMU, estimated jointly by evaluating image error terms at t_j + d; temporal padding of 0.04 s bounds the admissible offset","not_applicable","batch","known calibration pattern geometry, known camera intrinsics (equidistant model), IMU noise and bias models from Allan variance, initial guesses for gravity and camera-IMU transform; time offset initialized at zero; initial pose spline from per-image PnP","time offset and extrinsic transform","offline batch on a MacBook Pro (2.4 GHz Intel Core i7, 8 GB RAM): for an about 80 s dataset each LM iteration takes about 18 s to build and 0.2 s to solve; 3 to 15 iterations, at most 5 min per dataset","https:\u002F\u002Fgithub.com\u002Fethz-asl\u002Fkalibr","BSD-3-Clause-style (LICENSE text checked, first clauses)",[49,53],{"relation":50,"title":51,"doi_or_url":52},"related_follow_up_same_group (journal-version relation not verified)","A General Approach to Spatiotemporal Calibration in Multisensor Systems (see rehder2016spatiotemporal)","https:\u002F\u002Fdoi.org\u002F10.1109\u002FTRO.2016.2529645",{"relation":54,"title":55,"doi_or_url":46},"code_release","Kalibr toolbox",{"id":5,"kind":57,"shortName":7,"title":8,"authors":58,"year":9,"venue":62,"venueType":63,"publisher":64,"volumeIssuePages":65,"doi":66,"arxivId":67,"url":68,"firstPublicDate":69,"publicationStatus":16,"metadataStatus":70,"fulltextStatus":15,"era":10,"classicReason":71,"codeUrl":46,"cluster":11,"topics":72,"mdpi":73,"verification":74,"label":6,"fulltextRoute":75,"versionRead":76,"addedByCensus":73},"method",[59,60,61],"Paul Furgale","Joern Rehder","Roland Siegwart","2013 IEEE\u002FRSJ International Conference on Intelligent Robots and Systems","conference","IEEE","pp. 1280-1286","10.1109\u002Firos.2013.6696514",null,"https:\u002F\u002Fdoi.org\u002F10.1109\u002FIROS.2013.6696514","2013-11","metadata_verified","principle reused: joint maximum-likelihood estimation of time offset and spatial extrinsics with continuous-time batch estimation; LI-Calib reviews this paper (its ref. [19]) among continuous-time calibration work and describes its own method as 'similar in spirit' to Rehder et al. 2014 (IROS, not in this cluster).",[11],false,"corrected","NTU institutional (curl)","IEEE\u002FRSJ IROS 2013 version of record, pp. 1280-1286 (IEEE Xplore PDF via NTU)",[78,84,88,93,97],{"category":79,"model":80,"canonical":80,"role":81,"dataset":67,"specs":82,"locator":83},"camera","Aptina MT9V034","method input","global shutter image sensors (multiple) in a custom-made sensor; 20 Hz frame rate; four fixed exposure times; equidistant intrinsic model; 0.5 px isotropic landmark noise assumed","Sec. V, Sec. V-B",{"category":85,"model":86,"canonical":86,"role":81,"dataset":67,"specs":87,"locator":83},"imu","Analog Devices ADIS16488","tactical grade; 200 Hz; noise parameters from Allan variance",{"category":89,"model":90,"canonical":90,"role":81,"dataset":67,"specs":91,"locator":92},"other","FPGA (model not reported)","all sensor streams routed through it; timestamps taken when image sensors are triggered and IMU data requests start","Sec. V-B",{"category":89,"model":94,"canonical":94,"role":81,"dataset":67,"specs":95,"locator":96},"static checkerboard calibration pattern (dimensions not reported)","known geometry; defines the world frame","Sec. III-B, Fig. 1, Fig. 6",{"category":98,"model":99,"canonical":99,"role":100,"dataset":67,"specs":101,"locator":102},"compute","MacBook Pro","compute for runtime","2.4 GHz Intel Core i7, 8 GB RAM; CHOLMOD sparse