Stochastic map
本文提出「隨機地圖（stochastic map）」：把機器人與各物件之間的空間關係組成一個狀態向量，同時保存其平均值與完整共變異數矩陣，以描述關係之間的相依性。作者以一階線性化推導位姿複合（compounding）與反轉運算的共變異數傳遞，並以（擴展）卡爾曼濾波器（Kalman filter）在新量測加入時遞迴更新整張地圖。文中明示兩項前提：角度誤差須夠小以支持線性化，且只估計前兩階動差即足以支援決策（Sec. 6）。
本頁內容
Represents all uncertain spatial relations in one state vector with full covariance, propagates uncertainty through first-order compounding, and updates the map with an (extended) Kalman filter.
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 | 未記錄 |
|---|---|
| 原文測試平台 | ["simulation"] |
| 狀態估計 | extended Kalman filter on a joint state of robot and object frames (iterated EKF also given) |
| 資料關聯 | no dedicated data-association algorithm; the running example uses the stochastic map to decide that a newly sensed object cannot be the previously mapped object #1 (Sec. 2.3), Sec. 6 mentions ignoring sensor results that are too improbable, and the developed example assumes the sensor identifies the re-observed object as object #1, noting that in practice the new object would first be compared with the old ones (Sec. 5, Step 4) |
| 時間表示 | discrete poses (discrete motion approximation, Sec. 4) |
| 去畸變 | 不適用 |
| 迴圈閉合 | implicit: re-sensing a previously mapped object is incorporated as a constraint that reduces the uncertainty of the robot and all correlated objects (Sec. 2.3 example); no separate loop-closure module |
| 全域最佳化 | none (recursive filtering) |
| 地圖表示 | stochastic map: vector of object/robot frame relations with full covariance matrix |
| 先驗資訊 | world frame fixed at the initial robot pose (Sec. 5); prior knowledge can enter as new objects with given world locations (Case I-a, Sec. 4.2.1) or as geometric constraints such as colinearity, coplanarity or a possibly 'noisy' rectangle constraint that is modelled like a sensor measurement (Sec. 4.2, 4.2.2, Sec. 5, Figure 6) |
| 可輸出幾何 | mean and covariance of relative spatial relationships between frames (2D in text; 6-DoF Jacobians in Appendix A) |
| 計算需求 | no runtime or hardware reported; a robot motion changes only the robot entry and its row and column of the covariance matrix (Sec. 4.1); precomputed composite Jacobians are more efficient than the recursive method (Sec. 3.2.3) |
使用設備
尚未收錄此方法的設備紀錄；設備資料仍在分批查證，沒有紀錄不代表原文未使用任何設備。
作者報告的優勢與限制
優勢
- Probabilistic estimates are presented as less conservative than earlier worst-case min-max bounds (abstract; Sec. 1).
- Allows expressing the uncertainty of any frame relative to any other frame and predicting in advance whether accumulated uncertainty will make an operation fail (Sec. 1; Sec. 6).
限制
- ["Relies on small angular errors because inherently nonlinear relations are linearized (Sec. 6).", "Assumes the first two moments are adequate for decision making (Sec. 6).", "The EKF is a sub-optimal nonlinear estimator
- the iterated EKF is offered to reduce the error due to nonlinearities in the measurement function (Sec. 4.2.3).", "The 6-DoF Jacobians contain singular angle combinations near which covariance accuracy decreases
- avoidance methods were still being explored (Appendix A).", "Full-covariance filtering implies computation growing with the square of the number of landmarks, as later noted by Durrant-Whyte and Bailey (2006, Part I Sec. II) and Dissanayake et al. (2001, Sec. V)."]
營建工程相關證據
未在營建場域測試。其「共變異數傳遞與關係相依性」觀念是之後討論 SLAM 點雲座標不確定性與誤差累積的理論起點（推論）。
原文驗證環境：模擬
報告的性能數據
性能數據仍在分批查證，目前尚未收錄此方法的報告值。
來源
Smith et al., 1990
（1990）Estimating Uncertain Spatial Relationships in RoboticsAutonomous Robot Vehicles (book, Springer New York), pp. 167-193
DOI 10.1007/978-1-4613-8997-2_14arXiv 1304.3111
同儕審查已出版已讀全文經典查證後修正
相關版本
- 會議版：Estimating uncertain spatial relationships in robotics (Proc. 1987 IEEE ICRA, p. 850, one-page record) 10.1109/robot.1987.1087846
- 會議版：Estimating Uncertain Spatial Relationships in Robotics (Uncertainty in Artificial Intelligence 2, Machine Intelligence and Pattern Recognition, Elsevier 1988, pp. 435-461) 10.1016/b978-0-444-70396-5.50042-x
- 預印本：Authors' typeset full-length version posted on arXiv (v2 comment: as published in UAI 2 (1988) and reprinted in Autonomous Robot Vehicles (1990)) https://arxiv.org/abs/1304.3111
- 會議版：Estimating Uncertain Spatial Relationships in Robotics (shorter version in Proc. 2nd Conference on Uncertainty in Artificial Intelligence, UAI 1986, pp. 267-288; scanned as arXiv 1304.3111 v1) https://arxiv.org/abs/1304.3111v1