SLAM 點雲圖鑑Point clouds for construction
M-01 · 2023

IKFoM

本文提出在流形上建構迭代誤差狀態擴展卡爾曼濾波（IESEKF）的通用符號化方法：以 ⊞、⊟ 與 ⊕ 運算把機器人系統寫成離散時間的流形標準形式，使濾波各步驟中的流形約束與系統特定部分分離，並證明其最小參數化在整個工作空間內沒有奇異點。作者據此開發 C++ 工具包 IKFoM，支援 R^n、SO(3)、SE_N(3) 與 S^2 等原始流形及其組合，使用者只需提供系統描述即可呼叫預測與更新。期刊版以兩個緊耦合 LiDAR 慣性系統驗證：重新實作 FAST-LIO 並加入線上 LiDAR 與 IMU 外參估計（六組資料的漂移與手推版本相當，執行時間略增），以及以 IKFoM 取代 LINS 的手推濾波器（在 LIO-SAM Campus 資料上執行時間較短）。

估計框架或函式庫近十年已讀全文同儕審查已出版估計後端與最佳化

閱讀版本
Version of record, IEEE Trans. Ind. Electron. 70(12):12533-12544 (Date of Publication 2023-01-23), IEEE Xplore HTML full text (document 10024988) read in Chrome with National Taiwan University access; Tables I-III read from the IEEE table images; the online Supplementary Material (proofs, manifold examples, extra results) was not read
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國立臺灣大學機構訂閱
本頁內容

A generic symbolic formulation and C++ toolkit (IKFoM) for iterated error-state EKFs on compound manifolds that separates manifold constraints from system models; verified by re-implementing FAST-LIO with online LiDAR-IMU extrinsics and LINS, matching hand-derived drift with slightly higher (FAST-LIO) or lower (LINS) runtime.

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 LiDAR (Livox AVIA solid-state LiDAR)、IMU (built into the Livox AVIA)、spinning multiline LiDAR and IMU data of the public LIO-SAM Campus sequences for the LINS re-implementation (sensor models not stated)
原文測試平台UAV (indoor flight, V1)、handheld (UAV held by hand and quickly shaken in V2-01; the carrying mode in V3 outdoor random walk is not stated in the TIE text)、public dataset (LIO-SAM Campus-small and Campus-large)
狀態估計iterated error-state extended Kalman filter on compound manifolds in canonical form x_{k+1} = x_k oplus (dt f(x_k,u_k,w_k)); toolkit supports R^n, SO(3), SE_N(3) and S^2(r) primitives; experiment state manifold R3 x R3 x SO(3) x R3 x R3 x S2 x SO(3) x R3 with at most 5 iterations (Sec. III-H; Sec. IV-B; Sec. IV-C)
資料關聯point-to-plane residuals of LiDAR points to planar features of the map, identical to FAST-LIO [14] (Sec. IV-A, Eq. 30); the LINS re-implementation keeps the original LINS feature extraction and outlier rejection (Sec. IV-C3)
時間表示discrete time (canonical form x_{k+1} = x_k oplus dt f(x_k,u_k,w_k))
去畸變原文未報告 in the TIE article (system taken from FAST-LIO [14]; motion compensation is not described)
迴圈閉合none
全域最佳化none
地圖表示global point cloud map (as in FAST-LIO)
先驗資訊none
可輸出幾何IMU state (position, velocity, rotation, biases, gravity), online LiDAR-IMU extrinsic, and a point cloud map
計算需求onboard computer with a 1.8 GHz quad-core Intel i7-8550U and 8 GB RAM; average time per iteration 6.0 to 36.3 ms for IKFoM versus 5.7 to 34.5 ms for the hand-derived FAST-LIO filter; LINS re-implementation 8.4 and 10.3 ms versus 15.5 and 21.8 ms (Sec. IV; Tables II-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
LiDARLivox AVIA歸入：Livox Avia方法輸入未標示solid-state LiDAR with a built-in IMU(He et al., 2023b, Sec. IV)
慣性量測單元（IMU）原文未報告 (built-in IMU of the Livox AVIA)方法輸入未標示原文未報告(He et al., 2023b, Sec. IV)
載具平台UAV (model not reported)方法輸入未標示flown indoors (V1); held by hand and quickly shaken in V2-01; carrying mode in V3 outdoor random walk not stated in the TIE text(He et al., 2023b, Sec. IV-C)
運算硬體Intel i7-8550U onboard computer執行運算平台未標示1.8 GHz quad-core CPU, 8 GB RAM(He et al., 2023b, Sec. IV; Sec. IV-C3)
其他Vicon motion capture system參考或真值量測未標示covers the start and end area of V2-01(He et al., 2023b, Sec. IV-C1; Fig. 6)

