基于贝叶斯原理和蒙特卡罗方法的高分辨方位估计新方法研究
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摘要
阵列处理的高分辨技术一直是国内外十分关注的研究热点，其中高分辨多目标定向技术是国内外集中力量研究的重点，该项技术的突破对声纳、雷达、地质勘探、生物医学工程及水中兵器均有重要意义。尤其是对水下多目标方位的高分辨精确估计，是目前加强海防、进行海洋开发迫切希望有所突破的一项关键技术。本文在国家自然科学基金、航空基础科学基金和“九五”重点预研项目的资助下，对贝叶斯高分辨方法进行了深入的研究和总结，并且针对原贝叶斯高分辨方位估计方法计算量大的问题，给出了基于吉布斯采样法的贝叶斯高分辨多目标方位估计新方法，使得贝叶斯高分辨方法向实时应用迈进了重要的一步。本文的主要工作及研究进展有：
1．全面研究并总结了贝叶斯高分辨方位估计方法的性能。
本文首先简要介绍了贝叶斯高分辨方位估计方法的理论，总结了该方法在不同信噪比下的估计性能。在高信噪比(20dB)下贝叶斯高分辨方位估计方法的角度分辨门限高达1／18波束宽度，低信噪比(-10dB)下也能达到1／3波束宽度。其次通过大量计算机仿真，深入分析了快怕数和阵元数对贝叶斯高分辨目标方位估计方法性能的影响。定量地给出了这两个因素与贝叶斯高分辨方法性能之间的关系。
2．给出了基于吉布斯采样法的贝叶斯高分辨多目标方位估计新方法
在研究了蒙特卡罗方法和吉布斯采样方法的基础上，本文给出了基于吉布斯采样法的贝叶斯高分辨多目标方位估计新方法的理论推导，降低了原贝叶斯高分辨方位估计方法的计算量，提高了贝叶斯高分辨方法的实时性。而且在理论研究的基础上，对新方法的性能进行了大量的计算机仿真和统计分析。结果表明，新方法在继承了原贝叶斯高分辨方位估计方法的优越性能同时，随着K的增加，将原方法的计算复杂度从指数增长的O(L~K)降低到线性增长的O(K×J×N_s)(其中L为栅格数，K为目标源个数，J为采样个数，N_s为迭代次数)，显著提高了原贝叶斯高分辨方位估计方法的实时性，并且成功地将贝叶斯高分辨方法的应用扩展到多目标源。
3．进行了新方法、原贝叶斯高分辨方位估计方法与多重信号特征法(MUSIC)和极大似然估计法(MLE)的性能比较研究，揭示了新方法的优越性。
主要从信噪比的变化、角度分辨能力、低信噪比下的估计性能几个方面进行了深入的对比分析。新方法不仅具有很高的分辨能力，而且在低信噪比时也具有
西北工业大学硕士学位论文
摘要
比MLE和MUSIC更加优越的估计性能。在估计三目标源的情况下，比较了新方
法和MUSIC法，仿真结果表明新方法在多目标情况下的性能也远比MUSIC法优
越。这些工作将贝叶斯高分辨方法的研究从理论分析向实际应用推进了一步。
High-resolution multi-source direction finding is always a hot research area in array signal processing. The breakthrough of this technique is greatly meaningful in many research fields such as sonar, radar, communication, biomedical engineering, geology and so on. Especially the underwater acoustics high-resolution multi-source direction finding technique is the key to underwater searching and ocean exploration. Sponsored and supported by the National natural Science Foundation, the Aviation Science Foundation as well as the National Pre-research Project, Bayesian high-resolution method is thoroughly studied and summarized in this thesis. The novel Bayesian high-resolution DOA estimator based on Gibbs sampling is given to improve the real-time performance of original Bayesian high-resolution DOA estimator. The new progresses and main results are summarized as follows:
1. The performance of Bayesian high-resolution method is investigated and summarized comprehensively.
Bayesian high-resolution method is introduced briefly. Its angular resolution ability under different SNR is summarized comprehensively. The highest resolution of Bayesian method is 1/18 bandwidth of the beam main lobe i n high SNR (20dB) and 1/3 bandwidth in low SNR (-lOdB). The effects on its performance by the factors such as sanpshots and number of array sensors are investigated and their relations are also qutitantively analyzed.
