STEAM-LIO (GP continuous-time LIO)
本文以高斯過程（白雜訊加速度，即近似等速）作為連續時間運動先驗，在滑動視窗（約兩個 LiDAR 影格）中批次估計 SE(3) 位姿、機體速度與 IMU 偏差。因角速度屬於狀態，陀螺儀直接作為狀態量測；加速度計則只預積分成相對速度因子，其餘位置積分交給高斯過程。LiDAR 點以連續時間點到平面因子加入，每個點的位姿由相鄰兩個估計時刻的後驗內插取得，因此去畸變與配準在同一最佳化中反覆更新；由於先驗為稀疏的馬可夫形式，預積分與內插的計算量隨估計時刻數線性增加。同一框架也用於二維旋轉雷達，形成雷達慣性里程計。
本頁內容
Continuous-time radar- and lidar-inertial odometry that uses an exactly sparse white-noise-on-acceleration Gaussian-process prior in a two-frame sliding window, treats gyroscope readings as direct state measurements, preintegrates only accelerometer readings into relative-velocity factors, and builds point-to-plane (or Doppler-compensated radar) factors by posterior GP interpolation at each measurement time.
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 | 3D spinning LiDAR (Velodyne Alpha-Prime 128-beam on Boreas; 64-beam Ouster in Newer College; 64-beam Velodyne in KITTI-raw, LiDAR-only)、IMU (Applanix raw IMU at 200 Hz on Boreas; Ouster internal IMU at 100 Hz in Newer College)、2D spinning radar (Navtech CIR304-H) for the radar-inertial variant |
|---|---|
| 原文測試平台 | vehicle (Boreas and KITTI-raw)、handheld (Newer College sensor mast) |
| 狀態估計 | sliding-window batch continuous-time estimation (window of two LiDAR frames, about 200 ms) with a white-noise-on-acceleration Gaussian-process prior on SE(3) pose and body-centric velocity, direct gyroscope factors, preintegrated accelerometer relative-velocity factors and bias random-walk priors; Gauss-Newton with outer re-association loops and marginalization (Sec. III, IV, IV-C) |
| 資料關聯 | continuous-time point-to-plane factors from a coarsely voxelized scan (default 1.5 m) to a sliding local voxel map (1.0 m voxels, up to 20 points, minimum spacing 0.1 m), weighted by a planarity heuristic; radar uses Doppler-compensated point-to-point factors with a Cauchy loss (Sec. IV, IV-A, IV-D) |
| 時間表示 | continuous-time Gaussian process (WNOA prior, exactly sparse, linear cost) with estimation times at scan start and end; measurement factors built by posterior GP interpolation at each timestamp; timestamps binned (400 Hz on Boreas) to limit interpolations (Sec. III, IV-A, V) |
| 去畸變 | each outer iteration undistorts the scan with the posterior continuous-time trajectory of the previous iteration (Sec. IV-A, Alg. 1) |
| 迴圈閉合 | none explicit; on Newer College the incrementally built map allows implicit loop closure when areas are revisited (Sec. V) |
| 全域最佳化 | none |
| 地圖表示 | sliding local voxel point map centred on the robot; on Boreas voxels unobserved for about one second are cleared (Sec. IV, V) |
| 先驗資訊 | gravity orientation estimated from accelerometer data assuming the robot is stationary at startup; tuned power spectral density diag(Q) = {50, 50, 50, 5, 5, 5} (Sec. IV-B, V) |
| 可輸出幾何 | continuous-time trajectory (pose and body-centric velocity with covariance) and lidar or radar point maps (Figs. 1, 9, 18) |
| 計算需求 | real time on an Intel Xeon E5-2698 v4 with 16 threads: STEAM-LIO 74 ms per frame on Newer College and 97 ms on Boreas; STEAM-LO 89 ms on KITTI-raw (Tables I-III) |
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 |
|---|---|---|---|---|---|
| LiDAR | Velodyne Alpha-Prime 128-beam | 資料集感測器 | Boreas | 128-beam lidar on the Boreas data collection platform | (Burnett et al., 2025, Fig. 14; Sec. V-D) |
| LiDAR | Ouster 64-beam LiDAR (model not stated) | 資料集感測器 | Newer College Dataset | handheld sensor mast | (Burnett et al., 2025, Sec. V-B) |
| LiDAR | Velodyne 64-beam LiDAR (model not stated) | 資料集感測器 | KITTI-raw | motion-distorted raw point clouds | (Burnett et al., 2025, Sec. V-A) |
| 慣性量測單元（IMU） | Applanix IMU (raw measurements from the GNSS/INS logs) | 資料集感測器 | Boreas | 200 Hz | (Burnett et al., 2025, Sec. V-D; Fig. 3) |
