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研究生:劉正瑜
研究生(外文):Liu Cheng-Yu
論文名稱:一般化M估測式特性及其應用之研究
指導教授:龔明覺李守誠李守誠引用關係
指導教授(外文):Kung Ming-ChioLee Sou-Chen
學位類別:博士
校院名稱:中正理工學院
系所名稱:國防科學研究所
學門:軍警國防安全學門
學類:軍事學類
論文種類:學術論文
論文出版年:1998
畢業學年度:86
語文別:中文
論文頁數:119
中文關鍵詞:一般化M估測式強韌性估測式參數估測動態系統初始調平重返載具彈道估測
外文關鍵詞:Generalized M estimatorRobust estimatorParameters estimationDynamic systemInitial levelingReentry vehicleTrajectroy estimation
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參數估測為應用相當廣泛之工具,目前最常用之估測方法,首推最小平方
估測式及最大相似估測法,然其對密度函數與異常樣本甚為敏感,往往因
嚴重之量測雜訊,而導致估測之失敗。本文應用M估測式理論,發展應用
範圍廣泛且具強韌性之一般化M估測式,及即時估測所須之遞歸法則,並
証明其一致性與收斂性,經由模擬結果亦可証明其性能,確係可資應用之
估測方法。固裝式慣性導航之初始調平,與導航精度息息相關,但因調平
過程中有外力輸入,而造成調平角估測收斂慢與誤差大,本文則以一般化
M估測式之輸入估測為基礎,結合Kalman濾波器,建立適應性Kalman濾波
器,以達成迅速與準確之初始調平。於反戰術彈道飛彈作戰中,即時彈道
估測為不可或缺之技術,由於雷達之量測量不足,且模式誤差極為嚴重,
本文亦擴展適應性Kalman濾波器,以估測重返載具之彈道,獲致強韌與精
準之估測結果。經由模擬與實測資料之驗証,適應性Kalman濾波器確能滿
足應用所需,從而証明本文所發展之一般化M估測式,深具實用價值。
Parameter estimation has found extensive engineering applications.
Least-squares and maximum likelihood estimators are two conventional
estimators. However, these two estimators have a higher sensitivity
to density functions and outliers, subsequently incurring large
estimation errors or divergence problems under heavy measurement
noises. In this work, we present the robust generalized M estimator
and its recursive algorithm applied towards on-line estimation
based on the M estimation theory. Consistency and convergence
properties are also verified. Simulation results verify the
reliability of the proposed robust estimator. In addition,
accuracy of a strapdown inertial navigation system heavily
relies on the initial leveling of accelerometers. Nevertheless,
under a large and abrupt deterministic input, large estimation
errors and slow convergence or divergence problem could arise.
Herein, we associate the generalized M estimator of input with
Kalman filter to form the adaptive Kalman filter, which is capable
of providing rapid and accurate initial leveling. On-line
trajectory estimation of a reentry vehicle plays an important
role in anti tactical ballistic missile warfare. Model validation
is the underlying issue of the trajectory estimation problem.
The adaptive Kalman filter is extended to three-dimensional
formation to sequentially estimate the model errors and identify
the reentry vehicle*s trajectory. Moreover, the proposed filter
is evaluated by simulation data and flight data measured by a
single radar in tests. That evaluation confirms the effectiveness
of this method for implementation purposes.
封面
目錄
1 緒論
1.1研究背景
1.2研究動機與 目的
1.3論文架構
2 M 估測式
2.1前言
2.2定義
2.3影響曲線
2.4漸近特性
2.4.1一致性
2.4.2漸近高斯分佈
2.4.3強韌特性
2.5常見之 M 估測式
2.5.1Huber估測式
2.5.2Tukey估測式
2.5.3Hampel估測式
2.6討論
3 一般化 M 估測式
3.1 前言
3.2定義
3.2.1 一般化密度函數
3.2.2 一般化 M 估測式
3.3一致性
3.4動態 系統參數之即時估測
3.4.1數學模式結構
3.4.2整批式估測
3.4.3即時估測
3.5例題
3.6討論
4 固 裝式慣性導航系統之初始調平
4.1前言
4.2調平角 估測之數學模式
4.2.1載具運動方程式
4.2.2隨機相 關力
4.2.3動態方程式
4.3適應性 Kalman濾波器
4.3.1架構
4.3.2強韌輸入估測式
4.3.3輸入偵測
4.3.4適應性F;alman濾波器
4.4模擬驗証
4.5 討論
5 重返裁兵彈道之估測
5.1前言
5.2彈道估測之數學模式
5.2.1載具運動方程式
5.2.2修正之運動方程式
5.2.3重返載具濾波器
5.2.4擴展型Kalman濾波器
5.3適應性Kalman濾波器
5.3.1強韌輸入估測
5.3.2輸入偵測
5.3.3適應性Kalman濾波器
5.4測試驗証
5.4.1具側向加速度之彈道
5.4.2六自由度之彈道
5.4.3實測彈道
5.5討論
6結論
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