[{"data":1,"prerenderedAt":548},["ShallowReactive",2],{"method-legentil2020gpm":3},{"method":4,"reference":46,"equipment":65,"figures":94,"results":95},{"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":25,"sensors":32,"platform":35,"estimator":37,"association":38,"timeModel":39,"deskew":40,"loopClosure":38,"globalOptimization":38,"mapRepresentation":38,"prior":41,"outputGeometry":42,"compute":43,"codeUrl":44,"codeLicense":38,"relatedVersions":45},"legentil2020gpm","Le Gentil et al., 2020","Gaussian Process Preintegration (GPM)","Gaussian Process Preintegration for Inertial-Aided State Estimation",2020,"recent","C03","estimation_framework_or_library","本文以高斯過程（GP）連續表示慣性量測，並對 GP 核函數施加線性運算子，推導出「高斯預積分量測」（GPM）。旋轉僅繞單一軸時，旋轉與速度、位置增量都可解析積分；若含三維旋轉，旋轉增量仍需先以 GP 上取樣再數值積分，速度與位置增量則由重投影到起始 IMU 座標後的加速度計訊號以 GP 推論。此法不需明確運動模型，也沒有離散積分雜訊，適合非同步的慣性輔助估計；作者並推導偏差與感測器間時間偏移的一階修正 Jacobian。模擬比較中 GPM 與 UPM 的誤差約比離散預積分低一個數量級，並整合進 LiDAR 慣性定位與建圖框架 IN2LAAMA 驗證可用性。","Gaussian-process preintegration models IMU signals as GPs and applies linear operators to the kernels, giving analytic preintegration over arbitrary intervals when rotation is about a single axis (3D rotations still need GP upsampling and numerical integration of Delta R), with first-order bias and inter-sensor time-shift corrections; benchmarked in simulation and validated inside the IN2LAAMA lidar-inertial framework.","full_text_reviewed","peer_reviewed_published","supplementary","未在營建場域驗證。真實資料僅為 UTS 實驗室（既有建物）內 6.2 m 的手持 VLP-16 軌跡；以人工分割平牆的平均點到平面距離比較（離散預積分 9.0 mm，GPM 6.3 mm）[Sec. V-B]。這是本群集少數直接量測點雲幾何品質的結果，但規模極小、無獨立參考，其工程意義有限（推論）。",[20,21],"simulation","completed_building",[23,24],"Analytical integration over any time interval; no explicit motion model and no numerical integration noise (abstract)","Outperformed upsampled and on-manifold discrete preintegration in simulated accuracy tests (Sec. V-A; Sec. VI)",[26,27,28,29,30,31],"Cubic computational complexity of GPs; close-to-real-time only (Sec. VI)","Assumes constant bias during preintegration; releasing this is future work (Sec. VI)","GPMs are much slower for motions with 3D rotations because Delta R is computed numerically (Sec. V-A3, Table III)","With 3D rotations the accuracy gain over UPMs is smaller because both share the numerical rotation step (Sec. V-A2)","Query rates above about 2 Hz do not allow hyper-parameter training from scratch for each interval (Sec. VI)","(inference) Real-data validation is a single 6.2 m hand-held run and no ground-truth reference is reported (Sec. V-B)",[33,34],"IMU","3D LiDAR (validation within IN2LAAMA)",[20,36],"handheld (Velodyne VLP-16 3D lidar + MTi3 Xsens IMU, as written)","preintegrated measurements from GP models (square exponential kernel) of IMU signals with linear operators on kernels: analytic integral inference for single-axis rotation, numerical integration after GP upsampling for 3D rotation; velocity and position inferred from GP models of accelerometer data reprojected into the IMU frame at t1; first-order post-integration bias and time-shift Jacobians","not_applicable","continuous representation of inertial signals","not described in this paper; the authors state that GPMs can be used with asynchronous platforms and rolling-shutter-like sensors, citing spinning lidars as such sensors (Sec. I); how IN2LAAMA [23] handles lidar motion distortion is not described here","none","preintegrated measurements (Delta R, Delta v, Delta p with covariance) over any time interval; within IN2LAAMA a lidar point-cloud map and trajectory are produced (Fig. 4)","benchmarks in single-thread, non-optimised Matlab on a laptop with an Intel i5-6300U at 2.40 GHz and 24 GiB RAM; GPM inference 1.3 to 212 ms (single-axis) and 10.2 to 817 ms (3D rotation) for 0.05 to 5 s intervals, plus