本論文提出對未知跳頻參數(跳頻頻率、時間等)之跳頻訊源來向角估測方法。
本論文之來向角估測方法大致可分為三個階段，分別為跳頻訊號偵測、訊號來向角初步估測、及精準訊號來向角估測。首先以低複雜度之短時距傅立葉轉換方法進行時頻分析來偵測跳頻訊號，再利用得到的跳頻參數以虛擬都卜勒 快速定向方法進行訊號來向角之初步估測；最後將初估角度代入最大概似性方法進行來向角之精準估測。
本論文以Simulink軟體產生藍芽訊號作為訊號源進行模擬，以驗證此來向角估測混合方法之效能；並比較有無虛擬都卜勒初步估測，對最大概似性估測方法產生的影響。模擬結果證明加入虛擬都卜勒初步估測，不僅能有效加快最大概似性估測方法之收斂速度，且可以避免最大概似性之估測結果收斂至局部最小值的問題，故此混合定向方法可有效提升跳頻訊源來向角估測之精準度。

In this thesis, we propose a blind direction of arrival (DOA) estimation of a frequency hopping signal source without a priori information of its hopping pattern.
The DOA estimation can be divided into 3 stages, including frequency hopping signal detection, preliminary DOA estimation, and accurate DOA estimation. First, we use low complexity short-time Fourier transform (STFT) time-frequency analysis to detect the hopping pattern of a frequency hopping signal, and then applying the estimated hopping pattern to a quick pseudo Doppler direction finder to perform the preliminary DOA estimation. Finally, we substitute the preliminary estimation result into a maximum likelihood (ML) scheme as the initial value and obtain the accurate estimation result.
Computer simulations are used to verify the performance of the hybrid DOA estimation, where Bluetooth signals generated by Simulink software are used as sources. After comparing the maximum likelihood estimation with or without pseudo Doppler scheme, the results show that hybrid DOA estimation not only can accelerate the convergence speed of maximum likelihood estimation, but also prevent the maximum likelihood estimation from converging to a local minimum problem. Consequently, the hybrid DOA estimation can effectively improve the accuracy of DOA estimation of a frequency hopping signal.

[1]J. G. Proakis, Digital communications, Boston, McGraw-Hill, 2000.
[2]Rohde&Schwarz, “Bluetooth 4.0 Low Energy technology and RF testing,” Available:http://www.digitimes.com.tw/tw/b2b/seminar/service/download/.pdf
[3]H. Luan and H. Jiang, "Blind Detection of Frequency Hopping Signal Using Time-Frequency Analysis," in Wireless Communications Networking and Mobile Computing (WiCOM), 6th International Conference on, 2010, pp. 1-4
[4]M. P. Fargues, H. F. Overdyk, and R. Hippenstiel, "Wavelet-based detection of frequency hopping signals," in Signals, Systems & Computers, Conference Record of the Thirty-First Asilomar Conference on, 1997, pp. 515-519 vol.1.
[5]S. Barbarossa and A. Scaglione, "Parameter estimation of spread spectrum frequency-hopping signals using time-frequency distributions," in Signal Processing Advances in Wireless Communications, First IEEE Signal Processing Workshop on, 1997, pp. 213-216.
[6]C. Aubel, D. Stotz, and H. Bolcskei, "Super-resolution from short-time Fourier transform measurements," in Acoustics, Speech and Signal Processing (ICASSP), IEEE International Conference on, 2014, pp. 36-40.
[7]L. Feng, M. W. Marcellin, N. A. Goodman, and A. Bilgin, "Compressive Detection of Multiple Frequency-Hopping Spread Spectrum Signals," in Data Compression Conference (DCC) on, 2014, pp. 415-415.
[8]D. Adamy, EW 101 : a first course in electronic warfare. Boston: Artech House, 2001.
[9]"Direction Finding and Radiolocation Basics," Available: https://academy.itu.int/moodle/pluginfile.php/64750/mod_folder/content/9/Direction finding and radio location Basic, 2013.
[10]D. Wei and X. Shuguo, "Mutual coupling analysis of Adcock Watson Watt direction finding system based on the receiving mutual impedance," in Antennas, Propagation & EM Theory (ISAPE), 10th International Symposium on, 2012, pp. 302-305.
[11]"A comparison of radio direction-finding technologies," Available: http://www.denisowski.org/Articles/Denisowski-ComparisonofRadioDirection-FindingTechnologie, 2013.
[12]"Introduction into Theory of Direction Finding," Available: http://www.rohde-schwarz-ad.com/docs/ewtest/intro_theory_of_direction_finding, 2013
[13]K. A. Struckman, "Copy capture aided correlation interferometer direction finding," in Antennas and Propagation Society International Symposium, 2008. AP-S. IEEE, 2008, pp. 1-4.
[14]H. W. Wong and Y. G. Sung, "Performance analysis and comparison of correlative interferometers for direction finding," in Signal Processing (ICSP), IEEE 10th International Conference on, 2010, pp. 393-396.
[15]W. J. Rung, D. H. Hong, and D. Chi-biao, "An improved method to sort and pair TDOA based on the correlation between TDOAs," in Radar (Radar), IEEE CIE International Conference on, 2011, pp. 1041-1044.
[16]W. J. Rung, D. H. Hong, and D. Chi-biao, "An improved method to sort and pair TDOA based on the correlation between TDOAs," in Radar (Radar), IEEE CIE International Conference on, 2011, pp. 1041-1044.
[17]J. FaIk, P. Handel, and M. Jansson, "Effects of frequency and phase errors in electronic warfare TDOA direction-finding systems," in Military Communications Conference, MILCOM '03. IEEE on, 2003, pp. 118-123 Vol.1.
[18]W. Gerok, J. Peissig, and T. Kaiser, "TDOA assisted RSSD localization in UWB," in Positioning Navigation and Communication (WPNC), 9th Workshop on, 2012, pp. 196-200.
[19]F. Vincent, O. Besson, and E. Chaumette, "Approximate Unconditional Maximum Likelihood Direction of Arrival Estimation for Two Closely Spaced Targets," Signal Processing Letters, IEEE, vol. 22, pp. 86-89, 2015.
[20] J. W.Shin, Y. J. Lee, and H. N. Kim, "Reduced-Complexity Maximum Likelihood Direction-of-Arrival Estimation Based on Spatial Aliasing," Signal Processing, IEEE Transactions on 2014, vol. 62, pp. 6568-6581.
[21]M. Kossor., A Doppler Radio-Direction Finder, 1999, Available: http://traktoria.org/files/rdf/a_doppler_radio-direction_part_1.pdf.
[22]Balint, "Software Defined Radio Direction Finding (SDRDF) ", 2012, Available: http://nvlpubs.nist.gov/nistpubs/jres/65D/jresv65Dn3p197_A1b.pdff.
.[23]R. Hidayat, I. N. Rifai, W. Widada, and A. P. Adi, "Doppler circular array antenna principle for determining azimuth angle of radio transmitter," in Intelligent Signal Processing and Communications Systems (ISPACS),International Symposium on, 2011, pp. 1-4.
[24]J. J. Keaveny, R. M. Buehrer, J. Reed, and W. Tranter, "Analysis and Implementation of a Novel Single Channel Direction Finding Algorithm on a Software Radio Platform," Master thesis of the Virginia Polytechnic Institute and State University, 2005.

