[{"data":1,"prerenderedAt":177},["ShallowReactive",2],{"method-furgale2015ct":3},{"method":4,"reference":59,"equipment":80,"figures":113,"results":114},{"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":23,"limitations":28,"sensors":35,"platform":40,"estimator":42,"association":43,"timeModel":44,"deskew":45,"loopClosure":46,"globalOptimization":47,"mapRepresentation":48,"prior":49,"outputGeometry":50,"compute":51,"codeUrl":52,"codeLicense":53,"relatedVersions":54},"furgale2015ct","Furgale et al., 2015","Temporal basis functions (continuous-time batch)","Continuous-time batch trajectory estimation using temporal basis functions",2015,"classic","C03","estimation_framework_or_library","作者指出離散時間估計在 IMU、捲簾快門相機或掃描式雷射等高頻感測器下，需為每個量測時間加入位姿變數，使狀態維度過大。本文把完整的 MAP 估計移到連續時間，在高斯假設下推導目標函數，並以少量時間基底函數的係數作為待估狀態，以批次 Gauss-Newton 法求解，再由系統矩陣的逆取得共變異數。論文以三次 B 樣條的矩陣形式實作，旋轉以 Cayley-Gibbs-Rodrigues 參數表示，程式碼已併入 Kalibr 校正工具箱。實驗包含相機與 IMU 外參校正（模擬 1000 次，以及以 Vicon 為參考的實測資料）與捲簾快門相機對圓點圖板的定位，作者並指出節點數量與配置仍是未解問題。","Formulates full MAP estimation in continuous time, representing the trajectory by coefficients of temporal basis functions (cubic B-splines with Cayley-Gibbs-Rodrigues rotations, released in Kalibr), solved by batch Gauss-Newton and validated on camera-IMU calibration and rolling-shutter localization against Vicon.","full_text_reviewed","peer_reviewed_published","background","not_reported。實驗為模擬，以及 Toronto 大學航太研究所（UTIAS）以 Vicon 動作捕捉為參考的手持相機與 IMU 外參校正，另有捲簾快門相機對圓點圖板的定位；未使用 LiDAR，也未評估點雲幾何。作者雖以旋轉式雷射作為連續時間估計的動機，但本文沒有以雷射資料驗證。",[20,21,22],"simulation","controlled_experiment","independent_reference",[24,25,26,27],"Keeps state size tractable for high-rate sensors: 2 min 20 s of data represented with a few hundred knots instead of about 190,200 discrete time-varying states (abstract; Sec. 6.3.2)","Estimated calibration uncertainty matches the error histogram over 1000 simulation trials (Sec. 6.3.1)","The continuous-time model gives a significantly better rolling-shutter motion estimate than the discrete-time model (Sec. 7.3.2)","Derivation structured by increasingly specific assumptions to enable other continuous-time estimators (abstract)",[29,30,31,32,33,34],"Choice of basis and the number and placement of knots remain open; uniform knots can underfit or overfit (Sec. 7.3.1; Sec. 7.4; Sec. 8)","Without a motion model, extra knots overfit rolling-shutter data or let the spline oscillate between global-shutter images (Sec. 7.3.1)","Rolling-shutter estimates degrade under extreme angular motion compared with global shutter (Sec. 7.3.2)","Spline evaluation and Jacobians add computation and produce less sparse block-banded systems than discrete time (Sec. 7.4)","Adaptive knot selection has only been shown offline; online operation is future work (Sec. 7.4; Sec. 8)","Knot selection for spline-based continuous-time methods remains unresolved according to talbot2025ctsurvey (Sec. V-A)",[36,37,38,39],"stereo camera (Point Grey Research Bumblebee XB3, 24 cm baseline) for camera-IMU calibration","IMU (MicroStrain 3DM-GX2)","rolling-shutter camera (Matrix Vision BlueCougar-X102d)","global-shutter camera (Matrix Vision BlueCougar-X012b) used for comparison",[20,41],"handheld (sensor head moved by hand over point landmarks; camera rig waved in front of a dot-pattern board)","batch MAP estimation in continuous time under Gaussian assumptions; state represented by coefficients of cubic B-spline basis functions (Cayley-Gibbs-Rodrigues rotation parameters) and