演算法LLL與白化濾波應用於導航衛星相位模稜搜尋

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陳揚仁(Yang-Zen Chen) 查詢紙本館藏

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土木工程學系

論文名稱

演算法LLL與白化濾波應用於導航衛星相位模稜搜尋
(Searching the Ambiguity of Navigation Satellite Carrier-phase Using the LLL Algorithm and the Whitening Filter)

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摘要(中)

一般而言，GNSS載波相位定位之精度較電碼定位高，利用載波相位觀測量進行衛星測量求解位置時，如何快速得到正確的整數相位模稜值，是求解精度與效率的關鍵。但是參數間彼此高相關，會使這個目標變得困難。這個問題能夠藉由衛星幾何的改變來改善，但是卻因此而加長觀測時間。因此LLL技術以及白化濾波即將原在高相關空間的參數，投影至另一低相關空間。使數學變換過程等效於衛星幾何改變，進而可在較短觀測時段裡求解。
LLL是將一正定對稱矩陣分解為上下三角矩陣，再利用Gram–Schmidt正交變換將三角矩陣之向量轉變為彼此間皆正交，接著藉由正交化後之上下三角矩陣相乘得到一具備對角優勢之協方差矩陣。
白化濾波是利用Crout 因子分解，使一正定對稱矩陣分解為對角線矩陣與單位上下三角矩陣之連乘。應用其矩陣對角線化的特性於相位模稜實數解的協方差矩陣上，產生具備對角優勢之協方差矩陣。
應用此協方差矩陣可大幅減少整數相位模稜的候選解。最後將候選解逐一代入觀測式中重新進行平差演算，求取一殘差二次形為最小之解。

摘要(英)

Generally, the GNSS carrier-phase is more accurate then the pseudorange. While using carrier-phase for positioning, the key point is how to obtain the correct integer ambiguity quickly and efficiently. However the high correlation between parameters makes it to be difficult. The problem can be improved by the changing of the geometric of satellites. But it needs longer observation time to reach. Therefore the LLL algorithm and the whitening filter are techniques mapping the parameters from a higher correlation space to a lower correlation space. And the effects of mathematics changing and the geometric changing can be the same. Then the result can be gotten within a short observation period.
The LLL algorithm decomposes a positive-definite symmetrical matrix into the upper/lower triangular matrix. Then uses the Gram–Schmidt orthogonalization to transform vectors of the matrix into orthogonal each other. Then the diagonal covariance matrix can be gotten by the transpose of the orthogonal matrix multiplying to the orthogonal matrix.
Whitening filter uses crout factorization to decompose a positive-definite symmetrical matrix into the continue multiplication of diagonal matrix and unit upper/lower triangular matrix. Applying the specifics of its diagonal matrix condition to covariance matrix can get the diagonal covariance matrix.
Using the diagonal covariance matrix can reduce the number of candidates for integral ambiguity. Final, the candidates are inserted into the observation equations to determine the solution again. It is believed that the integer candidate which produces the smallest sum of squares of the residual is the most likely solution we want.

關鍵字(中)

★ 相位模稜
★ 高相關

關鍵字(英)

★ higher correlation
★ Carrier-phase

論文目次

目錄 I
圖目錄 III
表目錄 V
第一章緒論 1
1.1 文獻回顧 1
1.2 研究動機 5
1.3 論文架構 6
第二章理論基礎 7
2.1 觀測方程式 7
2.1.1 虛擬距離觀測方程式 7
2.1.2 載波相位觀測方程式 9
2.2 差分模式 10
2.3 費雪統計檢定 12
第三章 LLL、白化濾波與相位模稜搜尋 13
3.1 平差模式 13
3.2 觀測資料之隨機模式 14
3.3 協方差、搜索域與轉換矩陣 15
3.4 矩陣分解 19
3.4.1 Crout因子分解 19
3.4.2 Cholesky矩陣分解 21
3.5 LLL理論與相位模稜搜尋 22
3.6 白化濾波理論與相位模稜搜尋 28
第四章實驗成果與分析 31
4.1 實驗資料背景 31
4.2 實驗處理流程 32
4.3 實驗成果與分析 33
4.3.1 基線SPP0–MUST (21.3 km) 35
4.3.2 基線SPP0–XINU (24.6 km) 37
4.3.3 基線SPP0–NTPU (37.2 km) 40
4.3.4 基線SPP0–SINP (39.0 km) 42
4.3.5 基線SPP0–PCCU (40.1 km) 45
4.3.6 基線SPP0–LANY (64.6 km) 47
4.3.7 基線SPP0–CKGM (239.3 km) 50
4.3.8 基線SPP0–CKGM OTF解算使用時刻分析 53
4.3.9 空載資料之成果 55
第五章結論與展望 58
5.1 結論 58
5.2 展望 59
參考文獻 61

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指導教授

吳究(Joz Wu)

審核日期

2009-7-1

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