2. A novel Bayesian high-resolution multi-source DOA estimator based on Gibbs sampling is proposed.
To improve the real-time performance of Bayesian high-resolution method, a novel Bayesian high-resolution multi-source DOA estimator based on Gibbs sampling is proposed. On the basis of theoretical study, large amount of computer simulation and statistical analysis is conducted to investigate the perfomance of the new method. The research indicates that the new method not only contains the super performance of original Bayesian high-resolution method but also significantly reduces the computation quantity from 0(LK ) to 0(KxJxNs). And the new method can be successfully extended to the case of multiple sources.
3. The new method and original Bayesian high-resolution DOA estimator are compared with other typical methods like MUSIC and MLE, and the superiority of the new method is revealed.
The new method and original Bayesian method are compared with the other two
methods in the aspects like angular resolution ability, performance in low SNR. It is proved that the new method possesses better performance than MLE and MUSIC, especially in low SNR In the case of three sources, the simulation results show that the performance of new method is much more superior than MUSIC.
1．全面研究并总结了贝叶斯高分辨方位估计方法的性能。
本文首先简要介绍了贝叶斯高分辨方位估计方法的理论，总结了该方法在不同信噪比下的估计性能。在高信噪比(20dB)下贝叶斯高分辨方位估计方法的角度分辨门限高达1／18波束宽度，低信噪比(-10dB)下也能达到1／3波束宽度。其次通过大量计算机仿真，深入分析了快怕数和阵元数对贝叶斯高分辨目标方位估计方法性能的影响。定量地给出了这两个因素与贝叶斯高分辨方法性能之间的关系。
2．给出了基于吉布斯采样法的贝叶斯高分辨多目标方位估计新方法
在研究了蒙特卡罗方法和吉布斯采样方法的基础上，本文给出了基于吉布斯采样法的贝叶斯高分辨多目标方位估计新方法的理论推导，降低了原贝叶斯高分辨方位估计方法的计算量，提高了贝叶斯高分辨方法的实时性。而且在理论研究的基础上，对新方法的性能进行了大量的计算机仿真和统计分析。结果表明，新方法在继承了原贝叶斯高分辨方位估计方法的优越性能同时，随着K的增加，将原方法的计算复杂度从指数增长的O(L~K)降低到线性增长的O(K×J×N_s)(其中L为栅格数，K为目标源个数，J为采样个数，N_s为迭代次数)，显著提高了原贝叶斯高分辨方位估计方法的实时性，并且成功地将贝叶斯高分辨方法的应用扩展到多目标源。
3．进行了新方法、原贝叶斯高分辨方位估计方法与多重信号特征法(MUSIC)和极大似然估计法(MLE)的性能比较研究，揭示了新方法的优越性。
主要从信噪比的变化、角度分辨能力、低信噪比下的估计性能几个方面进行了深入的对比分析。新方法不仅具有很高的分辨能力，而且在低信噪比时也具有
西北工业大学硕士学位论文
摘要
比MLE和MUSIC更加优越的估计性能。在估计三目标源的情况下，比较了新方
法和MUSIC法，仿真结果表明新方法在多目标情况下的性能也远比MUSIC法优
越。这些工作将贝叶斯高分辨方法的研究从理论分析向实际应用推进了一步。
High-resolution multi-source direction finding is always a hot research area in array signal processing. The breakthrough of this technique is greatly meaningful in many research fields such as sonar, radar, communication, biomedical engineering, geology and so on. Especially the underwater acoustics high-resolution multi-source direction finding technique is the key to underwater searching and ocean exploration. Sponsored and supported by the National natural Science Foundation, the Aviation Science Foundation as well as the National Pre-research Project, Bayesian high-resolution method is thoroughly studied and summarized in this thesis. The novel Bayesian high-resolution DOA estimator based on Gibbs sampling is given to improve the real-time performance of original Bayesian high-resolution DOA estimator. The new progresses and main results are summarized as follows:
1. The performance of Bayesian high-resolution method is investigated and summarized comprehensively.
Bayesian high-resolution method is introduced briefly. Its angular resolution ability under different SNR is summarized comprehensively. The highest resolution of Bayesian method is 1/18 bandwidth of the beam main lobe i n high SNR (20dB) and 1/3 bandwidth in low SNR (-lOdB). The effects on its performance by the factors such as sanpshots and number of array sensors are investigated and their relations are also qutitantively analyzed.