| 慣性量測單元（IMU） | Ouster internal IMU | 資料集感測器 | Newer College Dataset | 100 Hz; used to avoid LiDAR-IMU synchronization problems | (Burnett et al., 2025, Sec. V-B) |
| GNSS 接收器 | Applanix GNSS/INS (model not stated) | 參考或真值量測 | Boreas | post-processed ground truth with GPS corrections, IMU and wheel encoders; raw 200 Hz IMU extracted without bias correction for the method | (Burnett et al., 2025, Sec. V-D; Fig. 14) |
| GNSS 接收器 | OXTS RTK GPS (model not stated) | 參考或真值量測 | KITTI-raw | ground truth | (Burnett et al., 2025, Sec. V-A) |
| 相機 | FLIR Blackfly S | 資料集感測器 | Boreas | not used by the method | (Burnett et al., 2025, Fig. 14) |
| 雷達 | Navtech CIR304-H | 資料集感測器 | Boreas | mechanical spinning 2D radar, 360 deg horizontal FOV, 1600 Hz azimuth measurements; no Doppler output | (Burnett et al., 2025, Sec. IV-D; Fig. 14) |
| 載具平台 | handheld sensor mast (Newer College Dataset) | 資料集感測器 | Newer College Dataset | aggressive high-frequency motions, dynamic swinging of the mast | (Burnett et al., 2025, Sec. V; Sec. V-B) |
| 載具平台 | Boreas data collection vehicle | 資料集感測器 | Boreas | repeated route at the University of Toronto over one year; 102 km or 4.3 h test set | (Burnett et al., 2025, Sec. V-D; Fig. 14) |
| 運算硬體 | Intel Xeon CPU E5-2698 v4 | 執行運算平台 | 未標示 | 16 threads | (Burnett et al., 2025, Sec. V) |
作者報告的優勢與限制
優勢
- On Newer College, STEAM-LIO had the lowest RMS ATE on 01-Short (0.3042 m) and the lowest overall ATE when errors of all sequences are concatenated (0.2946 m versus 0.3152 m FAST-LIO2 and 0.3048 m DLIO), running in real time (74 ms) (Table II, Sec. V-B)
- Continuous-time LiDAR-only STEAM-LO did not fail on 06-Dynamic Spinning, where KISS-ICP and the constant-velocity baseline failed (Table II)
- Most of the inertial gain came from the gyroscope; adding the accelerometer gave only a minor further improvement (Sec. V-B, VI)
- STEAM-LIO was much less sensitive to the prior power spectral density than STEAM-LO, which failed when Q was doubled (Table IV)
- Adding an IMU improved radar odometry by 43% (1.68% to 0.95% average drift on Boreas) (Table III, Sec. V-D)
- Estimated uncertainty was nearly consistent (NEES 1.04 on a Boreas snowstorm sequence) (Sec. V-D)
限制
- On Boreas the IMU gave little improvement over LiDAR-only odometry for a slow ground vehicle (0.45% versus 0.46% average drift) (Table III, Sec. V-D)
- Relies on the robot being stationary at startup for gravity initialization (Sec. IV-B)
- Including acceleration in the state (white-noise-on-jerk or Singer priors) improved some datasets but made the pipeline less reliable, so it was left out (Sec. I)
- Posterior-interpolated measurement factors are an approximation rather than exact marginalization of measurement times (Sec. IV)
- No explicit loop closure; maps drift slightly (Sec. V-D)
營建工程相關證據
論文未涉及營建場域，驗證為城市車載（KITTI-raw、Boreas 一年四季含暴雪）與 Newer College 手持劇烈運動資料。它把本資料庫的 STEAM 高斯過程理論（Barfoot et al., 2014）落實為可即時運作的 LiDAR 慣性里程計，並示範同一框架可用於在雪、霧、粉塵中較不受影響的旋轉雷達；營建工地常見粉塵與手持劇烈晃動，雷達慣性與連續時間去畸變的組合有潛在價值，但雷達為二維且精度明顯低於 LiDAR（推論）。
原文驗證環境：公開基準、獨立參考量測、跨場域
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 7 個比較組，合計 88 筆紀錄。以下列出本方法紀錄最多的 4 組，其餘 3 組列在最後，並連到性能比較頁。
Burnett et al., 2025 · Table III 本方法 41 筆
表格設定（擷取紀錄原文）：Boreas test set (102 km, 4.3 h, repeated route over one year incl. snowstorms); KITTI-style translational drift (%) and rotational drift (deg/100 m); first three methods evaluated in SE(3), last four in SE(2) (radar is 2D) (Burnett et al., 2025, Table III)
translational drift，Boreas · Seq. Avg. (13 sequences)
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 Burnett et al., 2025 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(Burnett et al., 2025, Table III)
| 方法（原文寫法） | 報告值 | 出處 |
|---|---|---|
| VTR3-Lidar [1] | 0.54% | (Burnett et al., 2025, Table III) |
| STEAM-LO本方法原文提出 | 0.46% | (Burnett et al., 2025, Table III) |
| STEAM-LIO本方法原文提出 | 0.45% | (Burnett et al., 2025, Table III) |