about 0.28 to 7.1 s of hyper-parameter training when not reused (Table III); cubic GP complexity, close to real time (Sec. VI)",null,[],{"id":5,"kind":47,"shortName":7,"title":8,"authors":48,"year":9,"venue":52,"venueType":53,"publisher":54,"volumeIssuePages":55,"doi":56,"arxivId":44,"url":57,"firstPublicDate":58,"publicationStatus":16,"metadataStatus":59,"fulltextStatus":15,"era":10,"classicReason":38,"codeUrl":44,"cluster":11,"topics":60,"mdpi":61,"verification":62,"label":6,"fulltextRoute":63,"versionRead":64,"addedByCensus":61},"component",[49,50,51],"Cedric Le Gentil","Teresa Vidal-Calleja","Shoudong Huang","IEEE Robotics and Automation Letters","journal","IEEE","5(2):2108-2114","10.1109\u002Flra.2020.2970940","https:\u002F\u002Fopus.lib.uts.edu.au\u002Fbitstream\u002F10453\u002F145251\u002F3\u002FGaussian%20Process%20Preintegration%20for%20Inertial-Aided%20State%20Estimation.pdf","2020-02-04","metadata_verified",[11],false,"corrected","author copy","Accepted author version 'IEEE Robotics and Automation Letters. Preprint version. Accepted January, 2020' deposited in UTS OPUS (hdl 10453\u002F145251, OpenAlex version submittedVersion), with the IEEE personal-use notice on page 1; the IEEE version of record was not opened",[66,72,77,82,88],{"category":67,"model":68,"canonical":68,"role":69,"dataset":44,"specs":70,"locator":71},"lidar","Velodyne VLP-16","method input","3D lidar","Sec. V-B",{"category":73,"model":74,"canonical":75,"role":69,"dataset":44,"specs":76,"locator":71},"imu","MTi3 Xsens IMU","Xsens MTi-3","not_reported",{"category":78,"model":79,"canonical":79,"role":69,"dataset":44,"specs":80,"locator":81},"platform","hand-held sensor suite","moved up and down while walking in the UTS lab; 6.2 m trajectory, maximum estimated velocity 1.7 m\u002Fs","Sec. V-B; Fig. 4",{"category":73,"model":83,"canonical":83,"role":84,"dataset":85,"specs":86,"locator":87},"simulated IMU","dataset sensor","simulated sinusoidal trajectories","100 Hz; accelerometer noise sd 0.02 m\u002Fs2; gyroscope noise sd 0.002 rad\u002Fs","Table I caption; Table III caption",{"category":89,"model":90,"canonical":90,"role":91,"dataset":44,"specs":92,"locator":93},"compute","Intel i5-6300U","compute for runtime","laptop; 2.40 GHz; 24 GiB RAM; single-thread Matlab code, not optimised for high performance","Sec. V-A3",[],{"totalRows":96,"groupCount":97,"groups":98,"others":541},58,5,[99,304,438,514],{"slug":100,"group":101,"sourceId":5,"sourceLabel":6,"table":102,"selfRows":103,"metrics":104,"seqs":111,"entrants":145,"cells":152,"outcomes":297,"locators":298,"hardware":299,"wordings":301,"notes":302},"legentil2020gpm-table-iii","legentil2020gpm:Table III","Table III",32,[105,109],{"label":106,"unit":107,"statistic":108,"alignment":38},"average hyper-parameter training time per preintegrated measurement","ms","mean",{"label":110,"unit":107,"statistic":108,"alignment":38},"average inference time per preintegrated measurement",[112,115,117,119,121,123,125,127,129,131,133,135,137,139,141,143],{"dataset":113,"sequence":114,"environment":20},"simulated IMU trajectories","1D rotations, interval 0.05 s",{"dataset":113,"sequence":116,"environment":20},"1D rotations, interval 0.1 s",{"dataset":113,"sequence":118,"environment":20},"1D rotations, interval 0.5 s",{"dataset":113,"sequence":120,"environment":20},"1D rotations, interval 1 s",{"dataset":113,"sequence":122,"environment":20},"1D rotations, interval 2 s",{"dataset":113,"sequence":124,"environment":20},"1D rotations, interval 3 s",{"dataset":113,"sequence":126,"environment":20},"1D rotations, interval 4 s",{"dataset":113,"sequence":128,"environment":20},"1D rotations, interval 5 s",{"dataset":113,"sequence":130,"environment":20},"3D rotations, interval 0.05 