2. A novel Bayesian high-resolution multi-source DOA estimator based on Gibbs sampling is proposed.
To improve the real-time performance of Bayesian high-resolution method, a novel Bayesian high-resolution multi-source DOA estimator based on Gibbs sampling is proposed. On the basis of theoretical study, large amount of computer simulation and statistical analysis is conducted to investigate the perfomance of the new method. The research indicates that the new method not only contains the super performance of original Bayesian high-resolution method but also significantly reduces the computation quantity from 0(LK ) to 0(KxJxNs). And the new method can be successfully extended to the case of multiple sources.
3. The new method and original Bayesian high-resolution DOA estimator are compared with other typical methods like MUSIC and MLE, and the superiority of the new method is revealed.
The new method and original Bayesian method are compared with the other two
methods in the aspects like angular resolution ability, performance in low SNR. It is proved that the new method possesses better performance than MLE and MUSIC, especially in low SNR In the case of three sources, the simulation results show that the performance of new method is much more superior than MUSIC.
引文
[1] 陈建峰，水下高分辨定向关键技术研究，西北工业大学博士学位论文，1999年3月，西安
[2] 黄建国，水下多目标方位估计的高分辨新技术研究，国家自然科学基金申请书，1997年3月
[3] 杨克虎，阵列天线雷达的低角跟踪方向估计，西安电子科技大学博士学位论文，1994年，西安
[4] 孙超，李斌，加权子空间拟合算法理论与应用，西北工业大学出版社，1994年7月
[5] R. O. Schimidt, Multiple emitter location and signal parameter estimation, Proc. RADC Spectral Estimation Workshop, Griffiss AFBS, NY, 1979
[6] R. Kumaresan, D. W. Tufts, Estimation the angles of arrival of multiple plane waves, IEEE Trans. AES, vol. 19, no. 1, pp. 134-139, Jan. 1983
[7] R. Roy, T. Kailath, ESPRIT-Estimation of signal parameters via rotation invariance techniques, IEEE-ASSP, vol.37, no.7, pp. 984-995, 1989
[8] A. J. Barabell, Improving the resolution performance of eigenstructure-based direction-finding algorithms, Proc. IEEE ICASSP, pp.336-339, 1983
[9] P. Stoica, K. C. Sharman, Maximum likelihood methods for direction-of-arrival estimation, IEEE T-ASSP, vol.38, no.7, pp. 1132-1142, July 1990
[10] M. Viberg, B. Ottersten, Sensor array processing based on subspace fitting, IEEE, T-SP, vol.39, pp. 1110-1120, 1991
[11] 黄建国，高分辨技术研究总结报告，中国船舶工业科技报告，1996年
[12] Steven M. Kay, Fundamentals of statistical signal processing estimation theory, Prentice Hall, Englewood Cliffs, New Jersey, 1992
[13] 张尧庭，陈汉峰，贝叶斯统计推断，科学出版社，1991年
[14] 廖文，陈安贵等译，S．James，Press著，贝叶斯统计学：原理、模型及应用，中国统计出版社，1992年
[15] Petar M. Djuric, Hsiang-Tsun Li, Bayesian spectrum estimation of harmonic signals, IEEE Signal Processing Letters, Nov.1995
[16] Jianguo Huang, Jianfeng Chen, Chunming Liu and Petar M. Djuric, A Bayesian approach to high resolution direction-of-arrival estimation, Proceedings of the Fourth International Conference on Signal Processing, Beijing, China, October, 1998