| STEAM-LO (SE2)本方法原文提出 | 0.16% | (Burnett et al., 2025, Table III) |
| VTR3-Radar [1] | 2.02% | (Burnett et al., 2025, Table III) |
| STEAM-RO本方法原文提出 | 1.68% | (Burnett et al., 2025, Table III) |
| STEAM-RIO本方法原文提出 | 0.95% | (Burnett et al., 2025, Table III) |
Burnett et al., 2025 · Table II 本方法 24 筆
表格設定（擷取紀錄原文）：Newer College Dataset (handheld, 6 km); RMS ATE after Umeyama alignment; star = explicit loop closures, dagger = results from DLIOM [71], double dagger = uses camera; other baselines as originally published (Burnett et al., 2025, Table II)
root mean squared ATE，Newer College Dataset · 01-Short
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 Burnett et al., 2025 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(Burnett et al., 2025, Table II)
| 方法（原文寫法） | 報告值 | 出處 |
|---|---|---|
| CT-ICP* [18] (explicit loop closures) | 0.36 m | (Burnett et al., 2025, Table II) |
| KISS-ICP [5] (result from [71]) | 0.6675 m | (Burnett et al., 2025, Table II) |
| FAST-LIO2 [10] (result from [71]) | 0.3775 m | (Burnett et al., 2025, Table II) |
| DLIO [11] | 0.3606 m | (Burnett et al., 2025, Table II) |
| SLICT* [52] (explicit loop closures) | 0.3843 m | (Burnett et al., 2025, Table II) |
| CLIO* [60] (loop closures, uses camera) | 0.408 m | (Burnett et al., 2025, Table II) |
| Constant Velocity (ablation baseline)本方法 | 0.8558 m | (Burnett et al., 2025, Table II) |
| STEAM-LO (Ours)本方法原文提出 | 0.3398 m | (Burnett et al., 2025, Table II) |
| STEAM-LO + Gyro (Ours)本方法原文提出 | 0.3055 m | (Burnett et al., 2025, Table II) |
| STEAM-LIO (Ours)本方法原文提出 | 0.3042 m | (Burnett et al., 2025, Table II) |
Burnett et al., 2025 · Table IV 本方法 12 筆
指標ATE
表格設定（擷取紀錄原文）：Ablation: ATE on Newer College 01-Short when scaling the default power spectral density diag(Q) = {50, 50, 50, 5, 5, 5} (Burnett et al., 2025, Table IV)
ATE，Newer College Dataset · 01-Short, Q x1/4
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 Burnett et al., 2025 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(Burnett et al., 2025, Table IV)
| 方法（原文寫法） | 報告值 | 出處 |
|---|---|---|
| STEAM-LO本方法原文提出 | 0.3098 m | (Burnett et al., 2025, Table IV) |
| STEAM-LIO本方法原文提出 | 0.308 m | (Burnett et al., 2025, Table IV) |
Burnett et al., 2025 · Table I 本方法 6 筆
表格設定（擷取紀錄原文）：KITTI-raw (motion-distorted, LiDAR only, 22 km); KITTI relative translation error; Overall = average over all segments of all sequences, Seq. Avg. = mean of per-sequence values; sequence 03 not available; STEAM-LO evaluated at the newest pose of the window (Burnett et al., 2025, Table I)
KITTI RTE，KITTI-raw · Overall (00-10 without 03)
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 Burnett et al., 2025 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(Burnett et al., 2025, Table I)
| 方法（原文寫法） | 報告值 | 出處 |
|---|---|---|
| CT-ICP [18] | 0.55% | (Burnett et al., 2025, Table I) |
| KISS-ICP [5] | 0.55% | (Burnett et al., 2025, Table I) |
| STEAM-ICP [12] | 0.52% | (Burnett et al., 2025, Table I) |
| Constant Velocity (ablation baseline)本方法 | 0.66% | (Burnett et al., 2025, Table I) |
| STEAM-LO (Ours, LiDAR only)本方法原文提出 | 0.53% | (Burnett et al., 2025, Table I) |
其他比較組
來源
Burnett et al., 2025
（2025）Continuous-Time Radar-Inertial and Lidar-Inertial Odometry Using a Gaussian Process Motion PriorIEEE Transactions on Robotics, 41:1059-1076
DOI 10.1109/tro.2024.3521856arXiv 2402.06174程式碼
同儕審查已出版已讀全文近十年查證後修正
相關版本
- 預印本：arXiv 2402.06174 (v1 2024-02-09, v2 2024-11-20 accepted version) https://arxiv.org/abs/2402.06174
- 程式碼釋出：utiasASRL/steam_icp (STEAM-LO, STEAM-LIO, STEAM-RO, STEAM-RIO) https://github.com/utiasASRL/steam_icp
- 前身方法：Exactly sparse GP trajectory estimation (STEAM) theory barfoot2014gp
程式碼：https://github.com/utiasASRL/steam_icp（授權：MIT (LICENSE file checked)）。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。