[{"data":1,"prerenderedAt":102},["ShallowReactive",2],{"method-barfoot2014gp":3},{"method":4,"reference":55,"equipment":74,"figures":101,"results":48},{"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":27,"sensors":33,"platform":36,"estimator":38,"association":39,"timeModel":40,"deskew":41,"loopClosure":42,"globalOptimization":43,"mapRepresentation":44,"prior":45,"outputGeometry":46,"compute":47,"codeUrl":48,"codeLicense":49,"relatedVersions":50},"barfoot2014gp","Barfoot et al., 2014","Exactly sparse GP trajectory (STEAM)","Batch Continuous-Time Trajectory Estimation as Exactly Sparse Gaussian Process Regression",2014,"classic","C03","estimation_framework_or_library","本文把批次軌跡估計視為以時間為自變數的一維高斯過程（Gaussian process, GP）迴歸，先驗由白雜訊驅動的線性時變隨機微分方程定義（例如等速度模型）。作者證明這類先驗的逆核矩陣為精確稀疏的區塊三對角結構，因此能高效求解量測時間的狀態，並用 GP 內插查詢任意時間的狀態。量測為線性時結果等同傳統離散時間平滑；非線性時則對整條軌跡迭代，並以行動機器人資料示範同時軌跡估計與建圖（STEAM）。","Shows that GP trajectory priors generated by linear time-varying SDEs yield an exactly sparse inverse kernel, enabling efficient batch continuous-time estimation and interpolation (STEAM).","full_text_reviewed","peer_reviewed_published","background","未在營建場域驗證；實驗為室內平面環境與 17 根塑膠管地標，並以 Vicon 動作擷取系統提供軌跡與地標真值 [Sec. IV-D]。作者指出可先以相機估計軌跡，再於每個雷射取樣時間查詢位姿 [Sec. I]，此能力與移動掃描點雲的時間對位有關（推論）。",[20,21],"controlled_experiment","independent_reference",[23,24,25,26],"Exactly sparse (block-tridiagonal) inverse kernel enables efficient solution and interpolation (abstract; Sec. VI)","Separates prior over trajectories from odometry measurement noise (Sec. V)","Overall cost O(M + N) for M measurement times and N query times instead of O(M^3 + M^2 N) without sparsity (Sec. III-F)","GP-Traj-Sparse converged in fewer iterations than the dense variants because the inverse kernel is built directly, which improved numerical stability (Sec. IV-D)",[28,29,30,31,32],"Demonstrated on a planar mobile-robot example (Sec. IV); 3D extension handled in later work (inference from related versions and talbot2025ctsurvey)","Exact sparsity requires a Markovian state, e.g. stacking position and velocity for the constant-velocity prior; marginalizing the velocity makes the inverse kernel dense (Sec. III-D; Sec. V)","Without exploiting sparsity the stacked-state estimator (GP-Traj-Dense) was much slower than the original pose-only method of Tong et al. (Sec. IV-D)","No accuracy gain is claimed: the three estimators had similar accuracy on this dataset and the evaluation focuses on computational cost (Sec. IV-D)","Priors from nonlinear SDEs and online large-scale solvers are left to future work (Sec. V)",[34,35],"2D laser rangefinder (range\u002Fbearing to tube landmarks)","wheel odometry",[37],"wheeled UGV","batch GP regression with Markovian priors from linear time-varying SDEs, solved by Gauss-Newton iterations over the whole trajectory and landmarks with a sparse Cholesky decomposition that exploits the block-tridiagonal inverse kernel (O(L^3 + L^2 M) per iteration); GP interpolation queries the state at other times in O(1) each","not_reported (range and bearing measurements to the 17 plastic-tube landmarks of the Tong et al. dataset are used; the paper does not describe how measurements are associated with landmarks)","continuous-time (Gaussian process prior, e.g., white-noise-on-acceleration constant velocity)","not implemented; Sec. I motivates continuous-time priors for scanning-while-moving sensors and proposes querying an estimated camera trajectory at every laser acquisition time","not_reported","batch estimation over full trajectory and landmarks (STEAM)","landmarks","GP motion prior (white noise on acceleration, i.e. constant velocity, with a stacked position and velocity state); power spectral density Q_C modelled as diagonal and obtained by fitting Gaussians to the state accelerations in the training data (measurement noise determined from the training data in the same way); first trajectory state locked (held fixed) in the factor graph","trajectory queryable at any time via GP interpolation, plus landmark positions","MATLAB implementation timed on a MacBook Pro (2.7 GHz i7, 16 GB 1600 MHz DDR3 RAM); for GP-Traj-Sparse the kernel construction, per-iteration optimization and total time grow linearly with trajectory length and interpolation time per query is constant (Sec. IV-D, Fig. 5)",null,"not_applicable",[51],{"relation":52,"title":53,"doi_or_url":54},"journal_extension","Batch nonlinear continuous-time trajectory estimation as exactly sparse Gaussian process regression (Autonomous Robots 39(3):221-238, 2015; Anderson, Barfoot, Tong, Särkkä)","10.1007\u002Fs10514-015-9455-y",{"id":5,"kind":56,"shortName":7,"title":8,"authors":57,"year":9,"venue":61,"venueType":62,"publisher":63,"volumeIssuePages":42,"doi":64,"arxivId":48,"url":65,"firstPublicDate":66,"publicationStatus":16,"metadataStatus":67,"fulltextStatus":15,"era":10,"classicReason":68,"codeUrl":48,"cluster":11,"topics":69,"mdpi":70,"verification":71,"label":6,"fulltextRoute":72,"versionRead":73,"addedByCensus":70},"method",[58,59,60],"Timothy D. Barfoot","Chi Hay Tong","Simo Särkkä","Robotics: Science and Systems X","conference","RSS Foundation","10.15607\u002Frss.2014.x.001","https:\u002F\u002Fwww.roboticsproceedings.org\u002Frss10\u002Fp01.pdf","2014-07-12","metadata_verified","principle reused: the exactly sparse GP motion prior underlies GP-based continuous-time estimators, including later LiDAR and radar odometry according to talbot2025ctsurvey.",[11],false,"corrected","publisher OA","Version of record: Robotics: Science and Systems X (2014) online proceedings PDF rss10\u002Fp01.pdf (9 pages)",[75,82,86,92,96],{"category":76,"model":77,"canonical":77,"role":78,"dataset":79,"specs":80,"locator":81},"lidar","laser rangefinder (model not reported)","dataset sensor","Tong et al. indoor tube-landmark dataset (paper ref. [46])","range and bearing to 17 plastic-tube landmarks; odometry and landmark measurements at 1 Hz","Sec. IV-B; Sec. IV-D",{"category":83,"model":84,"canonical":84,"role":78,"dataset":79,"specs":85,"locator":81},"wheel_or_leg_odometry","wheel odometry (robot-oriented longitudinal and rotational speed)","1 Hz",{"category":87,"model":88,"canonical":88,"role":89,"dataset":79,"specs":90,"locator":91},"other","Vicon motion capture system","reference or ground truth","ground truth for robot trajectory and landmark positions","Sec. IV-D",{"category":93,"model":94,"canonical":94,"role":78,"dataset":79,"specs":95,"locator":91},"platform","mobile robot (model not reported)","indoor, planar environment",{"category":97,"model":98,"canonical":98,"role":99,"dataset":48,"specs":100,"locator":91},"compute","MacBook Pro (2.7 GHz i7, 16 GB 1600 MHz DDR3 RAM)","compute for runtime","all three estimators implemented in MATLAB",[],1790510661250]