Sliding window filter
本文以延遲狀態邊際化（delayed state marginalization）提出滑動視窗濾波器（SWF），用於提升行星著陸時長距離立體視覺的地表結構估計精度。方法在 k 個位姿的視窗內以含 Huber 核的穩健 Gauss-Newton 同時最佳化位姿與地標，並以 Schur 補把最舊位姿與不再被觀測的地標邊際化為先驗資訊；視窗涵蓋全部時間時等同完整 BA，只保留一個時間步時等同 EKF 的時間更新，逐步邊際化時則成為固定時間的方法。作者在實驗室以兩台 Point Grey Flea 相機組成的立體相機朝貼有 HiRISE 影像的平面牆移動，以 1:10 比例模擬著陸，結果顯示 3 至 5 影格的視窗已接近批次解；作者另指出在 10 個影格內，SWF 的誤差比視覺里程計低約 76%。但過早邊際化會鎖住線性化誤差，且邊際化使迴圈閉合難以處理。
本頁內容
A sliding window filter based on delayed marginalization spans full bundle adjustment (window over all time) to the EKF (one time step); in laboratory-emulated Mars descent stereo experiments, 3 to 5 frame windows approach the batch solution, and the authors report that over 10 frames the SWF error is about 76% lower than visual odometry, while early marginalization risks divergence and loop closures are effectively precluded.
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 | stereo |
|---|---|
| 原文測試平台 | laboratory stereo rig (two Point Grey Flea cameras, about 10 cm baseline) on a tripod moved in 15 cm steps along a translation stage from 10 m to 1 m toward a planar wall covered with printed MRO HiRISE imagery, emulating the last 100 m to 10 m of Mars descent at 1:10 scale、simulation (run-time and state-size experiments with 0.5 px image noise) |
| 狀態估計 | sliding window filter: robust Gauss-Newton (Huber kernel, typically 4 to 10 iterations) over all measurements of a k-pose window with a kinematic process model and a prior information term; the oldest poses and landmarks without active support are marginalized by the Schur complement into the prior (k = 1 reproduces the first-order EKF time step, a window over all time equals full BA or full SLAM) |
| 資料關聯 | sum-of-absolute-differences patch matching of Harris corners, Lucas-Kanade subpixel refinement with projective patch warping (local plane with normal along the first optical axis), Moravec's rigid-consistency check (greedy maximal clique) against gross outliers, then Huber M-estimation over the whole window |
| 時間表示 | discrete poses |
| 去畸變 | 不適用 |
| 迴圈閉合 | not handled: the authors state that marginalization makes re-observing landmarks difficult, which effectively precludes loop closures (not an issue for descent and landing) |
| 全域最佳化 | window-limited; equivalent to full BA if the window covers all time |
| 地圖表示 | sparse 3D point landmarks (tracked surface features) with a possibly dense prior information block created by marginalization |
| 先驗資訊 | no external map or survey prior; the internal prior information matrix collects the information of marginalized poses and landmarks, and a kinematic compound-operation process model links consecutive poses |
| 可輸出幾何 | sparse 3D landmark positions on the target surface; map error evaluated as the shortest distance from each landmark to a plane fitted to the wall (plane from the batch solution with fiducials) |
| 計算需求 | constant run time independent of frame number shown in simulation averaged over 20 runs (10- and 20-frame windows with about 132 and 172 state parameters; Fig. 14a); computing hardware and absolute timings are not stated in the text; per-iteration patch re-alignment is described as expensive |
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 |
|---|---|---|---|---|---|
| 雙目相機 | Point Grey Research Flea | 方法輸入 | 未標示 | two Flea cameras forming one stereo rig; about 10 cm baseline; narrow-field-of-view lenses (about 25 deg); grayscale images 1024 x 768 px; calibrated and rectified with CAHVOR camera models | (Sibley et al., 2010, Sec. 4 (Experimental Results); Fig. 10(c)) |
| 其他 | tripod on a linear translation stage slotted onto a floor-fixed measuring rule (model not reported) | 參考或真值量測 | 未標示 | stereo rig moved repeatedly to predetermined locations in 15 cm steps from 10 m to 1 m from the wall; sequences taken with and without fiducials on the wall | (Sibley et al., 2010, Sec. 4 (Experimental Results); Fig. 11(a)) |
作者報告的優勢與限制
優勢
- Constant-time operation with results close to bundle adjustment (abstract; Fig. 14a)
- Scales from offline batch to fast online incremental solutions (abstract; Fig. 9)
- 3-, 4- and 5-frame windows come close to the batch solution in the moving convergence experiment with 150 tracked features (Sec. 4 Moving Convergence; Fig. 13)
- Over 10 frames, SWF error about 76% lower than visual odometry and standard deviation about 3.5 times smaller, at the same computational complexity as VO (Sec. 4 Effect of Marginalization)