作者報告的優勢與限制

優勢

  • Minimal parameterization of the error state that is singularity-free in the whole workspace (Theorem 1, Sec. III-F)
  • Odometry drift of 0.055 to 0.496% over six datasets, comparable to 0.015 to 0.558% for the hand-derived FAST-LIO filter (Table I)
  • Online LiDAR-IMU extrinsic estimates agree across six datasets, with translation uncertainty 1 to 5 cm and rotation uncertainty below 3.5 deg (Sec. IV-C2; Fig. 7)
  • The IKFoM re-implementation of LINS runs faster than the original hand-derived filter (Table III)

限制

  • (inference) Filter without loop closure or global optimization; long-term drift is not addressed by the estimator itself
  • Drift is judged from start and end pose coincidence, with Vicon ground truth only near the start and end of V2-01 (Sec. IV-C1)
  • The toolkit-based FAST-LIO implementation is slightly slower than the hand-derived version because of toolkit overhead and six extra extrinsic states (Sec. IV-C3; Table II)
  • Filter stability depends on the chosen boxplus and oplus operations and on the system; its analysis is left out of scope (Sec. III-G)

營建工程相關證據

原文未報告。TIE 版實驗為室內 UAV 飛行、辦公區手持快速晃動（起訖點附近有 Vicon）與戶外隨機行走，另以 LIO-SAM Campus 公開序列比較運算時間；皆為既有建物或校園環境，沒有營建工地，也未評估點雲幾何精度。

原文驗證環境：受控實驗、已完工建築、獨立參考量測、公開基準

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 3 個比較組，合計 14 筆紀錄。

He et al., 2023b · Table I 本方法 6 筆

指標odometry drift (%)

表格設定（擷取紀錄原文）：Odometry drift (%) of the FAST-LIO based LiDAR-inertial system implemented with IKFoM (with online extrinsics) versus the hand-derived IESEKF of FAST-LIO, from start and end pose coincidence, six datasets, at most 5 iterations (He et al., 2023b, Table I)

odometry drift (%)，own datasets (trial 01 by the authors; trial 02 from the FAST-LIO paper) · V1-01

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。

這些是 He et al., 2023b 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。

統計量：原文未報告；對齊方式：未對齊；單位：%；場景：indoor UAV flight

資料來源作者報告值(He et al., 2023b, Table I)

數值與出處
方法（原文寫法）報告值出處
IKFoM-based本方法原文提出0.414%(He et al., 2023b, Table I)
Hand-derived [14] (FAST-LIO)0.527%(He et al., 2023b, Table I)

He et al., 2023b · Table II 本方法 6 筆

資料集與序列own datasets (trial 01 by the authors; trial 02 from the FAST-LIO paper) · V1-01

表格設定（擷取紀錄原文）：Average running time of one complete iteration of LiDAR-inertial navigation, IKFoM-based (six more states for extrinsics) versus hand-derived FAST-LIO, both on the UAV onboard computer; '±' term printed without definition (He et al., 2023b, Table II)

average running time per iteration (printed as 6.6±0.0047)，own datasets (trial 01 by the authors; trial 02 from the FAST-LIO paper) · V1-01

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 He et al., 2023b 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。

統計量：平均值（mean）；對齊方式：原文未報告；單位：ms；場景：indoor UAV flight

數值與出處
方法（原文寫法）報告值出處
IKFoM-based本方法原文提出硬體：onboard computer, 1.8 GHz quad-core Intel i7-8550U, 8 GB RAM6.6 ms(He et al., 2023b, Table II)

He et al., 2023b · Table III 本方法 2 筆

資料集與序列LIO-SAM open sequences · Campus-small

表格設定（擷取紀錄原文）：Average running time of one complete state-estimation iteration of LINS with its hand-derived IESEKF replaced by IKFoM versus the original LINS, on LIO-SAM open sequences, same onboard computer; '±' term printed without definition (He et al., 2023b, Table III)

average running time per iteration (printed as 8.4±0.0042)，LIO-SAM open sequences · Campus-small

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 He et al., 2023b 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。

統計量：平均值（mean）；對齊方式：原文未報告；單位：ms；場景：public LIO-SAM sequence (environment not described in the TIE text)

數值與出處
方法（原文寫法）報告值出處
IKFoM-based本方法原文提出硬體：onboard computer, 1.8 GHz quad-core Intel i7-8550U, 8 GB RAM8.4 ms(He et al., 2023b, Table III)

來源

  • He et al., 2023b

    Dongjiao He, Wei Xu, Fu Zhang（2023）Symbolic Representation and Toolkit Development of Iterated Error-State Extended Kalman Filters on ManifoldsIEEE Transactions on Industrial Electronics, 70(12):12533-12544

    DOI 10.1109/tie.2023.3237872arXiv 2102.03804程式碼

    同儕審查已出版已讀全文近十年查證後修正

程式碼：https://github.com/hku-mars/IKFoM（授權：GPL-2.0）。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。

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