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研究生:董士豪
研究生(外文):Shih-Hao Tung
論文名稱:轉換子空間旋轉法在一維與二維空間方向估測之研究
論文名稱(外文):Research of Transform Subspace Rotation Approach to One and Two Dimensional Direction-of-Arrival Estimation
指導教授:張豫虎
指導教授(外文):Yuh-Huu Chang
學位類別:碩士
校院名稱:中原大學
系所名稱:電子工程研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:103
中文關鍵詞:子空間旋轉法方向估測特徵分解
外文關鍵詞:EigendecompositionESPRITDOA
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  • 被引用被引用:0
  • 點閱點閱:220
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  • 下載下載:15
  • 收藏至我的研究室書目清單書目收藏:0

通訊技術的發達,導致了我們生活上的便利,人們不斷地在求新、求進步,絞盡腦汁去想出更好、更快的方法,單是就訊息信號的方向估測 (Directions-of-Arrival estimation) 方面,70年代以後,就不斷地有重大的突破;若是信號以陣列的形式呈現,我們可以採用線性代數中的特徵性質結構技術 (Eigenstructure method techniques),經過適當的計算得到答案。簡單來說,就是利用陣列狀的天線接收訊息資料,形成相關矩陣,再使用線性代數理論處理,以獲得入射信號方向的資訊。
由這種方式估測方向的方法,最有名的有MUSIC [1] (MUltiple SIgnal Classification 的簡稱) 演算法以及ESPRIT [3] (Estimation of Signal Parameter via Rotational Invariance Techniques ) 演算法。1986年,在Schmidt所提出的MUSIC演算法中,是將天線接收到的入射信號形成相關矩陣,再將其矩陣作特徵分解 (Eigendecomposition) 分成信號子空間與雜訊子空間,利用信號子空間和雜訊子空間正交性,將入射信號的方向估測出來。而ESPRIT演算法是利用兩組特性一樣的子陣列,其相對應的元素間等距離,來求出相位差。以上兩者方法應用在一維空間上的方向估測,都擁有甚佳的執行效能,但是推廣在二維空間估測上,卻會造成複雜的運算量及角度配對的問題。
這份論文中,我們對一維與二維空間方向估測提出一連串新的高解析度演算法,在這個方法中,我們將透過數個天線輸出信號的特徵性質結構特性來估測天線的脈衝響應,架構上藉著利用兩組特性一樣的陣列天線(Sensor array invariance)來進行方向估測,針對二維空間上的問題,不僅可以達到良好的執行效能,並且可為角度作自動配對。在可接受的結果之下和其他一、二維空間方向估測的演算法相比較,我們覺得所提出的演算法能夠減少相當的運算量。在二維空間方向估測的發展與應用上是一新的突破。
最後,我們經由模擬來展現我們所企盼的結果。


DOA (Direction-Of-Arrival) estimation is an important issue in radar, sonar etc. Over the passed three decades, there are many encourage progress in this area. The basic approach is based on the eigenstructure techniques to estimate DOA.
In 1986, Schmidt formed a covariance matrix of the received signal from the antennas and eigendecomposited it into signal subspace and noise subspace. Due to orthogonality between signal and noise subspace, the DOA can be estimated; it is known as MUSIC algorithm [1]. ESPRIT algorithm [3] exploited the subspaced rotated invariance of the subarray to estimate DOA.
These two algorithms have been successfully applied on the DOA estimation in one and two-dimensional and it will cause complex computation and the auto-pair problem in two-dimensional DOA estimation.
In this paper, we propose the high-resolution subspace rotate algorithm to estimate the DOA in one-dimensional (1-D) and two-dimensional (2-D) space. In this method, we can not only reduce the complexity of computation, but also pair the angle automatically. Compared with other algorithm of 2-D DOA estimation, the new algorithm really reduces the computation with a promising performance.


