頁籤選單縮合
題 名 | 自適應卡門濾波及其應用於洪水預報=The Adaptive Kalman Filter and Its Application to the Flood Forecasting |
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作 者 | 王如意; 周建明; | 書刊名 | 農業工程學報 |
卷 期 | 46:3 2000.09[民89.09] |
頁 次 | 頁1-10 |
分類號 | 443.42 |
關鍵詞 | 自適應卡門濾波; 穩健性推估; ARX模式; 洪水預報; Adaptive kalman filter; Robust estimation; ARX model; Flood forecasting; |
語 文 | 中文(Chinese) |
中文摘要 | 卡門濾波為一種即時校正模式,其可用以處理非穩定系統內之資訊,且根據推估誤差為最小之原則以決定最佳之濾波增益。一般濾波之方法係於系統模式中動態噪音及觀測噪音之統計特性為已知之情況下進行演算;惟在實際應用中,系統之動態噪音及觀測噪音之統計特性常不能完全確知。如此,無法得到最佳濾波之結果,並且有可能發生發散之情況。 為有效控制濾波發散及獲得最佳化之推估,本文應用自適應卡門濾波進行颱洪期間流域逕流量之預測。首先建立卡門濾波與特殊最小平方迴歸問題之相等關係,再使用M-穩健推估法求解此迴歸問題。M-穩健性推估子可在推估狀態變數之際,同時自適應地推估事先未知之動態及觀測噪音之統計性質。文中採用具外來投入自迴歸模式(autoregressive model with exogenous input,簡稱ARX模式)模擬降雨—逕流之歷程。應用自適應卡門濾波於ARX模式,可以即時校正並更新系統之狀態,以從事洪水之模擬、推估及預報。 |
英文摘要 | The Kalman filter is one of the real-time correction models. It can be used to handle the information in an unstable system, and to determine the optimal filtering gain based upon the criterion that minimum estimation error is presented in the recursive process. The conventional Kalman filter algorithm would be carried out when the statistical information of the system dynamic and measurement noise was known. In practice, there is little or no prior knowledge of the system dynamic and measurement noise. In this case, the estimate results are not optimal and may lead to the divergence. To control the divergence of the filter efficaciously and obtain the estimate optimally, an adaptive Kalman filter is applied for predicting the flow of rivers during flooding. The equivalence between the Kalman filter and a particular least squares regression problem is established and the regression problem is solved robustly using a statistical M-estimation approach. M-robust estimators are derived for adaptive estimation of the unknown a priori state and observation noise statistics simultaneously with the system state. The adopted rainfall-runoff model is the autoregressive model with exogenous input (ARX) model. The adaptive Kalman filter is added to the ARX model for real-time modifying and updating the system state so as to be applied in flood simulation, estimation and forecasting. |
本系統中英文摘要資訊取自各篇刊載內容。