solved by Gauss-Newton; covariance recovered from the inverse of the Gauss-Newton system matrix; white-noise Gaussian-process motion prior acts as regularizer (Secs. 3-6)","known correspondences: point landmarks observed by the camera, with initial camera poses from OpenCV solvePnP (Sec. 6.2); known circle-grid positions on the pattern board (Sec. 7.1); no data-association search is described","continuous-time state (cubic B-spline, uniform knots) with discrete-time measurements, each evaluated at its own timestamp; rolling-shutter measurement time inferred from the image row and the line delay (Eq. 79)","no LiDAR deskew; rolling-shutter distortion handled by evaluating the spline at the capture time of each image row (Sec. 7.1); sweeping lasers discussed only as related work (Sec. 2)","none (batch calibration and localization experiments)","full batch Gauss-Newton over the whole dataset (up to about 2 min 20 s; limited to four iterations in the real-data timing test) (Sec. 6.3.2)","sparse point landmarks estimated in calibration (priors on three landmarks); known dot-grid positions in rolling-shutter localization; no dense map","priors on the positions of three landmarks for observability; a-priori guesses for gravity, landmark positions and the camera-IMU transform (Secs. 6.1-6.2); known pattern-board geometry (Sec. 7.1)","continuous IMU or camera pose trajectory (spline) with covariance, camera-IMU transform, gravity, IMU bias splines and landmark positions (Secs. 6.1, 6.2, 7.1)","offline batch; simulation: three or four Gauss-Newton iterations took about 12 s per trial; real data (1639 stereo images, 14,211 IMU measurements) converged in about 26 s with 300 knots on a MacBook Pro (2.66 GHz Core 2 Duo, 4 GB RAM), dominated by the linear-system solve (Sec. 6.3)",null,"not_applicable",[55],{"relation":56,"title":57,"doi_or_url":58},"conference_version","Continuous-time batch estimation using temporal basis functions (ICRA 2012, pp. 2088-2095; authors Furgale, Barfoot, Sibley)","10.1109\u002FICRA.2012.6225005",{"id":5,"kind":60,"shortName":7,"title":8,"authors":61,"year":9,"venue":66,"venueType":67,"publisher":68,"volumeIssuePages":69,"doi":70,"arxivId":52,"url":71,"firstPublicDate":72,"publicationStatus":16,"metadataStatus":73,"fulltextStatus":15,"era":10,"classicReason":74,"codeUrl":52,"cluster":11,"topics":75,"mdpi":76,"verification":77,"label":6,"fulltextRoute":78,"versionRead":79,"addedByCensus":76},"method",[62,63,64,65],"Paul Furgale","Chi Hay Tong","Timothy D. Barfoot","Gabe Sibley","The International Journal of Robotics Research","journal","SAGE","34(14):1688-1710","10.1177\u002F0278364915585860","https:\u002F\u002Fapi.crossref.org\u002Fworks\u002F10.1177\u002F0278364915585860","2012-05","metadata_verified","principle reused: formulating MAP estimation in continuous time with temporal basis functions is the basis of spline-based continuous-time estimators used for high-rate and sweeping sensors.",[11],false,"corrected","NTU institutional (Chrome)","Version of record, IJRR 34(14):1688-1710 (first published online 2015-08-05), SAGE HTML full text read in Chrome with National Taiwan University library access; MathML equations were only partly legible in the extracted text",[81,87,92,98,103,107],{"category":82,"model":83,"canonical":83,"role":84,"dataset":52,"specs":85,"locator":86},"stereo_camera","Point Grey Research Bumblebee XB3","method input","wide-baseline (24 cm) stereo cameras","Fig. 4 caption; Sec. 