請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/82274完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 劉俊麟(Chun-Lin Liu) | |
| dc.contributor.author | Yung-Hsuan Teng | en |
| dc.contributor.author | 滕永萱 | zh_TW |
| dc.date.accessioned | 2022-11-25T06:34:48Z | - |
| dc.date.copyright | 2021-11-05 | |
| dc.date.issued | 2021 | |
| dc.date.submitted | 2021-10-21 | |
| dc.identifier.citation | [1] Harry L. Van Trees. Optimum Array Processing: PartIV of Detection, Estimation, and Modulation Theory. Wiley, 2002. [2] S. Haykin, J. Litva, and T. J. Shepherd. Radar Array Processing. Springer-Verlag, Berlin, Heidelberg, 1993. [3] S. Haykin. Array signal processing. Englewood Cliffs, 1985. [4] P. Stoica and K.C. Sharman. Maximum likelihood methods for direction-of-arrival estimation. IEEE Transactions on Acoustics, Speech, and Signal Processing, 38(7):1132–1143, 1990. [5] P. Stoica and Arye Nehorai. MUSIC, maximum likelihood, and Cramer-Rao bound. IEEE Transactions on Acoustics, Speech, and Signal Processing, 37(5):720–741,1989. [6] P. Stoica and A. Nehorai. Performance study of conditional and unconditional direction-of-arrival estimation. IEEE Transactions on Acoustics, Speech, and Signal Processing, 38(10):1783–1795, 1990. [7] R. Schmidt. Multiple emitter location and signal parameter estimation. IEEE Transactions on Antennas and Propagation, 34(3):276–280, 1986. [8] S. U. Pillai and B. H. Kwon. Forward/backward spatial smoothing techniques for coherent signal identification. IEEE Transactions on Acoustics, Speech, and Signal Processing, 37(1):8–15, 1989. [9] C. Liu and P. P. Vaidyanathan. Remarks on the Spatial Smoothing Step in Coarray MUSIC. IEEE Signal Processing Letters, 22(9):1438–1442, 2015. [10] A. Barabell. Improving the resolution performance of eigenstructure-based direction-finding algorithms. In ICASSP’83. IEEE International Conference on Acoustics, Speech, and Signal Processing, volume 8, pages 336–339, 1983. [11] R. Roy and T. Kailath. ESPRIT-estimation of signal parameters via rotational invariance techniques. IEEE Transactions on Acoustics, Speech, and Signal Processing, 37(7):984–995, 1989. [12] B. D. Van Veen and K. M. Buckley. Beamforming: A versatile approach to spatial filtering. IEEE assp magazine, 5(2):4–24, 1988. [13] I. Ziskind and M. Wax. Maximum likelihood localization of multiple sources by alternating projection. IEEE Transactions on Acoustics, Speech, and Signal Processing, 36(10):1553–1560, 1988. [14] J.A. Fessler and A.O. Hero. Space-alternating generalized expectation-maximization algorithm. IEEE Transactions on Signal Processing, 42(10):2664–2677, 1994. [15] M. Wang and A. Nehorai. Coarrays, MUSIC, and the Cramér–Rao Bound. IEEE Transactions on Signal Processing, 65(4):933–946, 2017. [16] J. Steinwandt, F. Roemer, and M. Haardt. Performance analysis of ESPRIT-Type algorithms for co¬array structures. In 2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), pages1–5, 2017. [17] P. Pal and P. P. Vaidyanathan. Nested Arrays: A Novel Approach to Array Process¬ing With Enhanced Degrees of Freedom. IEEE Transactions on Signal Processing, 58(8):4167–4181, 2010. [18] C. Liu and P. P. Vaidyanathan. Super Nested Arrays: Linear Sparse Arrays With Reduced Mutual Coupling—Part I: Fundamentals. IEEE Transactions