Lupton-Sukkarieh preintegration
本文為消防等第一應變人員的人員攜帶定位需求，提出在上一個位姿的機體座標系中積分 IMU 量測，形成不需初始條件的「預積分慣性增量觀測」（位置修正項 Δp+、速度增量與姿態增量，姿態以 Euler 角表示），並以 Jacobian 在積分後修正 IMU 偏差。導航座標系改固定於第一個位姿的機體座標，使初始姿態已知，改以線性方式估計重力向量與初始速度；理論上三個位姿的相對位置即可線性恢復初始條件，不需特殊初始化。系統以資訊空間的圖式 SLAM 實作，並以「滑動視窗強制獨立」（SWFI，30 個影像位姿）移除舊位姿與其觀測以維持固定計算時間；視覺前端為 Harris 角點、金字塔 LK 光流與 RANSAC 基本矩陣剔除。作者以手持 Honeywell HG1900 IMU 與 Bumblebee2 立體相機在雪梨大學辦公建物中驗證。Forster 等人與 GTSAM 文件把 IMU 預積分概念歸於此工作。
本頁內容
Preintegrates IMU measurements in the body frame of the previous pose into delta observations (Delta p+, Delta v, Delta phi in Euler angles) with post-integration bias Jacobians, and fixes the navigation frame to the first body pose so that gravity and initial velocity become linearly observable after three poses; implemented as information-form graphical SLAM with sliding window forced independence (30 poses) and validated with a hand-held HG1900 IMU and Bumblebee2 stereo camera in office buildings; later cited as the origin of IMU preintegration.
技術屬性
欄位內容為文獻擷取紀錄的原文用語（英文），以原文為據；「未查證」表示本研究尚未讀到該資訊，不代表該方法不具備此能力。
| 感測輸入 | IMU (Honeywell HG1900, 600 Hz)、stereo camera (Point Grey Research Bumblebee2 with 2.1 mm wide-angle lenses, 6.25 Hz, 12 cm baseline)、monocular camera (left camera of the stereo pair only, Sec. VIII-G) |
|---|---|
| 原文測試平台 | handheld (human-carried sensor suite) |
| 狀態估計 | information-space graphical SLAM (delayed-state filter that can relinearize past observations and re-assess data association) with preintegrated inertial delta observations; sliding window forced independence removes poses older than the 30-image window together with all their observations; state: positions, velocities and Euler attitudes of window poses, gravity vector, IMU-to-camera rotation and offset, IMU biases and tracked landmarks |
| 資料關聯 | Harris corners (20 to 50 per image) tracked with pyramidal Lucas-Kanade optical flow; RANSAC fundamental-matrix test between consecutive images; graph edge-energy test (above 2 sigma) to re-assess data association after insertion; no descriptor-based re-acquisition |
| 時間表示 | discrete poses at the camera rate (6.25 Hz stereo); 600 Hz IMU samples integrated between poses in the body frame of the previous pose |
| 去畸變 | 不適用 |
| 迴圈閉合 | none; loop closure detection is listed as future work |
| 全域最佳化 | none; windowed graphical SLAM with sliding window forced independence; a common frame for the whole trajectory is kept only by re-anchoring the oldest window pose |
| 地圖表示 | sparse 3D point landmarks for features currently tracked within the window; removed when no longer observed |
| 先驗資訊 | none for initial conditions; in the monocular-inertial run a weak range prior between the first two poses is applied until ten image pairs are observed |
| 可輸出幾何 | platform position, velocity and attitude plus gravity vector, IMU-camera alignment and IMU biases; no dense map |
| 計算需求 | constant-time processing bounded by the sliding window (abstract; Sec. VII-B; Sec. IX-A); computing hardware not reported |
使用設備
原文使用的感測器、運算硬體與載具（equipment）。型號保留原文寫法，連結到設備頁中同一型號的歸併名稱；角色依原文用途分為方法輸入、資料集感測器、執行運算平台、參考或真值量測（reference or ground truth）與比較對象設備。
| 類別 | 型號（原文寫法） | 角色 | 資料集 | 原文規格 | 出處 |
