臺灣博碩士論文加值系統

　　本文提出「適應性卡曼濾波演算法」，它改良Wang(2001)提出之卡曼濾波演算法。根據Wang(2001)的構想，她定義（假設）卡曼濾波器在格點上的計算順序就是時間順序，藉以套用卡曼濾波器演算法於已知的、現有的、已經存在的DEM、或DSM資料，進行地表高程推估、高程雜訊過濾與粗差偵測。
　　本研究主要的貢獻在於提出「適應性卡曼濾波演算法」，它提供給測量與空間資訊領域另一個內插近似的新方法。此外，它運用最小二乘擬合法來自動選擇一個對局部幾何物面類型具「適應性」的合宜卡曼濾波推估模式，使其能適用於不同類型的局部區域數值表面模型（Digital Surface Model, DSM），以偵測隱含於空載光達點雲資料中的高程異常點位。
　　本研究採用台中交流道附近的空載光達實測資料進行測試，分析此演算法的高程推估值與格點高程值之差值、以及異常點偵測能力。由本研究的實驗成果顯示，全區光達點雲高程先驗精度經點雲擬合平面計算，得整體平均估值約為±22cm，此值將作為演算法邊界區格點高程推估協變方矩陣所需的先驗參考資訊。由卡曼濾波器計算所得之高程推估值精度之RMS值約為9.3cm，高程推估值與格點高程值之差值的精度之RMS值約為36.3cm。

　This study proposes an adaptive Kalman filtering algorithm which is an extended version of the Kalman filtering algorithm developed by Dr. Ping Wang in 2001. In her algorithm, a series of computation points is regarded as a series of time signal. Though all heights on the grid points in a DEM or DSM are all known and available before Kalman filtering computation, the algorithm still utilizes the principle of Kalman filtering for ‘height estimation’ instead of ‘height prediction’, height noise filtering, and blunder point detection as well.
　The main contribution of this study is under the circumstances to propose an adaptive Kalman filtering algorithm for singular point detection in airborne LIDAR points. This algorithm also provides a novel approach for approximation in the field of geodesy and geomatics. Moreover, a least-square fitting approach is utilized to automatically judge the surface type of a local DSM, so that the prediction model can be selected automatically and adaptively. This approach makes the algorithm adaptive.
　The feasibility of the proposed algorithm is tested by using some airborne LIDAR data in the area with different types of topography in Taichung. The test results verify the ability of the proposed algorithm for detecting singular points. Also, the relative height precision of ±22cm is derived from those test data by fitting local LIDAR points on a planar object surface onto a mathematical plane in a least squares manner. It is then used as a priori standard deviation of heights for all LIDAR points. On the other hand, the adaptive Kalman filtering algorithm figures out that the accuracy of heights estimated equals ±9.3cm, and the accuracy of the difference between the height observation and the height estimated by the algorithm on a grid point is about ±36.3cm.

中文摘要………………………………………………………………Ⅰ
英文摘要………………………………………………………………Ⅱ
誌謝……………………………………………………………………Ⅲ
目錄……………………………………………………………………Ⅴ
表目錄…………………………………………………………………Ⅶ
圖目錄…………………………………………………………………Ⅷ
第一章 前言…………………………………………………………1
§1-1 異常點之定義………………………………………………….1
§1-2 研究動機與目的……………………………………………….1
§1-3 相關文獻回顧………………………………………………….2
§1-4 論文架構……………………………………………………….4

第二章 卡曼濾波演算法與基本公式………...…….……….5
§2-1 卡曼濾波器計算原理………………………………………….5
§2-2 基本假設與演算模式之建立……………………………….…7
§2-3 公式推導……………………………………………...………..9
§2-4 演算流程……………………………………………..……….12

第三章 空載雷射掃描理論………...…….………………...14
§3-1 空載光達點雲資料特性分析………………………………...14
§3-2 光達點雲資料前置處理…..……………………………….…17


第四章 適應性卡曼濾波演算法之設計………...…….…...19
§4-1 適應性卡曼濾波演算法之設計概念………………….……..19
§4-2 網格結構……………………………………………………...21
§4-3 狀態向量之設計……………………………………………...21
§4-3-1 狀態向量模式一：一階多項式……………………22
§4-3-2 狀態向量模式二：零階多項式…………………….22
§4-3-3 狀態向量模式三：二階多項式…………………….24
§4-4 最小二乘擬合與推估模式…………………………………...25
§4-5 異常點偵測條件……………………………………………...26
§4-6 邊界問題……………………………………………………...27
§4-7 演算流程……………………………………………………...29

第五章 實驗成果與分析…………………………………...38
§5-1 實驗資料說明………………………………………………...38
§5-2 點雲高程精度測試…………………………………………...40
§5-2-1 點雲擬合平面之數學模式………………………...40
§5-2-2 測試成果…………………………………………...42
§5-3 異常點偵測案例分析………………………………………..45
§5-3-1 適應性卡曼濾波器推估模式選擇……….………..45
§5-3-2 高程推估值與格點高程值之較差分析…………...46
§5-3-3 精度分析……………………….…………………..48
§5-3-4 異常點偵測成果……………….…………………..48

第六章 結論與建議…………………………………………51
參考文獻……………………………………………………………….55

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