Kalibr (unified temporal-spatial calibration)
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。
本頁內容
Joint continuous-time maximum-likelihood estimation of temporal offset and spatial transformation between sensors.
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 | global-shutter cameras (Aptina MT9V034 image sensors in a custom visual-inertial sensor)、IMU (Analog Devices ADIS16488, tactical grade) |
|---|---|
| 原文測試平台 | 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) |
| 狀態估計 | 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 |
| 資料關聯 | checkerboard corner detections with known correspondence to calibration-pattern points (assumed known) |
| 時間表示 | 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 |
| 去畸變 | 不適用 |
| 迴圈閉合 | 不適用 |
| 全域最佳化 | batch |
| 地圖表示 | 不適用 |
| 先驗資訊 | 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 |
| 可輸出幾何 | time offset and extrinsic transform |
| 計算需求 | 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 |
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） | Analog Devices ADIS16488 | 方法輸入 | 未標示 | tactical grade; 200 Hz; noise parameters from Allan variance | (Furgale et al., 2013, Sec. V, Sec. V-B) |
| 相機 | Aptina MT9V034 | 方法輸入 | 未標示 | 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 | (Furgale et al., 2013, Sec. V, Sec. V-B) |
| 運算硬體 | MacBook Pro | 執行運算平台 | 未標示 | 2.4 GHz Intel Core i7, 8 GB RAM; CHOLMOD sparse solver | (Furgale et al., 2013, Sec. V) |
| 其他 | FPGA (model not reported) | 方法輸入 | 未標示 | all sensor streams routed through it; timestamps taken when image sensors are triggered and IMU data requests start | (Furgale et al., 2013, Sec. V-B) |
| 其他 | static checkerboard calibration pattern (dimensions not reported) | 方法輸入 | 未標示 | known geometry; defines the world frame | (Furgale et al., 2013, Sec. III-B, Fig. 1, Fig. 6) |
作者報告的優勢與限制
優勢
- 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)
限制
- 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)
營建工程相關證據
原文未報告
原文驗證環境：受控實驗、模擬
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 2 個比較組，合計 6 筆紀錄。
Furgale et al., 2013 · Text Sec. V 本方法 3 筆
資料集與序列authors' calibration dataset · about 80 s dataset
表格設定（擷取紀錄原文）：Runtime for an about 80 s dataset (over 12,400 design variables, 144,000 error terms, 50,000 x 50,000 sparse system) (Furgale et al., 2013, Text Sec. V)
time to build the linear system per LM iteration，authors' calibration dataset · about 80 s dataset
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 Furgale et al., 2013 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 |
|---|---|---|
| joint estimation (J)本方法原文提出硬體：MacBook Pro, 2.4 GHz Intel Core i7, 8 GB RAM | 18 s有附註註記（擷取紀錄）：stated as approximately 18 s | (Furgale et al., 2013, Sec. V) |
Furgale et al., 2013 · Text Sec. V-B 本方法 3 筆
資料集與序列authors' custom visual-inertial sensor datasets · 40 datasets
表格設定（擷取紀錄原文）：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 (Furgale et al., 2013, Text Sec. V-B)
slope of time offset versus exposure time，authors' custom visual-inertial sensor datasets · 40 datasets
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 Furgale et al., 2013 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(Furgale et al., 2013, Text Sec. V-B)
| 方法（原文寫法） | 報告值 | 出處 |
|---|---|---|
| joint estimation, camera plus gyroscopes plus accelerometers (J)本方法原文提出 | 0.498 | (Furgale et al., 2013, Sec. V-B, Fig. 7) |
| camera plus gyroscopes only (G) | 0.493 | (Furgale et al., 2013, Sec. V-B, Fig. 7) |
| separated estimation (S), reference implementation of Mair et al. 2011 | 0.531 | (Furgale et al., 2013, Sec. V-B, Fig. 7) |
| camera plus accelerometer only (A) | 0.553 | (Furgale et al., 2013, Sec. V-B, Fig. 7) |
來源
Furgale et al., 2013
（2013）Unified temporal and spatial calibration for multi-sensor systems2013 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 1280-1286
DOI 10.1109/iros.2013.6696514程式碼
同儕審查已出版已讀全文經典查證後修正
相關版本
- 同團隊後續研究（是否為期刊版未查證）：A General Approach to Spatiotemporal Calibration in Multisensor Systems (see Rehder et al., 2016) https://doi.org/10.1109/TRO.2016.2529645
- 程式碼釋出：Kalibr toolbox https://github.com/ethz-asl/kalibr
程式碼：https://github.com/ethz-asl/kalibr（授權：BSD-3-Clause-style (LICENSE text checked, first clauses)）。有公開程式碼不等於已被重現，也不代表目前版本與論文版本相同。