MSCKF
MSCKF 是以擴展卡爾曼濾波（EKF）為基礎的視覺輔助慣性導航演算法。其核心是推導一種量測模型：當靜態特徵被多個相機位姿觀測時，直接以這些位姿間的幾何約束更新濾波器，而不必把三維特徵座標放進狀態向量。因此計算量只與特徵數呈線性關係，狀態中只保留有限數量的過去相機位姿副本。作者以車載相機與 IMU 在都市住宅區 3.2 km 的行駛資料驗證。
本頁內容
An EKF that augments the state with past camera poses and uses multi-view constraints of static features without estimating feature positions, giving complexity linear in the number of features.
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 | monocular camera、IMU |
|---|---|
| 原文測試平台 | vehicle |
| 狀態估計 | EKF whose state holds the evolving IMU state (quaternion, gyro and accelerometer biases, velocity, position; 15-dimensional error state) plus up to Nmax cloned camera poses; each feature's stacked residual is projected onto the left nullspace of its feature Jacobian with Givens rotations, residuals of all features are compressed by QR decomposition before the update; when Nmax is reached, Nmax/3 evenly spaced poses starting from the second oldest are removed after processing their features, and the oldest pose is always kept; Nmax = 30 in the experiment |
| 資料關聯 | SIFT feature extraction and matching; each feature triangulated by Gauss-Newton with an inverse-depth parameterization while camera poses are treated as known; multi-view geometric constraints of static features; simple Mahalanobis distance test to discard features on moving objects |
| 時間表示 | discrete poses at camera rate (3 Hz images); IMU propagation at IMU rate (100 Hz) with 5th-order Runge-Kutta integration in an Earth-centered, Earth-fixed frame including the planet's rotation |
| 去畸變 | 不適用 |
| 迴圈閉合 | none |
| 全域最佳化 | none |
| 地圖表示 | no persistent map (features not kept in state) |
| 先驗資訊 | none (no nonholonomic constraints or street map used) |
| 可輸出幾何 | IMU pose and velocity trajectory with covariance |
| 計算需求 | dataset processed at 14 Hz on a single core of an Intel T7200 2 GHz; processing done offline on recorded data (Sec. IV) |
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） | Inertial Science ISIS IMU | 方法輸入 | 未標示 | 100 Hz | (Mourikis & Roumeliotis, 2007, Sec. IV) |
| 相機 | Pointgrey FireFly | 方法輸入 | 未標示 | 640 x 480 pixels at 3 Hz | (Mourikis & Roumeliotis, 2007, Sec. IV) |
| 載具平台 | car | 方法輸入 | 未標示 | camera/IMU system placed on a car driving in a residential area of Minneapolis | (Mourikis & Roumeliotis, 2007, Sec. IV) |
| 運算硬體 | Intel T7200 | 執行運算平台 | 未標示 | single core, 2 GHz; processing done off-line on recorded data | (Mourikis & Roumeliotis, 2007, Sec. IV) |
作者報告的優勢與限制
優勢
- Optimal up to linearization errors while avoiding 3D features in the state (abstract; Sec. V)
- Complexity linear in the number of features (abstract; Sec. III-F)
- Delayed linearization and inverse-depth triangulation improve robustness to linearization errors (Sec. III-F)
- Processed the 3 Hz dataset at 14 Hz on one core with 142903 features used along 3.2 km (Sec. IV)
- Outliers from moving objects (cars, pedestrians, trees) were discarded in the reported run (Sec. IV)
限制
- No ground-truth trajectory was available; accuracy judged from a map overlay and known parking spots (Sec. IV)
- No loop closing (Sec. IV)
- Update cost is at most cubic in the number of states in the window, so the number of cloned poses dominates the cost (Sec. III-F)
- Simulation results are not included in the paper for space reasons (Sec. IV)
- (inference) As an EKF, it does not relinearize past measurements, a limitation discussed for filters by Strasdat et al., 2012
營建工程相關證據
未在營建場域驗證；本文唯一呈現的實驗為明尼亞波利斯住宅區街道上的車載相機與 IMU 資料（模擬結果因篇幅未收錄），沒有 GPS 真值，以地圖疊合與起終點停車位推估終點誤差（Sec. IV）。
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 14 個比較組，合計 40 筆紀錄。以下列出本方法紀錄最多的 4 組，其餘 10 組列在最後，並連到性能比較頁。
Rosinol et al., 2020 · Table II 本方法 11 筆
指標RMSE ATE [m]
表格設定（擷取紀錄原文）：EuRoC ATE RMSE grouped as fixed-lag smoothing, full smoothing and PGO with loop closure; comparator values taken from Delmerico and Scaramuzza [77] (Sim(3) alignment per text) and VINS-Mono [24]; comparators use a monocular camera while Kimera uses stereo; Kimera aligned with SE(3); loop threshold alpha = 0.001 (Rosinol et al., 2020, Table II)
RMSE ATE [m]，EuRoC MAV · MH_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。
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 Rosinol et al., 2020 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(Rosinol et al., 2020, Table II)
| 方法（原文寫法） | 報告值 | 出處 |
|---|---|---|
| OKVIS | 0.16 m | (Rosinol et al., 2020, Table II) |