on Signal Processing, 64(15):3997–4012, 2016. [19]A. Moffet. Minimum-redundancy linear arrays. IEEE Transactions on Antennas and Propagation, 16(2):172–175, 1968. [20] P. Pal and P. P. Vaidyanathan. Coprime sampling and the music algorithm. In 2011 Digital Signal Processing and Signal Processing Education Meeting (DSP/SPE), pages 289–294, 2011. [21] G. S. Bloom and S. W. Golomb. Applications of numbered undirected graphs. Proceedings of the IEEE, 65(4):562–570, 1977. [22] S. Sedighi, B. S. M. R. Rao, and B. Ottersten. An Asymptotically Efficient Weighted Least Squares Estimator for Co-Array-Based DoA Estimation. IEEE Transactions on Signal Processing, 68:589–604, 2020. [23] J. B. Lasserre. Global Optimization with Polynomials and the Problem of Moments. SIAM Journal on Optimization, 11(3):796–817, 2001. [24] C. Liu, P. P. Vaidyanathan, and P. Pal. Coprime coarray interpolation for DOA estimation via nuclear norm minimization. In 2016 IEEE International Symposium on Circuits and Systems (ISCAS), pages 2639–2642, 2016. [25] C. Zhou, Y. Gu, X. Fan, Z. Shi, G. Mao, and Y. D. Zhang. Direction¬ of Arrival Estimation for Coprime Array via Virtual Array Interpolation. IEEE Transactions on Signal Processing, 66(22):5956–5971, 2018. [26] M. Laidacker. Another Theorem Relating Sylvester’s Matrix and the Greatest Common Divisor. Mathematics Magazine, 42:126–128, 1969. [27] M. Grant and S. Boyd. CVX: Matlab software for disciplined convex programming, version 2.1.http://cvxr.com/cvx, March 2014. [28] M. Grant and S. Boyd. Graph implementations for nonsmooth convex pro¬grams. In V. Blondel, S. Boyd, and H. Kimura, editors, Recent Advances in Learning and Control, Lecture Notes in Control and Information Sciences, pages95–110. Springer-Verlag Limited, 2008.http://stanford.edu/~boyd/graph_dcp.html. [29] C. Liu and P.P. Vaidyanathan. Cramér–Rao bounds for coprime and other sparse arrays, which find more sources than sensors. Digital Signal Processing, 61:43–61,2017. Special Issue on Coprime Sampling and Arrays. [30] C. Liu and P. P. Vaidyanathan. Super nested arrays: Sparse arrays with less mutual coupling than nested arrays. In 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 2976–2980, 2016. [31] C. Chen and P. P. Vaidyanathan. Minimum redundancy MIMO radars. In 2008 IEEE International Symposium on Circuits and Systems, pages 45–48, 2008. [32] A. Dollas, W.T. Rankin, and D. McCracken. A new algorithm for Golomb ruler derivation and proof of the 19 mark ruler. IEEE Transactions on Information Theory, 44(1):379–382, 1998. [33] T. Shan, M. Wax, and T. Kailath. On spatial smoothing for direction-of-arrival estimation of coherent signals. IEEE Transactions on Acoustics, Speech, and Signal Processing, 33(4):806–811, 1985. [34] B. Ottersten, M. Viberg, and T. Kailath. Performance analysis of the total least squares ESPRIT algorithm. IEEE Transactions on Signal Processing, 39(5):1122–1135, 1991. [35] M. Jansson, B. Goransson, and B. Ottersten. A subspace method for direction ofarrival estimation of uncorrelated emitter signals. IEEE Transactions on Signal Processing, 47(4):945–956, 1999. [36] S. Sedighi, B. S. M. R. Rao, S. Maleki, and B. Ottersten. Consistent Least Squares Estimator for Co-Array-Based DOA Estimation. In 2018 IEEE 10th Sensor Array and