s",{"dataset":113,"sequence":132,"environment":20},"3D rotations, interval 0.1 s",{"dataset":113,"sequence":134,"environment":20},"3D rotations, interval 0.5 s",{"dataset":113,"sequence":136,"environment":20},"3D rotations, interval 1 s",{"dataset":113,"sequence":138,"environment":20},"3D rotations, interval 2 s",{"dataset":113,"sequence":140,"environment":20},"3D rotations, interval 3 s",{"dataset":113,"sequence":142,"environment":20},"3D rotations, interval 4 s",{"dataset":113,"sequence":144,"environment":20},"3D rotations, interval 5 s",[146,150],{"name":147,"methodId":148,"linkable":149,"proposed":61,"self":61},"UPM (upsampled preintegration [17])","legentil2018lidarimucalib",true,{"name":151,"methodId":5,"linkable":149,"proposed":149,"self":149},"GPM",[153,157,160,162,164,166,168,170,172,175,177,179,181,184,186,188,190,193,195,197,199,201,203,205,207,210,212,214,216,219,221,223,225,228,230,232,234,237,239,241,243,246,248,250,252,255,257,259,261,264,266,268,270,273,275,277,279,282,284,286,288,291,293,295],[154,154,154,155,156,154,154,156,154],0,294,-1,[154,158,154,159,156,154,154,156,154],1,18.7,[158,154,154,161,156,154,154,156,154],356,[158,158,154,163,156,154,154,156,154],1.3,[154,154,158,165,156,154,154,156,154],335,[154,158,158,167,156,154,154,156,154],25.6,[158,154,158,169,156,154,154,156,154],399,[158,158,158,171,156,154,154,156,154],1.8,[154,154,173,174,156,154,154,156,154],2,392,[154,158,173,176,156,154,154,156,154],67.3,[158,154,173,178,156,154,154,156,154],396,[158,158,173,180,156,154,154,156,154],4.2,[154,154,182,183,156,154,154,156,154],3,498,[154,158,182,185,156,154,154,156,154],113,[158,154,182,187,156,154,154,156,154],502,[158,158,182,189,156,154,154,156,154],8.1,[154,154,191,192,156,154,154,156,154],4,1088,[154,158,191,194,156,154,154,156,154],279,[158,154,191,196,156,154,154,156,154],1085,[158,158,191,198,156,154,154,156,154],28.2,[154,154,97,200,156,154,154,156,154],2349,[154,158,97,202,156,154,154,156,154],534,[158,154,97,204,156,154,154,156,154],2332,[158,158,97,206,156,154,154,156,154],68.9,[154,154,208,209,156,154,154,156,154],6,4159,[154,158,208,211,156,154,154,156,154],824,[158,154,208,213,156,154,154,156,154],4144,[158,158,208,215,156,154,154,156,154],127,[154,154,217,218,156,154,154,156,154],7,6939,[154,158,217,220,156,154,154,156,154],1244,[158,154,217,222,156,154,154,156,154],6832,[158,158,217,224,156,154,154,156,154],212,[154,154,226,227,156,154,154,156,154],8,269,[154,158,226,229,156,154,154,156,154],16.9,[158,154,226,231,156,154,154,156,154],277,[158,158,226,233,156,154,154,156,154],10.2,[154,154,235,236,156,154,154,156,154],9,291,[154,158,235,238,156,154,154,156,154],22,[158,154,235,240,156,154,154,156,154],298,[158,158,235,242,156,154,154,156,154],11.1,[154,154,244,245,156,154,154,156,154],10,362,[154,158,244,247,156,154,154,156,154],60.2,[158,154,244,249,156,154,154,156,154],367,[158,158,244,251,156,154,154,156,154],24.8,[154,154,253,254,156,154,154,156,154],11,530,[154,158,253,256,156,154,154,156,154],121,[158,154,253,258,156,154,154,156,154],529,[158,158,253,260,156,154,154,156,154],51.9,[154,154,262,263,156,154,154,156,154],12,1148,[154,158,262,265,156,154,154,156,154],297,[158,154,262,267,156,154,154,156,154],1110,[158,158,262,269,156,154,154,156,154],138,[154,154,271,272,156,154,154,156,154],13,2347,[154,158,271,274,156,154,154,156,154],538,[158,154,271,276,156,154,154,156,154],2281,[158,158,271,278,156,154,154,156,154],270,[154,154,280,281,156,154,154,156,154],14,4352,[154,158,280,283,156,154,154,156,154],875,[158,154,280,285,156,154,154,156,154],4243,[158,158,280,287,156,154,154,156,154],482,[154,154,289,290,156,154,154,156,154],15,7295,[154,158,289,292,156,154,154,156,154],1392,[158,154,289,294,156,154,154,156,154],7102,[158,158,289,296,156,154,154,156,154],817,[],[102],[300],"laptop