|---|---|---|---|---|---|
| 慣性量測單元（IMU） | Honeywell HG1900 | 方法輸入 | 未標示 | 600 Hz sampling; measured accelerometer noise 0.0775 m/s2 (1 sigma), gyroscope noise 0.001 rad/s (1 sigma), accelerometer bias stability +/-0.003 m/s2, gyroscope bias stability +/-6.0e-5 rad/s | (Lupton & Sukkarieh, 2012, Sec. VIII-A; Table II) |
| 雙目相機 | Point Grey Research Bumblebee2 | 方法輸入 | 未標示 | 2.1 mm wide angle lenses; 6.25 Hz; 640 x 480 pixels; field of view 97 x 80 deg; angular resolution 0.2 deg at centre; stereo baseline 12 cm; range estimates accurate only to about 4 or 5 m (Sec. VIII-E) | (Lupton & Sukkarieh, 2012, Sec. VIII-A; Sec. VIII-E; Table III) |
| 載具平台 | hand-held sensor suite (stereo camera on top, IMU below) | 方法輸入 | 未標示 | hand held and carried around the buildings | (Lupton & Sukkarieh, 2012, Sec. VIII-A; Fig. 5) |
作者報告的優勢與限制
優勢
- Initial velocity and gravity recovered linearly after three poses; no special initialization, estimation started while moving (Sec. VI; Sec. VIII-F)
- Validation: the 9 m marks estimated within a few centimetres, final pose 16 cm from the start, velocities within 1 cm/s and attitude within 1 deg at the stationary points (Sec. VIII-C, Table IV)
- Gravity magnitude estimated as 9.796 m/s2 vs 9.797 m/s2 for Sydney, estimates within 0.06% and 0.12 deg of each other (Sec. VIII-C)
- Final position error 0.82 m (0.68%) and 2.5 m (1.39%) on walking datasets of about 120 m and 180 m (Sec. VIII-F)
- Inertial data bridged a rotation of about 90 deg/s where stereo-only tracking was lost and fixed scale where stereo-only estimated the 9 m mark at 10.4 to 10.8 m (Sec. VIII-E)
限制
- Delta attitude is converted back to Euler angles (Sec. III, eq. 12); Forster et al. later note singularities of this representation (Forster et al., 2017a, Sec. I)
- SWFI gives a slightly sub-optimal solution (Sec. IX-A)
- No loop closure; drift grows in periods with few visual features such as stair cases (Sec. VIII-F, Fig. 17; Sec. IX-B)
- Early gravity estimates after three images are inaccurate, so linearization problems remain until convergence (Sec. VI-C)
- Monocular-inertial final error 2.9 m versus 0.82 m for stereo-inertial on dataset 1 (Sec. VIII-G)
- Failure modes not yet studied systematically (Sec. IX-B)
營建工程相關證據
未在營建工地驗證。資料為手持感測器在雪梨大學 Rose St. 建物（辦公建物，兩個樓層）與相鄰的 Link 建物之間步行取得，路線含樓梯間、天橋與戶外（圖 12 另標示停車場），另有一般辦公室內兩個相距 9 m 地面標記的驗證（Sec. VIII-C、VIII-F）。樓梯間等特徵稀少時段造成較大漂移（第二組資料終點誤差 1.39%），這類情況與施工中室內環境相似，但此關聯屬於推論。
原文驗證環境：受控實驗、已完工建築
報告的性能數據
以下是原文作者報告的性能數值（author-reported results），不是本研究重新量測的結果。每張圖只並列同一個比較組（comparison group，同一張表、同一組實驗設定）內的方法；不同比較組之間的數值不可直接比較，也不構成排名。
本方法共出現在 5 個比較組，合計 55 筆紀錄。以下列出本方法紀錄最多的 4 組，其餘 1 組列在最後，並連到性能比較頁。
Lupton & Sukkarieh, 2012 · Table IV 本方法 45 筆
表格設定（擷取紀錄原文）：Validation in a normal office: hand-held unit carried back and forth between two floor marks 9 m apart and set down on each mark, where its true location and velocity are known; estimated states at the stationary poses; navigation frame fixed to pose 1 (north, east, down of the first body frame, not globally referenced) (Lupton & Sukkarieh, 2012, Table IV)
estimated north position at a marked stationary pose，office validation sequence (Sec. VIII-C) · pose 1