[17] 徐朴，多目标方位估计的贝叶斯高分辨新技术研究，西北工业大学博士后研究工作报告，1999年11月
[18] 鲁瑛，贝叶斯高分辨方位估计方法的性能分析与应用研究，西北工业大学硕士论文，2001年4月
[19] 胡广书，数字信号处理—理论、算法与实现，清华大学出版社，1997年
[20] 黄建国，武延祥，杨世兴译，Steven M．Kay著，现代谱估计，科学出版社，1994年
[21] 程运鹏，张凯院，徐仲，矩阵论，西北工业大学出版社，1989年
[22] 袁易全，雷家煜，姚治国，近代声学基阵原理及其应用，南京大学出版社，1994年
[23] 肖国有，屠庆平，声信号处理及其应用，西北工业大学出版社，1994年
[24] 刘春明，贝叶斯高分辨定向新技术研究，西北工业大学硕士学位论文，1998年3月
[25] Pu Xu, Ying Lu, Jianguo Huang, Research on Bayesian method of direction-finding, International Journal of Plant Engineering and Management, vol.3,no.2, pp. 321-324, 1998
[26] 陈建峰，黄建国，基于贝叶斯估计的高分辨定向方法，航空学报，vol．19，no．6，1998年
[27] L. Bretthorst, Bayesian spectrum analysis and parameter estimation, New York, NY: Springer verlag, 1989
[28] J. Lasenby, W. J. Fitzgerald, A Bayesian approach to high-resolution beamforming, IEEE Proceedings-F, vol. 138, no.6, pp. 539-544, 1991
[29] Chao-Ming Cho and Petar M. Djuric, Detector and estimation of DOA of signals via Bayesian predictive densities, IEEE Transactions on Signal Processing, vol.42, no. 11, pp. 3051-3060, 1994
[30] Chao-Ming Cho and Petar M. Djuric, Bayesian detection and estimation of Cisoids in colored noise, IEEE ,Trans. SP, vol.43, no. 12, 1995
[31] Q. T. (Keith) Zhang, Probability of resolution of the MUSIC algorithm, IEEETrans. Signal Processing, vol.43, no.4, pp. 978-987, 1995
[32] P. Stoica, A. Nehora, MUSIC, Maximum likelihood and Cramer-Rao Bound, IEEE T-ASSP, vol.37, no.5, pp. 720-741, 1989
[33] P. Stoica, A. Nehora, MUSIC, Maximum likelihood and Cramer-Rao Bound: further results and comparisons, IEEE T-ASSP, vol.38, no. 12, pp. 2140-2150, 1990
[34] P. Stoica, K. C. Sharman, Maximum likelihood methods for direction-of arrival estimation, IEEE T-ASSR vol.38, no.7, pp. 1132-1142, 1990
[35] J. E. Evans, J. R. Johnson, D. F. Sun, High resolution angular spectrum estimation techniques for terrain scattering analysis and angle of arrival estimation, in Proc. 1st Workshop Spectrum Estimation Hamilton, Ont. Canada, 1981
[36] Jun S.Liu, Monte Carlo Strategies in Scientific Computing, Springer-Verlag New York, Inc, 2001
[37] Ming-Hui Chen, Qi-Man Shao, Joseph G. Ibrahim, Monte Carlo Methods in Bayesian Computation, pringep-Verlag New York, Inc, 2000
[38] Xiaodong Wang, Rong Chen, Adaptive Bayesian Multiuser Detection for Synchronous CDMA with Gaussian and Impulsive Noise, IEEE Transaction on Signal Processing, VOL.47, No.7, July 2000
[39] Jayesh H. Kotecha, Petar M. Djuric, Gibbs Sampling Approach for Generation of Truncated Multivariate Gaussian Random Variables, EEEE Transaction on Signal Processing, VOL.47, No.7, March 2000
[40] G. Casellan and E. I. George, Explaining the Gibbs Sampler, Amer. Stat. Vol.46, PP.320-326, 1993
[41 ]W. R. Gilks, S. Richardson, and D. J. Spiegelhalter, Markov Chain Monte Carlo in Practice, New York: Chapman & Hall, 1996