with Intel i5-6300U CPU at 2.40 GHz and 24 GiB RAM; single-thread Matlab code, not optimised",[],[303],"Average computation time over 50 trials for different integration interval lengths; IMU 100 Hz, UPM upsampled to 1 kHz; for UPM and GPM the hyper-parameter training time and the inference time are listed separately",{"slug":305,"group":306,"sourceId":5,"sourceLabel":6,"table":307,"selfRows":308,"metrics":309,"seqs":318,"entrants":335,"cells":341,"outcomes":432,"locators":433,"hardware":434,"wordings":435,"notes":436},"legentil2020gpm-table-ii","legentil2020gpm:Table II","Table II",16,[310,313,316],{"label":311,"unit":312,"statistic":108,"alignment":41},"average absolute rotation error of preintegrated measurement","mrad",{"label":314,"unit":315,"statistic":108,"alignment":41},"average absolute position error of preintegrated measurement","mm",{"label":311,"unit":317,"statistic":108,"alignment":41},"rad (as printed; the 1D block uses 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[14])","forster2017preint",{"name":147,"methodId":148,"linkable":149,"proposed":61,"self":61},{"name":151,"methodId":5,"linkable":149,"proposed":149,"self":149},[342,344,346,348,350,352,354,356,358,360,362,364,366,368,370,372,374,376,378,380,382,384,386,387,388,390,392,394,396,397,398,399,401,403,405,407,409,411,413,415,417,419,421,423,425,427,429,430],[154,154,154,343,156,154,156,156,154],2.41,[154,158,154,345,156,154,156,156,154],5.61,[158,154,154,347,156,154,156,156,154],0.28,[158,158,154,349,156,154,156,156,154],0.6,[173,154,154,351,156,154,156,156,154],0.1,[173,158,154,353,156,154,156,156,154],0.02,[154,154,158,355,156,154,156,156,154],4.91,[154,158,158,357,156,154,156,156,154],12.1,[158,154,158,359,156,154,156,156,154],1.61,[158,158,158,361,156,154,156,156,154],1.32,[173,154,158,363,156,154,156,156,154],1.4,[173,158,158,365,156,154,156,156,154],0.16,[154,154,173,367,156,154,156,156,154],21.3,[154,158,173,369,156,154,156,156,154],61.3,[158,154,173,371,156,154,156,156,154],3.09,[158,158,173,373,156,154,156,156,154],7.19,[173,154,173,375,156,154,156,156,154],0.2,[173,158,173,377,156,154,156,156,154],0.61,[154,154,182,379,156,154,156,156,154],24.9,[154,158,182,381,156,154,156,156,154],125,[158,154,182,383,156,154,156,156,154],2.51,[158,158,182,385,156,154,156,156,154],12.6,[173,154,182,347,156,154,156,156,154],[173,158,182,171,156,154,156,156,154],[154,173,191,389,156,154,156,156,154],5.48,[154,158,191,391,156,154,156,156,154],6.06,[158,173,191,393,156,154,156,156,154],0.8,[158,158,191,395,156,154,156,156,154],0.65,[173,173,191,393,156,154,156,156,154],[173,158,191,353,156,154,156,156,154],[154,173,97,242,156,154,156,156,154],[154,158,97,400,156,154,156,156,154],13.1,[158,173,97,402,156,154,156,156,154],7.53,[158,158,97,404,156,154,156,156,154],2.27,[173,173,97,406,156,154,156,156,154],7.18,[173,158,97,408,156,154,156,156,154],0.48,[154,173,208,410,156,154,156,156,154],35.6,[154,158,208,412,156,154,156,156,154],65,[158,173,208,414,156,154,156,156,154],4.72,[158,158,208,416,156,154,156,156,154],7.29,[173,173,208,418,156,154,156,156,154],3.56,[173,158,208,420,156,154,156,156,154],1.74,[154,173,217,422,156,154,156,156,154],37.5,[154,158,217,424,156,154,156,156,154],159,[158,173,217,426,156,154,156,156,154],3.75,[158,158,217,428,156,154,156,156,154],15.9,[173,173,217,426,156,154,156,156,154],[173,158,217,431,156,154,156,156,154],10.3,[],[307],[],[],[437],"Simulated fast trajectories, 100 trials, fixed query rates of 1 to 20 Hz; average absolute error of the preintegrated measurement (the paper calls it absolute pose error); units as printed: mrad and mm for 1D rotations, 'rad' and mm for 3D