本論文提出了利用左右聲道訊號相位差做為線索，並且估計聲源抵達麥克風之時間差，用以判別聲源來向的方法。不同頻率在頻域之相位差會受到聲源和麥克風的距離影響而有所不同，但將相位差轉換回時間差之後則會相同。因此可以透過相位差作為線索做聲源來向的估測。此一演算法首先利用傅利葉轉換的振幅部分，透過移動平均 (moving average) 估計接收所得訊號的訊雜比。接下來利用此一訊雜比和事先取得的雜訊機率模型，建立相位差的機率模型，並且接著取得相位差的機率密度函數。此一機率模型會根據訊雜比高低給予各個頻率之相位差不同的機率密度函數，具有較高訊雜比的頻段會獲得較集中的機率密度函數，對最後結果的影響也較大，反之亦然。最後將所有頻率的相位差機率密度函數之訊息轉換為時間差機率密度函數並且相乘整理後，就可以得到聲源抵達左右聲道時間差的機率密度函數。此一方法除了提供聲源方向的估計之外，也量化了求得的聲源來向機率密度函數的測量可信度。另外我們也使用了高斯函數來近似相位的機率密度函數，用以簡化計算量。這使得此一演算法有機會能以即時運算實現。實驗結果顯示此一演算法比正規化互相關演算法 (general cross correlation, GCC) 和同樣以左右聲道相位差為線索的文獻 [1] 中所提出的演算法，在相同噪音程度下表現較佳且更為穩定。

This thesis proposes a method that estimates the time difference of arrival (TDOA) using the interaural phase difference as a cue to locate the direction of a sound source. The algorithm fist estimates the amplitude of the Fourier transform of the signal to obtain an approximated signal to noise ratio (SNR). The phase difference of each frequency bin is then modeled in terms of its probability density function. Through combining the information from all frequency bins, the probability density function of TDOA can be obtained. Instead of giving a direction as the final result, the probability density function provides a measure of confident in estimation. The Gaussian function is used to approx- imate the probability density function of phase in order to simplify the computation. This makes it possible to implement the algorithm in real-time. The experiment result also shows that the algorithm is more robust to noise in comparison with an existing algorithm published by [1], which uses power weighting and interaural phase spectrum (IPD) to determine interaural time difference (ITD).

Contents
Abstract
摘要
Acknowledgments
Contents
List of Figures
1 Introduction
1.1 ComparedMethod
2 Mathematical Notations and Noise Modeling
2.1 PhaseDifferenceandTimeDelayofArrival
2.2 NoiseModelling
3 The Proposed Algorithm
3.1 ProbabilisticModelsoftheTDOA
3.1.1 ProbabilisticModelandSNR
3.2 ComputationalSimplification
4 Simulation and Experiment
4.1 Simulation
4.2 Experiments
4.2.1 EquipmentandEnvironment
4.2.2 Results
5 Conclusion
Bibliography

[1] F. Fujii, N. Hogaki, and Y. Watanabe, “A simple and robust binaural sound source localization system using interaural time difference as a cue,” in 2013 IEEE International Conference on Mechatronics and Automation. IEEE, Aug. 2013, pp. 1095–1101.
[2] D. P. W. Ellis and J. C. Liu, “Speaker turn segmentation based on between-channel differences,” NIST ICASSP 2004 Meeting Recognition Workshop, Montreal, pp. 112–117, 2004.
[3] X. Anguera, C. Wooters, and J. Hernando, “Acoustic Beamforming for Speaker Diarization of Meetings,” IEEE Transactions on Audio, Speech and Language Processing, vol. 15, no. 7, pp. 2011–2022, Sep. 2007.
[4] Longji Sun and Qi Cheng, “Real-time microphone array processing for sound source separation and localization,” in 2013 47th Annual Conference on Information Sciences and Systems (CISS). IEEE, Mar. 2013, pp. 1–6.
[5] D. Pavlidi, A. Griffin, M. Puigt, and A. Mouchtaris, “Real-Time Multiple Sound Source Localization and Counting Using a Circular Microphone Array,” IEEE Transactions on Audio, Speech, and Language Processing, vol. 21, no. 10, pp. 2193–2206, Oct. 2013.
[6] R. Schmidt, “Multiple emitter location and signal parameter estimation,” IEEE Transactions on Antennas and Propagation, vol. 34, no. 3, pp. 276–280, Mar. 1986.
[7] Z. Zohny and J. Chambers, “Modelling interaural level and phase cues with Student’s t-distribution for robust clustering in MESSL,” in 2014 19th International Conference on Digital Signal Processing. IEEE, Aug. 2014, pp. 59–62.
[8] W. G. Gardner and K. D. Martin, “HRTF Measurements of a KEMAR,” The Journal of the Acoustical Society of America, vol. 97, no. 6, pp. 3907–3908, 1995.
[9] F. Keyrouz, Y. Naous, and K. Diepold, “A New Method for Binaural 3-D Localization Based on Hrtfs,” in 2006 IEEE International Conference on Acoustics Speed and Signal Processing Proceedings, vol. 5. IEEE, 2006, pp. V–341–V–344.
[10] Y.-I. Kim and R. M. Kil, “Estimation of Interaural Time Differences Based on Zero-Crossings in Noisy Multisource Environments,” IEEE Transactions on Audio, Speech and Language Processing, vol. 15, no. 2, pp. 734–743, Feb. 2007.
[11] S. Birchfield and R. Gangishetty, “Acoustic Localization By Interaural Level Difference,” in Proceedings. (ICASSP ’05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005., vol. 4. IEEE, 2005, pp. 1109–1112.
[12] M. I. Mandel and D. P. W. Ellis, “EM Localization and Separation using Interaural Level and Phase Cues,” in 2007 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics. IEEE, Oct. 2007, pp. 275–278.
[13] C. Knapp and G. Carter, “The generalized correlation method for estimation of time delay,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 24, no. 4, pp. 320–327, Aug. 1976.
[14] H. Liu and J. Zhang, “A binaural sound source localization model based on time-delay compensation and interaural coherence,” in 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, May 2014, pp. 1424–1428.
[15] H.-K. Hao, H.-M. Liang, and Y.-W. Liu, “Particle methods for real-time sound source localization based on the Multiple Signal Classification algorithm,” in 2014 International Conference on Intelligent Green Building and Smart Grid (IGBSG). IEEE, Apr. 2014, pp. 1–5.
[16] M. Usman, F. Keyrouz, and K. Diepold, “Real time humanoid sound source localization and tracking in a highly reverberant environment,” in 2008 9th International Conference on Signal Processing. IEEE, Oct. 2008, pp. 2661–2664.
[17] N. Semiconductor, “LM386 Low Voltage Audio Power Amplifier,” Tech. Rep., 2000.