IKF as Gauss-Newton
本文證明迭代卡爾曼濾波（iterated Kalman filter, IKF）的量測更新步驟，就是以 Gauss-Newton 法近似最大概似估計；只迭代一次時即為 EKF 更新，量測函數為仿射時兩者都退化為一般卡爾曼更新。作者以二維雙站測距的解析例子說明，當觀測越來越精確時，IKF 更新與最大概似估計都會正確收斂，而 EKF 更新會收斂到有偏的值，同時其誤差共變異數卻趨近於零。這提供了把迭代濾波理解為單步最佳化的理論基礎。
本頁內容
Shows that the iterated Kalman filter update is a Gauss-Newton method for a maximum-likelihood estimate, with an example where the EKF update fails to converge correctly.
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 | 未記錄 |
| 狀態估計 | iterated Kalman filter measurement update shown to generate the same iterates as Gauss-Newton applied to the maximum-likelihood (weighted least-squares) update problem that stacks the predicted state and the observation; a single iterate gives the EKF update |
| 資料關聯 | 不適用 |
| 時間表示 | discrete time |
| 去畸變 | 不適用 |
| 迴圈閉合 | 不適用 |
| 全域最佳化 | 不適用 |
| 地圖表示 | 不適用 |
| 先驗資訊 | 不適用 |
| 可輸出幾何 | 不適用 |
| 計算需求 | 不適用 |
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
- Formal equivalence between IKF update and Gauss-Newton (abstract)
- In the closed-form bistatic ranging example the IKF and ML updates converge to the true state as the observation becomes exact, whereas the EKF converges to a biased value while its covariance goes to zero (Sec. VII)
- The authors state this convergence and false-convergence behaviour holds generally when an exact measurement completely determines the state (Sec. I)
限制
- Equivalence concerns the measurement update step; Barfoot notes the IEKF-MAP correspondence holds only for the correction step at a single timestep (Barfoot, 2017, Sec. 4.2.6)
- The update problem is static: system dynamics do not enter the analysis (Sec. II)
- The IKF generally performs better than the EKF at the expense of more computation (Sec. I)
- The covariance expression assumes the measurement function is affine near the estimate and the true state (Sec. IV)
營建工程相關證據
不適用
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
Bell & Cathey, 1993
（1993）The iterated Kalman filter update as a Gauss-Newton methodIEEE Transactions on Automatic Control, 38(2):294-297
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