這張表在此指標與資料序列只列出本方法一筆，沒有可並列的其他方法，因此不畫圖，數值與出處見下表。這是 Lupton & Sukkarieh, 2012 在此表設定下報告的數值（author-reported results），不代表方法在其他資料或設定下的表現。
| 方法（原文寫法） | 報告值 | 出處 |
|---|---|---|
| stereo-inertial navigation with preintegrated inertial delta observations and SWFI (30-pose window)本方法原文提出 | 0 m | (Lupton & Sukkarieh, 2012, Table IV) |
Lupton & Sukkarieh, 2012 · Text Sec.VIII-F 本方法 4 筆
表格設定（擷取紀錄原文）：Real-world hand-held walking datasets that start while moving and end near the start; final error of the last pose relative to the first; no loop closure (Lupton & Sukkarieh, 2012, Text Sec.VIII-F)
final position error，University of Sydney buildings (Rose St. and Link) · dataset 1: Rose St. building, two floors, 713 image pairs, 114 s, about 120 m
這張表在此指標與資料序列只列出本方法一筆，沒有可並列的其他方法，因此不畫圖，數值與出處見下表。這是 Lupton & Sukkarieh, 2012 在此表設定下報告的數值（author-reported results），不代表方法在其他資料或設定下的表現。
| 方法（原文寫法） | 報告值 | 出處 |
|---|---|---|
| stereo-inertial navigation with preintegrated inertial delta observations and SWFI (30-pose window)本方法原文提出 | 0.82 m | (Lupton & Sukkarieh, 2012, Sec. VIII-F; Tables VI-VII) |
Lupton & Sukkarieh, 2012 · Text Sec.VIII-C gravity 本方法 3 筆
資料集與序列office validation sequence (Sec. VIII-C) · stationary poses
表格設定（擷取紀錄原文）：Gravity vector estimated independently in successive sliding windows at the stationary poses of Table IV, without supplying the true magnitude; true value for Sydney 9.797 m/s2 (Lupton & Sukkarieh, 2012, Text Sec.VIII-C gravity)
average estimated gravity magnitude，office validation sequence (Sec. VIII-C) · stationary poses
這張表在此指標與資料序列只列出本方法一筆，沒有可並列的其他方法，因此不畫圖，數值與出處見下表。這是 Lupton & Sukkarieh, 2012 在此表設定下報告的數值（author-reported results），不代表方法在其他資料或設定下的表現。
| 方法（原文寫法） | 報告值 | 出處 |
|---|---|---|
| stereo-inertial navigation with preintegrated inertial delta observations and SWFI (30-pose window)本方法原文提出 | 9.796 m/s2 | (Lupton & Sukkarieh, 2012, Sec. VIII-C) |
Lupton & Sukkarieh, 2012 · Text Sec.VIII-G 本方法 2 筆
指標final position error
資料集與序列University of Sydney buildings (Rose St. and Link) · dataset 1: Rose St. building
表格設定（擷取紀錄原文）：Dataset 1 processed with the left camera only plus IMU; weak range prior between the first two poses removed after ten image pairs; final position error compared with the stereo-inertial result (Lupton & Sukkarieh, 2012, Text Sec.VIII-G)
final position error，University of Sydney buildings (Rose St. and Link) · dataset 1: Rose St. building
只並列這張表在相同設定下報告的方法；以「本方法：」開頭者為本頁方法。失敗、未執行與未報告以標記呈現，不是 0。
按 Tab 進入圖表後，用上下方向鍵逐一瀏覽各類別，Esc 關閉提示框；也可開啟表格檢視閱讀全部數值。
這些是 Lupton & Sukkarieh, 2012 在此表設定下報告的數值（author-reported results），只能在同一個比較組內對照，不代表方法在其他資料或設定下的表現。
資料來源作者報告值(Lupton & Sukkarieh, 2012, Text Sec.VIII-G)
| 方法（原文寫法） | 報告值 | 出處 |
|---|---|---|
| monocular-inertial navigation (scale from accelerometer)本方法原文提出 | 2.9 m | (Lupton & Sukkarieh, 2012, Sec. VIII-G) |
| stereo-inertial navigation本方法原文提出 | 0.82 m | (Lupton & Sukkarieh, 2012, Sec. VIII-G) |
其他比較組
列出其餘 1 個比較組
來源
Lupton & Sukkarieh, 2012
（2012）Visual-Inertial-Aided Navigation for High-Dynamic Motion in Built Environments Without Initial ConditionsIEEE Transactions on Robotics, 28(1):61-76
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