[25]D. Musicki and W. Koch, "Geolocation using TDOA and FDOA measurements," in Information Fusion, 11th International Conference on, 2008, pp. 1-8.
[26]R. O. Schmidt, "Multiple emitter location and signal parameter estimation," Antennas and Propagation, IEEE Transactions on, vol. 34, pp. 276-280, 1986
[27]W. J. Zhi, C. C. Ko, and F. Chin, "Multi-hop ML based delay and angle estimation for multipath wideband FH signals," in Vehicular Technology Conference, 2004. VTC 2004-Spring. 2004 IEEE 59th, 2004, pp. 157-161 Vol.1.
[28]M. Pesavento and A. B. Gershman, "Maximum-likelihood direction-of-arrival estimation in the presence of unknown nonuniform noise," Signal Processing, IEEE Transactions on, vol. 49, pp. 1310-1324, 2001.
[29]K. T. Wong, "Blind beamforming/geolocation for wideband-FFHs with unknown hop-sequences," Aerospace and Electronic Systems, IEEE Transactions on, vol. 37, pp. 65-76, 2001.
[30]V. V. Krishna, J. V. Avadhanulu, K. Giridhar, and A. Paulraj, "Eigenstructure methods for direction-of-arrival estimation of frequency hop (FH) emitters," in Military Communications Conference, MILCOM '90, Conference Record, A New Era. IEEE, 1990, pp. 1133-1137 vol.3.
[31]X. Liu, N. D. Sidiropoulos, and A. Swami, "Blind high-resolution localization and tracking of multiple frequency hopped signals," Signal Processing, IEEE Transactions on, vol. 50, pp. 889-901, 2002.
[32]A. Polydoros and W. Kai, "LPI Detection of Frequency-Hopping Signals Using Autocorrelation Techniques," Selected Areas in Communications, IEEE Journal on, vol. 3, pp. 714-726, 1985.
[33]"Applications of the Gauss-Newton Method," Available: https://ccrma.stanford.edu/~wherman/gauss_newton.pdf
[34]"Gauss-Newton Algorithm for nonlinear least squares," Available: http://iacs-courses.seas.harvard.edu/courses/am205/slides/am205_lec06.pdf
[35]羅朝洪, 跳頻訊號的參數估計和調制識別, 成都電子科技大學碩士論文, 2009.
[36]J. J. Keaveny, “Analysis and Implementation of a Novel Single Channel Direction Finding Algorithm on a Software Radio Platform,” Virginia Polytechnic Institute and State University, Thesis for The Degree of Master of Engineering, 2005.
[37]N. K. Peng , “A correlation-based method for direction finding of multipath signals in frequency hopping systems,” National University of Singapore, Thesis for The Degree of Master of Engineering, 2005.
[38]"Bluetooth modulation and frequency hopping," Available: http://www.mathworks.com/matlabcentral/fileexchange/722-bluetooth-modulation-and-frequency-hopping