[42] Chen. M. H. And Schmeiser, B. W. (1993) , Performance of the Gibbs, hit-and-run, and Metropolis samplers, Journal of Computational and Graphical Statistics
[43] Cowles, M. K. And Carlin, B. P. (1996) , Markov Chain Monte Carlo convergence diagnostics: A compararive review, Journal of the American Satistical Association
[44] S. F. Arnold, "Gibbs sampling." In Handbook of Statistics. C. R. Rao Ed. New York Elsevier, 1993, vol.9
[45] F. M Smith and A. E. Gelfand. Bayesian statistics without tears: A sampling-resampling perspective, American Statistician, 1992．
[46] M. West, Approximating posterior distributions by mixtures, Journal of the Ro-yal Statistical Society (Ser. B), 1997
[2] 黄建国，水下多目标方位估计的高分辨新技术研究，国家自然科学基金申请书，1997年3月
[3] 杨克虎，阵列天线雷达的低角跟踪方向估计，西安电子科技大学博士学位论文，1994年，西安
[4] 孙超，李斌，加权子空间拟合算法理论与应用，西北工业大学出版社，1994年7月
[5] R. O. Schimidt, Multiple emitter location and signal parameter estimation, Proc. RADC Spectral Estimation Workshop, Griffiss AFBS, NY, 1979
[6] R. Kumaresan, D. W. Tufts, Estimation the angles of arrival of multiple plane waves, IEEE Trans. AES, vol. 19, no. 1, pp. 134-139, Jan. 1983
[7] R. Roy, T. Kailath, ESPRIT-Estimation of signal parameters via rotation invariance techniques, IEEE-ASSP, vol.37, no.7, pp. 984-995, 1989
[8] A. J. Barabell, Improving the resolution performance of eigenstructure-based direction-finding algorithms, Proc. IEEE ICASSP, pp.336-339, 1983
[9] P. Stoica, K. C. Sharman, Maximum likelihood methods for direction-of-arrival estimation, IEEE T-ASSP, vol.38, no.7, pp. 1132-1142, July 1990
[10] M. Viberg, B. Ottersten, Sensor array processing based on subspace fitting, IEEE, T-SP, vol.39, pp. 1110-1120, 1991
[11] 黄建国，高分辨技术研究总结报告，中国船舶工业科技报告，1996年
[12] Steven M. Kay, Fundamentals of statistical signal processing estimation theory, Prentice Hall, Englewood Cliffs, New Jersey, 1992
[13] 张尧庭，陈汉峰，贝叶斯统计推断，科学出版社，1991年
[14] 廖文，陈安贵等译，S．James，Press著，贝叶斯统计学：原理、模型及应用，中国统计出版社，1992年
[15] Petar M. Djuric, Hsiang-Tsun Li, Bayesian spectrum estimation of harmonic signals, IEEE Signal Processing Letters, Nov.1995
[16] Jianguo Huang, Jianfeng Chen, Chunming Liu and Petar M. Djuric, A Bayesian approach to high resolution direction-of-arrival estimation, Proceedings of the Fourth International Conference on Signal Processing, Beijing, China, October, 1998
[17] 徐朴，多目标方位估计的贝叶斯高分辨新技术研究，西北工业大学博士后研究工作报告，1999年11月
[18] 鲁瑛，贝叶斯高分辨方位估计方法的性能分析与应用研究，西北工业大学硕士论文，2001年4月
[19] 胡广书，数字信号处理—理论、算法与实现，清华大学出版社，1997年
[20] 黄建国，武延祥，杨世兴译，Steven M．Kay著，现代谱估计，科学出版社，1994年
[21] 程运鹏，张凯院，徐仲，矩阵论，西北工业大学出版社，1989年
[22] 袁易全，雷家煜，姚治国，近代声学基阵原理及其应用，南京大学出版社，1994年
[23] 肖国有，屠庆平，声信号处理及其应用，西北工业大学出版社，1994年
[24] 刘春明，贝叶斯高分辨定向新技术研究，西北工业大学硕士学位论文，1998年3月
[25] Pu Xu, Ying Lu, Jianguo Huang, Research on Bayesian method of direction-finding, International Journal of Plant Engineering and Management, vol.3,no.2, pp. 321-324, 1998
[26] 陈建峰，黄建国，基于贝叶斯估计的高分辨定向方法，航空学报，vol．19，no．6，1998年
