傳統聲源定位的方法，是藉由聲源到達麥克風陣列中每支麥克風的時間差(TDOA，Time Difference of Arrival)，來回推聲源的入射角度，這種方法雖然計算量並不大，但是在空間中的解析度卻會受到取樣頻率的影響。本論文引用了目前聲源定位的諸多方法中，解析度較高的MUSIC(Multiple Signal Classification)演算法，此演算法即使在多聲源的情況下，不但可以得知聲源的數目，更可同時找出個別的入射角度，再利用粒子定位法(Particle Localization Method)實現二維平面的聲源定位。但在實際操作後，發現此演算法的計算量非常龐大，以至於無法直接套用在real-time系統中。因此，我們也採用了幾種解決方案，解決計算量過大的問題。另外在非理想環境中，定位結果容易受到環境雜訊以及回聲的影響，造成定位不穩定。因此，本論文還引入了兩種線性預估的方法，粒子濾波器(Particle Filter)以及卡爾曼濾波器(Kalman Filter)，事先對聲源位置做預測，來改善定位結果。從實驗結果發現，卡爾曼濾波器的誤差收斂速度比粒子濾波器要快，且對於移動聲源的追蹤也較佳。

Traditional sound source localization algorithms employed the TDOA(Time Difference of Arrival) between microphones in a microphone array to estimate the angle of incidence. Even though the computations of these methods are not huge, the spatial resolution is affected by the sampling rate. In this thesis we use a high resolution algorithm called multiple signal classification (MUSIC). In the multiple-source case, this method not only can determine the number of sources, but also their angles of incidence. Then we use particle localization method (PLM) to realize two dimension sound source localization. In practice, we notice that the computation load of MUSIC algorithm is too heavy to realize in real time. So we adopt several methods to solve this problem. In practice, the performance of the system is also affected by reverberation, and the steadiness of this method is not ideal. Thus, to improve the performance we use Particle Filter and Kalman Filter to track the sound source. From the experiment results, we can notice that the Kalman filter converged faster than the particle filter. The bias of the Kalman filter when it converged is also smaller than the particle filter. The ability of the Kalman filter to track moving source is also better than the particle filter.

[1] S. Birchfield and R. Gangishetty, “Acoustic localization by interaural level difference,” International Conference on Acoustics, Speech and Signal Processing, vol. 2, pp. 1109–1112, 2005.
[2] W. Cui, Z. Cao, and J. Wei, “Dual-microphone source location method in 2-D space,” International Conference on Acoustics, Speech and Signal Processing, vol. 4, pp. 845–848, 2006.
[3] A. Pourmohammad and S. M. Ahadi, “TDE-ILD-based 2D half plane real time high accuracy sound source localization using only two microphones and source counting,” 2010 International Conference on Electronics and Information Engineering, vol. 1, pp. V1–566–V1–572, Aug. 2010.
[4] Z. Liang, X. Ma, and X. Dai, “Robust tracking of moving sound source using multiple model Kalman filter,” Applied Acoustics, vol. 69, no. 12, pp. 1350–1355, Dec. 2008.
[5] Z. Liang, X. Ma, and X. Dai, “Robust tracking of moving sound source using scaled unscented particle filter,” Applied Acoustics, vol. 69, no. 8, pp. 673–680, Aug. 2008.
[6] R. Schmidt, “Multiple emitter location and signal parameter estimation,” IEEE Transactions on Antennas and Propagation, vol. 34, no. 3, pp. 276–280, 1986.
[7] Mingsian R. Bai, Acoustic Array Systems, 1st ed. Singapore ; Hoboken : John Wiley & Sons, Inc., 2013.
[8] H. K. Hwang, Z. Aliyazicioglu, M. Grice, and A. Yakovlev, “Direction of Arrival Estimation using a Root-MUSIC Algorithm,” in International MultiConference of Engineers and Computer Scientists, 2008, vol. II, pp. 19–21.
[9] 曾政傑, “基於多重訊號分類之聲源方位偵測,” 國立台灣科技大學, 2008.
[10] W. Tager, “Near Field Superdirectivity,” in Acoustic, Speech and Signal Processing, IEEE, 1998, pp. 2045–2048.