限制
- Short windows (the EKF as a 1-frame SWF, or a 2-frame SWF) marginalize too early, lock in linearization errors and can diverge; a 10-frame window avoided this (Sec. 4 Effect of Early Marginalization; Fig. 15)
- Marginalization makes landmark re-observation difficult and effectively precludes loop closures (Sec. 4)
- Validation used a flat laboratory wall at 1:10 scale with printed orbital imagery; the authors note an image-scale mismatch with real landing imagery (Fig. 11 caption)
- Sparse (VSDF-style diagonal) marginalization transfers measurement information into the prior less effectively than full marginalization (Sec. 4 Sparse Marginalization; Fig. 17)
- The patch-warping model assumes locally planar patches with normals along the first optical axis and would need extension for general use (Sec. 4 The Importance of Feature Patch Warping)
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 4 個比較組，合計 9 筆紀錄。
Li & Mourikis, 2013 · Table 3 本方法 3 筆
資料集與序列simulation from Cheddar Gorge dataset · Cheddar Gorge (29 km)
表格設定（擷取紀錄原文）：Monte Carlo simulation (50 trials) generated from the Cheddar Gorge dataset (29 km, 56 min driving, Xsens IMU at 100 Hz, images at 20 Hz); all methods use sliding windows of the same length (Li & Mourikis, 2013, Table 3)
Position RMSE (m)，simulation from Cheddar Gorge dataset · Cheddar Gorge (29 km)
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 Li & Mourikis, 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(Li & Mourikis, 2013, Table 3)
| 方法（原文寫法） | 報告值 | 出處 |
|---|---|---|
| FLS (information-form fixed-lag smoother based on Sibley et al. 2010)本方法 | 133.4 m | (Li & Mourikis, 2013, Table 3) |
| MSCKF | 146.2 m | (Li & Mourikis, 2013, Table 3) |
| MSCKF 2.0原文提出 | 97.7 m | (Li & Mourikis, 2013, Table 3) |
| 'Ideal' MSCKF | 100.2 m | (Li & Mourikis, 2013, Table 3) |
Li & Mourikis, 2013 · Text Sec.9 本方法 2 筆
資料集與序列own vehicle dataset (Riverside, CA) · 21.5 km drive
表格設定（擷取紀錄原文）：Real vehicle run in Riverside, CA: 37 min, about 21.5 km, Xsens MTi-G at 100 Hz, one camera of a Bumblebee2 at 20 Hz, GPS-INS ground truth (Li & Mourikis, 2013, Text Sec.9)
Largest position error (about)，own vehicle dataset (Riverside, CA) · 21.5 km drive
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 Li & Mourikis, 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(Li & Mourikis, 2013, Text Sec.9)
| 方法（原文寫法） | 報告值 | 出處 |
|---|---|---|
| MSCKF 2.0原文提出 | 58 m | (Li & Mourikis, 2013, Text Sec.9) |
| MSCKF | 230 m | (Li & Mourikis, 2013, Text Sec.9) |
| FLS本方法 | 202 m | (Li & Mourikis, 2013, Text Sec.9) |
Sibley et al., 2010 · Text Fig. 14 caption 本方法 2 筆
指標average size of the state vector
資料集與序列simulation
表格設定（擷取紀錄原文）：Simulation averaged over 20 runs, 76 landmarks tracked, about 20 features per frame, feature tracks about 10 frames, 0.5 px image noise; run-time curves themselves are plot-only (Sibley et al., 2010, Text Fig. 14 caption)
average size of the state vector，simulation
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 Sibley et al., 2010 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(Sibley et al., 2010, Text Fig. 14 caption)
| 方法（原文寫法） | 報告值 | 出處 |
|---|---|---|
| 10-frame SWF本方法原文提出 | 132 parameters | (Sibley et al., 2010, Fig. 14 caption) |
| 20-frame SWF本方法原文提出 | 172 parameters | (Sibley et al., 2010, Fig. 14 caption) |
Sibley et al., 2010 · Text Sec.4 Effect of Marginalization 本方法 2 筆
資料集與序列not stated in the text (Sec. 4 Effect of Marginalization; the paragraph refers to Fig. 12 and to Newman et al. 2009) · 10 frames
表格設定（擷取紀錄原文）：SWF versus visual odometry (VO, equivalent to deleting instead of marginalizing with k = 1) over 10 frames; the data set behind this comparison is not identified in the text (Sibley et al., 2010, Text Sec.4 Effect of Marginalization)
SWF error reduction relative to VO over 10 frames，not stated in the text (Sec. 4 Effect of Marginalization; the paragraph refers to Fig. 12 and to Newman et al. 2009) · 10 frames
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 Sibley et al., 2010 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 |
|---|---|---|
| SWF本方法原文提出 | 76% | (Sibley et al., 2010, Sec. 4 (Effect of Marginalization)) |
來源
Sibley et al., 2010
（2010）Sliding window filter with application to planetary landingJournal of Field Robotics, 27(5):587-608
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