solver","Sec. V",[],{"totalRows":105,"groupCount":106,"groups":107,"others":209},6,2,[108,152],{"slug":109,"group":110,"sourceId":5,"sourceLabel":6,"table":111,"selfRows":112,"metrics":113,"seqs":123,"entrants":130,"cells":134,"outcomes":144,"locators":146,"hardware":147,"wordings":149,"notes":150},"furgale2013unifiedcalib-text-sec-v","furgale2013unifiedcalib:Text Sec. V","Text Sec. V",3,[114,117,119],{"label":115,"unit":116,"statistic":18,"alignment":18},"time to build the linear system per LM iteration","s",{"label":118,"unit":116,"statistic":18,"alignment":18},"time to solve the linear system per LM iteration (CHOLMOD)",{"label":120,"unit":121,"statistic":122,"alignment":18},"maximum total time per dataset (3 to 15 LM iterations)","min","max",[124,127],{"dataset":125,"sequence":126,"environment":41},"authors' calibration dataset","about 80 s dataset",{"dataset":128,"sequence":129,"environment":41},"authors' calibration datasets","per dataset",[131],{"name":132,"methodId":5,"linkable":133,"proposed":133,"self":133},"joint estimation (J)",true,[135,139,142],[136,136,136,137,136,136,136,138,136],0,18,-1,[136,140,136,141,138,136,136,138,136],1,0.2,[136,106,140,143,138,136,136,138,136],5,[145],"stated as approximately 18 s",[102],[148],"MacBook Pro, 2.4 GHz Intel Core i7, 8 GB RAM",[],[151],"Runtime for an about 80 s dataset (over 12,400 design variables, 144,000 error terms, 50,000 x 50,000 sparse system)",{"slug":153,"group":154,"sourceId":5,"sourceLabel":6,"table":155,"selfRows":112,"metrics":156,"seqs":167,"entrants":172,"cells":181,"outcomes":199,"locators":201,"hardware":204,"wordings":205,"notes":206},"furgale2013unifiedcalib-text-sec-v-b","furgale2013unifiedcalib:Text Sec. V-B","Text Sec. V-B",[157,161,165],{"label":158,"unit":159,"statistic":18,"alignment":160},"slope of time offset versus exposure time","unitless","none",{"label":162,"unit":163,"statistic":164,"alignment":160},"RMS error with respect to a line of slope 0.5","ms","RMSE",{"label":166,"unit":163,"statistic":122,"alignment":160},"difference of offset estimate to line of best fit",[168],{"dataset":169,"sequence":170,"environment":171},"authors' custom visual-inertial sensor datasets","40 datasets","sensor waved in front of a static calibration pattern",[173,175,177,179],{"name":174,"methodId":5,"linkable":133,"proposed":133,"self":133},"joint estimation, camera plus gyroscopes plus accelerometers (J)",{"name":176,"methodId":67,"linkable":73,"proposed":73,"self":73},"camera plus gyroscopes only (G)",{"name":178,"methodId":67,"linkable":73,"proposed":73,"self":73},"separated estimation (S), reference implementation of Mair et al. 2011",{"name":180,"methodId":67,"linkable":73,"proposed":73,"self":73},"camera plus accelerometer only (A)",[182,184,186,188,190,192,194,196,198],[136,136,136,183,138,136,138,138,136],0.498,[140,136,136,185,138,136,138,138,136],0.493,[106,136,136,187,138,136,138,138,136],0.531,[112,136,136,189,138,136,138,138,136],0.553,[136,140,136,191,138,136,138,138,136],0.054,[140,140,136,193,138,136,138,138,136],0.165,[106,140,136,195,138,136,138,138,136],0.344,[112,140,136,197,138,136,138,138,136],0.572,[136,106,136,141,136,140,138,138,140],[200],"all 40 differences stated to lie within plus or minus 0.2 ms",[202,203],"Sec. V-B, Fig. 7","Sec. V-B, Fig. 5(b)",[],[],[207,208],"40 real datasets (4 exposure times x 10, about 90 s each); slope of estimated time offset versus exposure time (theory 0.5) and RMS error to a line of slope 0.5; values also shown in Fig. 7","Difference between each of the 40 time-offset estimates and the line of best fit (joint estimation)",[],1790510664066]