Multi channel Signal Processing Workshop (SAM), pages 524–528, 2018. [37] R. Kumaresan, L. Scharf, and A. Shaw. An algorithm for pole¬zero modeling and spectral analysis. IEEE Trans. Acoust. Speech Signal Process., 34:637–640, 1986. [38] P. Stoica and K. Sharman. Novel eigenanalysis method for direction estimation.1990. [39] M. Muramatsu, S. Kim, M. Kojima, and H. Waki. Aspects of SDP relaxation for Polynomial Optimization. https://www.mat.univie.ac.at/~neum/glopt/gicolag/talks/muramatsu.pdf. [40] D. Henrion, J. B. Lasserre, and J. Löfberg. GloptiPoly 3: Moments, Optimization and Semidefinite Programming. Optimization Methods and Software, 24, 10 2007. [41]M. Fazel. Matrix rank minimization with applications. PhD thesis, PhD thesis, Stanford University, 2002. [42]M. Fazel, H. Hindi, and S. Boyd. Rank minimization and applications in system theory. In Proceedings of the 2004 American Control Conference, volume 4, pages3273–3278 vol.4, 2004. [43]B. Recht, M. Fazel, and P. A. Parrilo. Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization. SIAM Review, 52(3):471–501, Jan 2010. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/82274 | - |
| dc.description.abstract | 本論文的目的是討論如何在基於有孔洞的協同陣列估計訊號的到達角度(DoA)。為了分析更多的信號源，透過使用稀疏陣列的協同陣列來增加樣本協方差矩陣的維數。稀疏陣列可以使用M個傳感器解析大約O(M2)個信號源。現有的DoA估計演算法中，S. Sedighi、B. S. M. R. Rao和B. Ottersten在2019年的研究中指出加權最小平方(WLS)估計器的均方根誤差(RMSE)已經能有效漸進到Cramér–Rao bound (CRB)。然而，對於不連續的協同陣列，例如互質陣列，最小孔數陣列的協同陣列等，由於目標函數變量之間的關係求解複雜，複雜度增加。因此，我們針對不連續的協同陣列提出一個更通用的實現方法。在實現中，這個方法通過使用Sylvester矩陣，以避免進行符號運算。然後我們運用核範數對目標函數進行近似。最終的目標函數可以通過凸函數求解器得到結果。我們在本論文中提供了所提出方法的一些數值模擬。藉由討論其性能，我們發現在某些情況下也能漸進達到CRB。在合理範圍內，可以使用相同的參數和停止條件，應用於不同大小和形式的一維陣列，仍可以獲得良好的結果。 | zh_TW |
| dc.description.provenance | Made available in DSpace on 2022-11-25T06:34:48Z (GMT). No. of bitstreams: 1 U0001-0610202101244900.pdf: 4763975 bytes, checksum: 4d46b2f01010bd1a4a27a4f8fa921e3b (MD5) Previous issue date: 2021 | en |
| dc.description.tableofcontents | 口試委員會審定書 i 致謝 iii 摘要 v Abstract vii Contents ix List of Figures xiii List of Tables xvii Notation xix Chapter 1 Introduction 1 Chapter 2 Preliminaries 5 2.1 System Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.1 Difference Coarray. . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Array Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2.1 Uniform Linear Array. . . . . . . . . . . . . . . . . . . . . . . . 13 2.2.2 Nested Array. . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2.3 Super Nested Array. . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2.4 Minimum Redundancy Array. . . . . . . . . . . . . . . . . . . . . 19 2.2.5 Coprime Array. . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2.6 Minimum Hole Array. . . . . . . . . . . . . . . . . . . . . . . . . 24 2.2.7 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.3 Subspace¬Based DoA Algorithms. . . . . . . . . . . . . . . . . . . 28 2.3.1 Coarray Multiple Signal Classification (MUSIC) Algorithm. . . . . 28 2.3.1.1 Coarray MUSIC Spectrum. . . . . . . . . . . . . . . 28 2.3.1.2 Coarray Root¬MUSIC. . . . . . . . . . . . . . . . . . 32 2.3.1.3 The Performance of Coarray MUSIC Algorithm. . . . 33 2.3.2 Coarray Least Square Estimation of Signal Parameters by Rotational Invariance Techniques(LS¬ESPRIT) algorithm. . . . . . . . . . . . 