[11] M. D. Zoltowski and C. P. Mathews, “Real-Time Frquency and 2-D Angle Estimation with Sub-Nyquist Spatio-Temporal Sampling,” IEEE Transactions on Signal Processing, vol. 42, pp. 2781–2794, 1994.
[12] Y. Tamai and S. Kagami, “Circular microphone array for robot’s audition,” in Sensors of IEEE, 2004, pp. 565–570.
[13] H. Zhang, H.-C. Wu, and S. Y. Chang, “Novel fast MUSIC algorithm for spectral estimation with high subspace dimension,” 2013 International Conference on Computing, Networking and Communications (ICNC), pp. 474–478, Jan. 2013.
[14] J. Vermaak and a. Blake, “Nonlinear filtering for speaker tracking in noisy and reverberant environments,” 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221), vol. 5, pp. 3021–3024.
[15] C. Liu, Y. Song, M. Garuba, and L. Burge, “HMMF: An Hidden Markov Model Based Approach for Motif Finding,” 2009 3rd International Conference on Bioinformatics and Biomedical Engineering, pp. 1–3, Jun. 2009.
[16] N. Bidargaddi, “Fuzzy profile hidden Markov models for protein sequence analysis,” CIBCB ’05. Proceedings of the 2005 IEEE Symposium on Computational Intelligence in Bioinformatics and Computational Biology, 2005., pp. 1–8, 2005.
[17] G. Welch and G. Bishop, “An Introduction to the Kalman Filter,” Citeseer.
[18] R. Kalman, “A new approach to linear filtering and prediction problems,” Journal of basic Engineering, vol. 82, no. Series D, pp. 35–45, 1960.
[19] R. Vullings, B. de Vries, and J. W. M. Bergmans, “An adaptive Kalman filter for ECG signal enhancement.,” IEEE transactions on bio-medical engineering, vol. 58, no. 4, pp. 1094–103, Apr. 2011.
[20] C. R. Z. Deng, “Two average weighted measurement fusion Kalman filtering algorithms in sensor networks,” 2008 7th World Congress on Intelligent Control and Automation, vol. 1, no. 6, pp. 2387–2391, 2008.
[21] J.-Y. Kim and T.-Y. Kim, “Soccer Ball Tracking Using Dynamic Kalman Filter with Velocity Control,” 2009 Sixth International Conference on Computer Graphics, Imaging and Visualization, pp. 367–374, Aug. 2009.
[22] R. Brown and P. Hwang, Introduction to random signals and applied Kalman filtering. Wiley, John & Sons, 1992.
[23] S. J. Julier and J. K. Uhlmann, “A New Extension of the Kalman Filter to Nonlinear Systems,” The University of Oxford, 1865.
[24] S. Julier and J. K. Uhlmann, “A General Method for Approximating Nonlinear Transformations of Probability Distributions,” The University of Oxford, 1996.
[25] D. Ward, “Particle filtering algorithms for tracking an acoustic source in a reverberant environment,” Speech and Audio Processing, IEEE, vol. 11, no. 6, pp. 826–836, 2003.
[26] M. M. Farrell, J. A. and Polycarpou, Adaptive and Learning Systems for Signal Processing, Communications, and Control. John Wiley & Sons, Inc., 2006.
[27] M. S. Arulampalam, S. Maskell, N. Gordon, and T. Clapp, “A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking,” IEEE Transactions on Signal Processing, vol. 50, no. 2, pp. 174–188, 2002.
[28] H. Anderson, “Metropolis, Monte Carlo, and the MANIAC,” Los Alamos Science. 1986.
[29] D. S. Lemons, A. Gythiel, and P. Langevin, “Paul Langevin ’ s 1908 paper ‘ On the Theory of Brownian Motion ’,” American Association of Physics Teachers, vol. 533, no. 1908, pp. 1079–1081, 1997.
[30] 梁翰銘, “利用粒子濾波器與麥克風陣列進行直角座標上多聲源之追蹤,” 國立清華大學, 2012.
[31] “LM386 Low Voltage Audio Power Amplifier.” 2000.