| MSCKF本方法 | 0.42 m | (Rosinol et al., 2020, Table II) |
| ROVIO | 0.21 m | (Rosinol et al., 2020, Table II) |
| VINS-Mono | 0.15 m | (Rosinol et al., 2020, Table II) |
| SVO-GTSAM (full smoothing) | 0.05 m | (Rosinol et al., 2020, Table II) |
| VINS-LC (loop closure) | 0.12 m | (Rosinol et al., 2020, Table II) |
Yang et al., 2020a · Table 6 本方法 6 筆
指標ATE (RMS)
表格設定（擷取紀錄原文）：EuRoC MAV test sequences (all others used for training); RMS of ATE after aligning with ground truth (alignment type not stated); M+I values from Delmerico and Scaramuzza; stereo methods exclude V2_03; X = failure; Dd, Dp, Du = deep depth, pose, uncertainty ablations (Yang et al., 2020a, Table 6)
ATE (RMS)，EuRoC MAV · MH_03_medium
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 Yang et al., 2020a 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(Yang et al., 2020a, Table 6)
| 方法（原文寫法） | 報告值 | 出處 |
|---|---|---|
| DSO [ 16 ] (monocular) | 0.18 | (Yang et al., 2020a, Table 6) |
| ORB [ 52 ] (monocular) | 0.08 | (Yang et al., 2020a, Table 6) |
| VINS [ 57 ] (monocular-inertial) | 0.13 | (Yang et al., 2020a, Table 6) |
| OKVIS [ 44 ] (monocular-inertial) | 0.24 | (Yang et al., 2020a, Table 6) |
| ROVIO [ 3 ] (monocular-inertial) | 0.25 | (Yang et al., 2020a, Table 6) |
| MSCKF [ 51 ] (monocular-inertial)本方法 | 0.23 | (Yang et al., 2020a, Table 6) |
| SVO [ 22 ] (monocular-inertial) | 0.12 | (Yang et al., 2020a, Table 6) |
| VI-ORB [ 54 ] (monocular-inertial) | 0.09 | (Yang et al., 2020a, Table 6) |
| VI-DSO [ 72 ] (monocular-inertial) | 0.12 | (Yang et al., 2020a, Table 6) |
| End-end VO (D3VO PoseNet only) (monocular)原文提出 | 1.8 | (Yang et al., 2020a, Table 6) |
| Dd (monocular)原文提出 | 0.12 | (Yang et al., 2020a, Table 6) |
| Dd+Dp (monocular)原文提出 | 0.09 | (Yang et al., 2020a, Table 6) |
| Dd+Du (monocular)原文提出 | 0.08 | (Yang et al., 2020a, Table 6) |
| D3VO (monocular)原文提出 | 0.08 | (Yang et al., 2020a, Table 6) |
| VINS [ 57 ] (stereo-inertial) | 0.23 | (Yang et al., 2020a, Table 6) |
| OKVIS [ 44 ] (stereo-inertial) | 0.23 | (Yang et al., 2020a, Table 6) |
| Basalt [ 71 ] (stereo-inertial) | 0.06 | (Yang et al., 2020a, Table 6) |
| D3VO (monocular, listed in the stereo-inertial block)原文提出 | 0.08 | (Yang et al., 2020a, Table 6) |
Zuo et al., 2019 · Table II 本方法 4 筆
指標average trajectory start-end error
表格設定（擷取紀錄原文）：Indoor handheld sequences at chest height, normal to low light, slow to aggressive motion; no ground truth; average start-end error after returning to the start; unit not printed in the table (sequence lengths given in m) (Zuo et al., 2019, Table II)
average trajectory start-end error，self-collected indoor sequences · Indoor-A (39m)
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 Zuo et al., 2019 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(Zuo et al., 2019, Table II)
| 方法（原文寫法） | 報告值 | 出處 |
|---|---|---|
| MSCKF本方法 | 0.99 | (Zuo et al., 2019, Table II) |
| LIC-Fusion原文提出 | 0.98 | (Zuo et al., 2019, Table II) |
| LOAM | 0.66 | (Zuo et al., 2019, Table II) |
Mourikis & Roumeliotis, 2007 · Text Sec.IV 本方法 3 筆
資料集與序列Minneapolis residential driving sequence · 3.2 km
表格設定（擷取紀錄原文）：Car-mounted camera and IMU in a residential area of Minneapolis, 1598 images (3 Hz) over about 9 min, 3.2 km; no GPS ground truth; final error inferred from known start and end parking spots (estimate [-7.92 13.14 -0.78] m vs approximately [0 7 0] m); no loop closing and no motion or map priors (Mourikis & Roumeliotis, 2007, Text Sec.IV)
final position error，Minneapolis residential driving sequence · 3.2 km
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 Mourikis & Roumeliotis, 2007 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 |
|---|---|---|
| MSCKF本方法原文提出 | 10 m有附註註記（擷取紀錄）：approximate (value stated as about 10 m) | (Mourikis & Roumeliotis, 2007, Sec. IV) |
其他比較組
列出其餘 10 個比較組
- Li & Mourikis, 2013 · Table 2
- Li & Mourikis, 2013 · Table 3
- Zuo et al., 2019 · Table I
- Li & Mourikis, 2013 · Text Sec.9
- von Stumberg & Cremers, 2022 · Table I
- Forster et al., 2017a · Text Sec.VIII-B2 (drift)
- Ghadimzadeh Alamdari et al., 2025 · Table 2
- Li & Mourikis, 2013 · Text Sec.3.4
- Leutenegger et al., 2015 · Text Sec.VII-B1
- Campos et al., 2021 · Table II
來源
Mourikis & Roumeliotis, 2007
（2007）A Multi-State Constraint Kalman Filter for Vision-aided Inertial NavigationProceedings 2007 IEEE International Conference on Robotics and Automation (ICRA), pp. 3565-3572
同儕審查已出版已讀全文經典查證後修正