rotations",{"slug":439,"group":440,"sourceId":5,"sourceLabel":6,"table":441,"selfRows":226,"metrics":442,"seqs":448,"entrants":457,"cells":461,"outcomes":508,"locators":509,"hardware":510,"wordings":511,"notes":512},"legentil2020gpm-table-i","legentil2020gpm:Table I","Table I",[443,446],{"label":444,"unit":445,"statistic":108,"alignment":41},"average relative rotation error of preintegrated measurement","%",{"label":447,"unit":445,"statistic":108,"alignment":41},"average relative position error of preintegrated measurement",[449,451,453,455],{"dataset":113,"sequence":450,"environment":20},"1D rotations, slow motion",{"dataset":113,"sequence":452,"environment":20},"1D rotations, fast motion",{"dataset":113,"sequence":454,"environment":20},"3D rotations, slow motion",{"dataset":113,"sequence":456,"environment":20},"3D rotations, fast motion",[458,459,460],{"name":337,"methodId":338,"linkable":149,"proposed":61,"self":61},{"name":147,"methodId":148,"linkable":149,"proposed":61,"self":61},{"name":151,"methodId":5,"linkable":149,"proposed":149,"self":149},[462,464,466,468,470,472,474,476,478,480,482,484,486,488,490,492,494,495,497,499,501,503,505,506],[154,154,154,463,156,154,156,156,154],0.253,[154,158,154,465,156,154,156,156,154],3.54,[158,154,154,467,156,154,156,156,154],0.038,[158,158,154,469,156,154,156,156,154],0.381,[173,154,154,471,156,154,156,156,154],0.028,[173,158,154,473,156,154,156,156,154],0.143,[154,154,158,475,156,154,156,156,154],0.221,[154,158,158,477,156,154,156,156,154],2.9,[158,154,158,479,156,154,156,156,154],0.024,[158,158,158,481,156,154,156,156,154],0.301,[173,154,158,483,156,154,156,156,154],0.008,[173,158,158,485,156,154,156,156,154],0.073,[154,154,173,487,156,154,156,156,154],0.316,[154,158,173,489,156,154,156,156,154],4.79,[158,154,173,491,156,154,156,156,154],0.035,[158,158,173,493,156,154,156,156,154],0.493,[173,154,173,491,156,154,156,156,154],[173,158,173,496,156,154,156,156,154],0.311,[154,154,182,498,156,154,156,156,154],0.308,[154,158,182,500,156,154,156,156,154],4.35,[158,154,182,502,156,154,156,156,154],0.031,[158,158,182,504,156,154,156,156,154],0.433,[173,154,182,502,156,154,156,156,154],[173,158,182,507,156,154,156,156,154],0.396,[],[441],[],[],[513],"Simulated random sinusoidal trajectories, integration interval 1 to 5 s, 100 trials; average relative error with respect to travelled linear or angular distance; IMU 100 Hz, accelerometer noise sd 0.02 m\u002Fs2, gyroscope noise sd 0.002 rad\u002Fs, UPM upsampled to 1 kHz",{"slug":515,"group":516,"sourceId":5,"sourceLabel":6,"table":517,"selfRows":158,"metrics":518,"seqs":521,"entrants":526,"cells":531,"outcomes":535,"locators":536,"hardware":537,"wordings":538,"notes":539},"legentil2020gpm-text-sec-v-b-real","legentil2020gpm:Text Sec.V-B real","Text Sec.V-B real",[519],{"label":520,"unit":315,"statistic":108,"alignment":41},"average point-to-plane distance on a flat wall",[522],{"dataset":523,"sequence":524,"environment":525},"UTS lab hand-held sequence","6.2 m trajectory","lab environment at the University of Technology Sydney (hand-held, moved up and down while walking)",[527,529],{"name":528,"methodId":44,"linkable":61,"proposed":61,"self":61},"IN2LAAMA with PM",{"name":530,"methodId":5,"linkable":149,"proposed":149,"self":149},"IN2LAAMA with GPM",[532,533],[154,154,154,235,156,154,156,156,154],[158,154,154,534,156,154,156,156,154],6.3,[],[81],[],[],[540],"Real hand-held run (Velodyne VLP-16 and MTi3 Xsens IMU) in the UTS lab, 6.2 m trajectory, maximum estimated speed 1.7 m\u002Fs; about 150k points on a manually segmented flat wall, plane fitted by PCA in each map; no independent reference",[542],{"group":543,"slug":544,"sourceLabel":6,"table":545,"selfRows":158,"datasets":546},"legentil2020gpm:Text Sec.V-B sim","legentil2020gpm-text-sec-v-b-sim","Text Sec.V-B sim",[547],"IN2LAAMA simulated lidar-inertial data",1790510658135]