Contents
Chapter 1 Introduction ………………………………………………1
Chapter 2 A New Method to 1-D DOA Estimation ………………… 3
2.1. Introduction ………………………………………………………………… 3
2.2. The Problem Model ………………………………………………………… 4
2.3. ESPRIT Algorithm ………………………………………………………… 5
2.4. Transform Subspace Rotation (TSR) Algorithm to DOA Estimation ………. 9
2.5. The Vandermonde Direction Matrix and Signal Vectors Estimation ………. 11
2.6. Computational Complexity ………………………………………………… 13
2.7. Simulations ………………………………………………………………… 15
2.8. Conclusion …………………………………………………………………. 19
Chapter 3 Introduction of 2-D DOA Estimation …………………… 20
3.1. Introduction ………………………………………………………………… 20
3.2. The 2-D Problem Model …………………………………………………… 21
3.3. Other Methods to 2-D DOA Estimation ……………………………………33
Chapter 4 TSR method to 2-D DOA estimation …………………… 37
4.1. Introduction ………………………………………………………………… 37
4.2. The Problem Models of TSR Algorithm In the Uniform Linear Arrays …... 37
4.3. A New Method to 2-D DOA Estimation ………………………………… 40
4.4. The Problem of Pairing ……………………………………………………42
4.5. Simulations ………………………………………………………………… 45
4.6. Conclusion …………………………………………………………………. 51
Chapter 5 2-D DOA Estimation Using TSR with Model B ………. 52
5.1. Introduction ……………………………………………………………… 52
5.2. The Problem Model ……………………………………………………… 52
5.3. TSR Method to 2-D DOA Estimation In the Planar Arrays ………………. 55
5.4. Simulations ……………………………………………………………… 58
5.5. Conclusion ………………………………………………………………… 67
Chapter 6 Other Method for 2-D DOA Estimation Using TSR Method —1
(2-D DOA Estimation With Model A Via Parallel Linear Arrays) ..… 68
6.1. Introduction ……………………………………………………………… 68
6.2. The Problem Model ……………………………………………………… 68
6.3. TSR Method to 2-D DOA Estimation …………………………………… 71
6.4. Simulations ……………………………………………………………… 73
6.5. Conclusion ………………………………………………………………… 80
Chapter 7 Other Method for 2-D DOA Estimation Using TSR Method - 2
(2-D DOA Estimation Technique Using Second-Order Statistics) ……. 82
7.1. Introduction ……………………………………………………………… 82
7.2. The Problem Model ……………………………………………………… 82
7.3. MTSR Method to 2-D DOA Estimation ………………………………… 86
7.4. Simulations ………………………………………………………………… 90
7.5. Conclusion ………………………………………………………………… 95
Chapter 8 Conclusion ……………………………………………… 96
Reference ……………………………………………………………… 97


Reference[1] A. Paulraj, R. Roy and T. Kailath, “Extensions to the subspace invariance approach to signal parameter estimation,” In Proc. Int. Conf. On Acoustics, Speech and Sig. Proc, Japan, 1986.[2] R. O. Schmidt, “Multiple Emitter Location and Signal Parameter Estimation,” IEEE Transactions on Antenna and Propagation, vol. AP-34, No. 3. March, 1986.[3] R Roy and T. Kailath,”ESPRIT-Estimation of signal parameters via rotational invariance techniques” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.37, No.7. July 1989, 984-995.[4] A. Paulraj, R. Roy and T. Kailath, “A subspace rotation approach to signal parameter estimation” IEEE Proceedings , vol. 74, No.7, July 1986.[5] G. Xu, S. Silverstein, R. Roy and T. Kailath, “Beamspace ESPRIT,” IEEE Transactions on Signal Processing, vol. 42, Feb. 1994, 349-356.[6] A. Swindlehurst, B. Ottersten, R. Roy, and T. Kailath, “Multiple invariance ESPRIT;” IEEE Transactions on Signal Processing, vol. 40, 4, Apr. 1992, 867-881.[7] C. Chang; Z. Ding; S. F. Yau. Chan, F.H.Y, “A matrix-pencil approach to blind separation of colored nonstationary signals,” IEEE Transactions on Signal Processing, vol. 48, March 2000, 900 —907.[8] Krekel, P.F.C.; Deprettere, E.F. “A two-dimensional version of the matrix pencil method to solve the DOA problem,” European Conference on Circuit Theory and Design, 1989, 435 —439.[9] Yin, Q.Y.; Newcomb, R.W.; Zou, L.H, “Estimating 2-D angles of arrival via two parallel linear arrays,” ICASSP-89, 1989 International Conference on Acoustics, Speech, and Signal Processing, vol.4, 1989, 2803 —2806.[10] F. Ayhan Sakarya, and Monson H. Hayes, ”Estimating 2-D DOA Using Nonlinear Array Configurations,” IEEE Transactions on Signal Processing, vol.43, Sep. 1995, 2212-2216.[11] A. Swindlehurst, and T. Kailath, “Azimuth/Elevation Direction Finding Using Regular Array Geometries,” IEEE Transactions on Aerospace and Electronic Systems, vol. 29, Jan. 1993, 145-156.[12] A. Swindlehurst, and T. Kailath, “2-D Parameter Estimation Using Arrays With Multimensional Invariance Structure,” 23ACSSC, vol. 29, Dec. 1989, 950-953.[13] M. Viberg, B. Ottersten, "Sensor array processing based on subspace fitting", IEEE Trans. Acoust., Speech, Signal Processing, vol.39, May 1991, 1110-1121.[14] M. D. Zoltowski, D. Stavrinides,” Sensor array signal processing via a procrustes rotations based eigenanalysis of the ESPRIT data pencil,” IEEE Transactions on Acoustics, Speech and Signal Processing , vol. 37, June 1989, 832 —861.[15] F. Ayhan Sakarya, and Monson H. Hayes, ”A Subspace Rotation-Based Technique For Estimating 2-D Arrival Angles Using Nonlinear Array Configurations,” IEEE Transactions on Signal Processing, vol.42, Sep. 1994, 409-411.[16] P. Bas Ober, Ed F. Deprettere and Alle-Jan van Veen, “Efficient Methods Compute Azimuth And Elevation In High Resolution DOA Estimation,” IEEE Transactions on Signal Processing, 1991, 3349-3352.[17] Tsung-Hsien Liu, and Jerry M. Mendel, “Azimuth and Elevation Direction Finding Using Arbitary Array Genmetries,” IEEE Transactions on Signal Processing, vol.46, July 1998, 2061-2065.

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