6.3.2",{"category":88,"model":89,"canonical":89,"role":84,"dataset":52,"specs":90,"locator":91},"imu","MicroStrain 3DM-GX2","not_reported","Fig. 4 caption",{"category":93,"model":94,"canonical":94,"role":95,"dataset":52,"specs":96,"locator":97},"other","Vicon motion capture system","reference or ground truth","tracked the sensor head and landmarks; 200 Hz timestamps used for rolling-shutter evaluation","Fig. 4 caption; Sec. 6.3.2; Fig. 13 caption",{"category":99,"model":100,"canonical":100,"role":84,"dataset":52,"specs":101,"locator":102},"camera","Matrix Vision BlueCougar-X102d","CMOS rolling-shutter camera, 1280 x 960 grayscale at 15 frames per second","Fig. 9 caption; Sec. 7.1",{"category":99,"model":104,"canonical":104,"role":105,"dataset":52,"specs":106,"locator":102},"Matrix Vision BlueCougar-X012b","compared device","CMOS global-shutter camera, 1280 x 960 grayscale at 15 frames per second, synchronized with the rolling-shutter camera",{"category":108,"model":109,"canonical":109,"role":110,"dataset":52,"specs":111,"locator":112},"compute","MacBook Pro","compute for runtime","2.66 GHz Core 2 Duo, 4 GB of 1067 MHz DDR3 RAM","Sec. 6.3.2",[],{"totalRows":115,"groupCount":116,"groups":117,"others":176},3,2,[118,153],{"slug":119,"group":120,"sourceId":5,"sourceLabel":6,"table":121,"selfRows":116,"metrics":122,"seqs":129,"entrants":132,"cells":136,"outcomes":144,"locators":146,"hardware":148,"wordings":149,"notes":150},"furgale2015ct-text-sec-6-3-1","furgale2015ct:Text Sec.6.3.1","Text Sec.6.3.1",[123,126],{"label":124,"unit":125,"statistic":90,"alignment":90},"time to run Gauss-Newton to convergence (three or four iterations) per trial, approximately","s",{"label":127,"unit":128,"statistic":90,"alignment":90},"spread of estimated standard deviations across 1000 trials, as a fraction of the standard deviation","%",[130],{"dataset":20,"sequence":131,"environment":20},"",[133],{"name":134,"methodId":5,"linkable":135,"proposed":135,"self":135},"continuous-time batch estimator (B-spline)",true,[137,141],[138,138,138,139,140,138,140,140,138],0,12,-1,[138,142,138,143,138,138,140,140,142],1,0.2,[145],"other: upper bound, reported as less than 0.2% (the quantity is the max-minus-min spread of estimated standard deviations over 1000 trials)",[147],"Sec. 6.3.1",[],[],[151,152],"Simulated 60 s sinusoidal trajectory, 1000 trials (120 monocular images, 5950 IMU measurements, 300 pose basis functions)","Simulated 60 s sinusoidal trajectory, 1000 trials; spread (maximum minus minimum) of estimated standard deviations relative to their value",{"slug":154,"group":155,"sourceId":5,"sourceLabel":6,"table":156,"selfRows":142,"metrics":157,"seqs":160,"entrants":164,"cells":166,"outcomes":169,"locators":170,"hardware":171,"wordings":173,"notes":174},"furgale2015ct-text-sec-6-3-2","furgale2015ct:Text Sec.6.3.2","Text Sec.6.3.2",[158],{"label":159,"unit":125,"statistic":90,"alignment":90},"time to iterate to convergence with 300 knots, approximately",[161],{"dataset":162,"sequence":131,"environment":163},"UTIAS hand-held calibration dataset","controlled experiment (laboratory with Vicon)",[165],{"name":134,"methodId":5,"linkable":135,"proposed":135,"self":135},[167],[138,138,138,168,140,138,138,140,138],26,[],[112],[172],"MacBook Pro, 2.66 GHz Core 2 Duo, 4 GB RAM",[],[175],"Real calibration dataset of about 2 min 20 s (1639 stereo images, 14,211 IMU measurements), 15 bias knots, pose spline with 300 knots, iterated to convergence",[],1790510660530]