34 2.4 Cramér–Rao Bound. . . . . . . . . . . . . . . . . . . . . . . . . . 37 Chapter 3 Review of WLS DoA Estimation Based on Difference Coarray43 3.1 Objective Function. . . . . . . . . . . . . . . . . . . . . . . . . 43 3.2 Implementation on Hole¬Free Coarray. . . . . . . . . . . . . . . . . 47 3.2.1 Polynomial Parameterization. . . . . . . . . . . . . . . . . . . . 47 3.2.2 Relaxation of Objective Function. . . . . . . . . . . . . . . . . . 50 3.2.3 Simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.2.3.1 RMSE vs Snapshot. . . . . . . . . . . . . . . . . . . 56 3.2.3.2 RMSE vs SNR. . . . . . . . . . . . . . . . . . . . . . 61 3.3 Implementation on Coarray with Holes. . . . . . . . . . . . . . . . 65 3.3.1 Objective Function. . . . . . . . . . . . . . . . . . . . . . . . . 65 3.3.2 Relaxation of Objective Function. . . . . . . . . . . . . . . . . . 68 3.3.3 Lasserre’s SDP Relaxation. . . . . . . . . . . . . . . . . . . . . 70 3.3.4 Simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 3.4 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Chapter 4 Proposed Method 81 4.1 The Application of The Sylvester Matrix. . . . . . . . . . . . . . . 84 4.2 The Application of The Nuclear Norm. . . . . . . . . . . . . . . . . 86 4.3 Implementation. . . . . . . . . . . . . . . . . . . . . . . . . . . 88 4.4 Simulation Result. . . . . . . . . . . . . . . . . . . . . . . . . . 93 4.4.1 How to Choose λ. . . . . . . . . . . . . . . . . . . . . . . . . . 93 4.4.2 RMSE vs Number of Iteration. . . . . . . . . . . . . . . . . . . . 96 4.4.3 RMSE vs SNR. . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 4.4.4 RMSE vs Snapshot. . . . . . . . . . . . . . . . . . . . . . . . . . 109 4.5 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 Chapter 5 Conclusion 115 Chapter 6 Future Outlook 117 References 119 | |
| dc.language.iso | en | |
| dc.subject | 到達角度 | zh_TW |
| dc.subject | 加權最小平方估計器 | zh_TW |
| dc.subject | 稀疏陣列 | zh_TW |
| dc.subject | 帶孔協同陣列 | zh_TW |
| dc.subject | 西爾維斯特矩陣 | zh_TW |
| dc.subject | 核範數 | zh_TW |
| dc.subject | Sylvester Matrix | en |
| dc.subject | Coarray with Holes | en |
| dc.subject | Weighted least squares estimator | en |
| dc.subject | Sparse Array | en |
| dc.subject | Direction of Arrival | en |
| dc.subject | Nuclear Norm | en |
| dc.title | 通過西爾維斯特矩陣和核範數實現基於帶孔協同陣列的加權最小平方到達方向估計 | zh_TW |
| dc.title | Implementation of Weighted Least Squares DoA Estimators for Coarray with Holes through the Sylvester Matrix and the Nuclear Norm | en |
| dc.date.schoolyear | 109-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 馮世邁(Hsin-Tsai Liu),蘇柏青(Chih-Yang Tseng) | |
| dc.subject.keyword | 到達角度,稀疏陣列,加權最小平方估計器,帶孔協同陣列,西爾維斯特矩陣,核範數, | zh_TW |
| dc.subject.keyword | Direction of Arrival,Sparse Array,Weighted least squares estimator,Coarray with Holes,Sylvester Matrix,Nuclear Norm, | en |
| dc.relation.page | 124 | |
| dc.identifier.doi | 10.6342/NTU202103568 | |
| dc.rights.note | 未授權 | |
| dc.date.accepted | 2021-10-22 | |
| dc.contributor.author-college | 電機資訊學院 | zh_TW |
| dc.contributor.author-dept | 電信工程學研究所 | zh_TW |
| dc.date.embargo-lift | 2023-11-01 | - |
| 顯示於系所單位： | 電信工程學研究所 | |
文件中的檔案：
| 檔案 | 大小 | 格式 | |
|---|---|---|---|
| U0001-0610202101244900.pdf 未授權公開取用 | 4.65 MB | Adobe PDF |
系統中的文件，除了特別指名其著作權條款之外，均受到著作權保護，並且保留所有的權利。