[27] L. Bretthorst, Bayesian spectrum analysis and parameter estimation, New York, NY: Springer verlag, 1989
[28] J. Lasenby, W. J. Fitzgerald, A Bayesian approach to high-resolution beamforming, IEEE Proceedings-F, vol. 138, no.6, pp. 539-544, 1991
[29] Chao-Ming Cho and Petar M. Djuric, Detector and estimation of DOA of signals via Bayesian predictive densities, IEEE Transactions on Signal Processing, vol.42, no. 11, pp. 3051-3060, 1994
[30] Chao-Ming Cho and Petar M. Djuric, Bayesian detection and estimation of Cisoids in colored noise, IEEE ,Trans. SP, vol.43, no. 12, 1995
[31] Q. T. (Keith) Zhang, Probability of resolution of the MUSIC algorithm, IEEETrans. Signal Processing, vol.43, no.4, pp. 978-987, 1995
[32] P. Stoica, A. Nehora, MUSIC, Maximum likelihood and Cramer-Rao Bound, IEEE T-ASSP, vol.37, no.5, pp. 720-741, 1989
[33] P. Stoica, A. Nehora, MUSIC, Maximum likelihood and Cramer-Rao Bound: further results and comparisons, IEEE T-ASSP, vol.38, no. 12, pp. 2140-2150, 1990
[34] P. Stoica, K. C. Sharman, Maximum likelihood methods for direction-of arrival estimation, IEEE T-ASSR vol.38, no.7, pp. 1132-1142, 1990
[35] J. E. Evans, J. R. Johnson, D. F. Sun, High resolution angular spectrum estimation techniques for terrain scattering analysis and angle of arrival estimation, in Proc. 1st Workshop Spectrum Estimation Hamilton, Ont. Canada, 1981
[36] Jun S.Liu, Monte Carlo Strategies in Scientific Computing, Springer-Verlag New York, Inc, 2001
[37] Ming-Hui Chen, Qi-Man Shao, Joseph G. Ibrahim, Monte Carlo Methods in Bayesian Computation, pringep-Verlag New York, Inc, 2000
[38] Xiaodong Wang, Rong Chen, Adaptive Bayesian Multiuser Detection for Synchronous CDMA with Gaussian and Impulsive Noise, IEEE Transaction on Signal Processing, VOL.47, No.7, July 2000
[39] Jayesh H. Kotecha, Petar M. Djuric, Gibbs Sampling Approach for Generation of Truncated Multivariate Gaussian Random Variables, EEEE Transaction on Signal Processing, VOL.47, No.7, March 2000
[40] G. Casellan and E. I. George, Explaining the Gibbs Sampler, Amer. Stat. Vol.46, PP.320-326, 1993
[41 ]W. R. Gilks, S. Richardson, and D. J. Spiegelhalter, Markov Chain Monte Carlo in Practice, New York: Chapman & Hall, 1996
[42] Chen. M. H. And Schmeiser, B. W. (1993) , Performance of the Gibbs, hit-and-run, and Metropolis samplers, Journal of Computational and Graphical Statistics
[43] Cowles, M. K. And Carlin, B. P. (1996) , Markov Chain Monte Carlo convergence diagnostics: A compararive review, Journal of the American Satistical Association
[44] S. F. Arnold, "Gibbs sampling." In Handbook of Statistics. C. R. Rao Ed. New York Elsevier, 1993, vol.9
[45] F. M Smith and A. E. Gelfand. Bayesian statistics without tears: A sampling-resampling perspective, American Statistician, 1992．
[46] M. West, Approximating posterior distributions by mixtures, Journal of the Ro-yal Statistical Society (Ser. B), 1997