基于CZT的多子带信号时差估计方法
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摘要
针对稀疏多子带信号多子带综合时差估计难,高分辨时差估计计算量大的问题,提出了一种基于线性调频Z变换(CZT)的稀疏多子带信号融合的快速高分辨时差估计算法。该方法通过CZT对各子带信号的互谱进行高分辨的谱分析得到各子带信号的高分辨互相关函数,通过分析各子带互相关函数的相位关系实现各子带互相关函数的相参积累。相比传统广义互相关算法,该方法在实现多子带相参积累的同时,大大降低了计算量。仿真结果表明:提出的基于CZT的多子带融合快速时差估计方法能精确地估计时差,相比单子带信号的时差估计性能可以获得明显提升。
Since there exists some problems in the time difference of arrival(TDOA) estimation of multi-band signals, such as the coherent accumulation of multi-band and the computation cost of high resolution TDOA estimation, a chirp-Z transform(CZT) based TDOA estimation method is proposed for multi-band signals, which can get high resolution and accurate TDOA estimation quickly through coherent accumulation of multi-band cross correlation. The proposed method utilizes the CZT to analyze the spectrum of each band signal's cross-spectrum to get high resolution cross correlation of each band. Then the phase relations of cross correlations between each band are analyzed, so the cross correlations of each band can be accumulated coherently to get a fused cross correlation. Compared to the traditional generalized cross correlation method, the proposed method also achieves coherent accumulation of multi-band and has much less computation. The results of computer simulations demonstrate that the proposed methods can get accurate TDOA estimation results, and the performance has been obviously improved compared to the estimation results of single band signal.
Since there exists some problems in the time difference of arrival(TDOA) estimation of multi-band signals, such as the coherent accumulation of multi-band and the computation cost of high resolution TDOA estimation, a chirp-Z transform(CZT) based TDOA estimation method is proposed for multi-band signals, which can get high resolution and accurate TDOA estimation quickly through coherent accumulation of multi-band cross correlation. The proposed method utilizes the CZT to analyze the spectrum of each band signal's cross-spectrum to get high resolution cross correlation of each band. Then the phase relations of cross correlations between each band are analyzed, so the cross correlations of each band can be accumulated coherently to get a fused cross correlation. Compared to the traditional generalized cross correlation method, the proposed method also achieves coherent accumulation of multi-band and has much less computation. The results of computer simulations demonstrate that the proposed methods can get accurate TDOA estimation results, and the performance has been obviously improved compared to the estimation results of single band signal.
引文
[1] GRIFFITHS H D, BAKER C J. Passive coherent location radar system-part I: performance prediction[J]. IEE Proceedings of Radar, Sonar and Navigation, 2005,152(3): 153-159.
[2] BAKER C J, GRIFFITHS H D. Passive coherent location radar system-part II: waveform properties[J]. IEE Proceedings of Radar, Sonar and Navigation, 2005, 152(3): 160-168.
[3] CHEUNG K W, SO H C, MA W K, et al. A constrained least squares approach to mobile positioning: algorithms and optimality[J]. EURASIP Journal on Applied Signal Processing, 2006(1): 20-38.
[4] TORRIERI D J. Statistical theory of passive location system[J]. IEEE Transactions on Aerospace and Electronic Systems, 1984, 20(2): 183-197.
[5] KNAPP C H, CARTER G C. The generalized method for estimation of time delay[J]. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1976, 24(4): 320-327.
[6] CARTER G C. Coherence and time delay estimation[J]. Proceedings of the IEEE, 1987, 75(2): 236-255.
[7] 黄桂根, 李品, 丁坚. 宽带干扰信号的数字相关检测与时差估计[J]. 现代雷达, 2015, 37(5): 21-24.HUANG Guigen, LI Pin, DING Jian. Digital correlation detection and TDOA estimation of broadband jamming signal[J]. Modern Radar, 2015, 37(5): 21-24.
[8] 王成, 胡卫东, 杜小勇, 等. 稀疏子带的多频段雷达信号融合超分辨距离成像[J]. 电子学报, 2006, 34(6): 985-990.WANG Cheng, HU Weidong, DU Xiaoyong, et al. The super-resolution range imaging based on sparse band multiple frequency bands radars signal fusion[J]. Acta Electronica Sinica, 2006, 34(6): 985-990.
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[10] TASDELEN A S, KOYMEN H. Range resolution improvement in passive coherent location radar systems using multiple FM radio channels[C]// 2006 IET Seminar on Waveform Diversity and Design in Communications, Radar and Sonar. London, UK: IEEE Press, 2006: 23-31.
[11] BONGIOANNI C, COLONE F, LOMBARDO P. Performance analysis of a multi-frequency FM based passive bistatic radar[C]// 2008 IEEE Radar Conference. Rome, Italy: IEEE Press, 2008: 1-6.
[12] STEIN S. Algorithms for ambiguity function processing[J]. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1981, 29(3): 588-599.
[13] 杨亦春, 马驰州, 李晓东, 等. 相关峰细化的精确时延估计快速算法研究[J]. 声学学报, 2003, 28(2): 159-166.YANG Yichun, MA Chizhou, LI Xiaodong, et al. Algorithm study of fast and time-delay estimation with fine interpolation of correlation peak[J]. Acta Acustica, 2003, 28(2): 159-166.
[14] 沈彩耀, 李红波, 张颋, 等. 带限信号时延估计快速算法研究[J]. 信息工程大学学报, 2007, 8(1): 77-80.SHEN Caiyao, LI Hongbo, ZHANG Ting, et al. Fast algorithm study on time dealy estimation of band-limited signal[J]. Journal of Information Engineering University, 2007, 8(1): 77-80.
[15] 郭莹, 邱天爽, 张艳丽. 基于共变谱的CZT多源时延估计新方法[J]. 大连理工大学学报, 2007, 47(5): 746-750.GUO Ying, QIU Tianshuang, ZHANG Yanli. A novel multi-source time delay estimation method based on CZT and covariation spectrum[J]. Journal of Dalian University of Technology, 2007, 47(5): 746-750.
[16] 吴瑛, 张莉, 张冬玲, 等. 数字信号处理[M]. 西安: 西安电子科技大学出版社, 2009.WU Ying, ZHANG Li, ZHANG Dongling, et al. Digital signal processing[M]. Xi′an: Xidian University Press, 2009.
[2] BAKER C J, GRIFFITHS H D. Passive coherent location radar system-part II: waveform properties[J]. IEE Proceedings of Radar, Sonar and Navigation, 2005, 152(3): 160-168.
[3] CHEUNG K W, SO H C, MA W K, et al. A constrained least squares approach to mobile positioning: algorithms and optimality[J]. EURASIP Journal on Applied Signal Processing, 2006(1): 20-38.
[4] TORRIERI D J. Statistical theory of passive location system[J]. IEEE Transactions on Aerospace and Electronic Systems, 1984, 20(2): 183-197.
[5] KNAPP C H, CARTER G C. The generalized method for estimation of time delay[J]. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1976, 24(4): 320-327.
[6] CARTER G C. Coherence and time delay estimation[J]. Proceedings of the IEEE, 1987, 75(2): 236-255.
[7] 黄桂根, 李品, 丁坚. 宽带干扰信号的数字相关检测与时差估计[J]. 现代雷达, 2015, 37(5): 21-24.HUANG Guigen, LI Pin, DING Jian. Digital correlation detection and TDOA estimation of broadband jamming signal[J]. Modern Radar, 2015, 37(5): 21-24.
[8] 王成, 胡卫东, 杜小勇, 等. 稀疏子带的多频段雷达信号融合超分辨距离成像[J]. 电子学报, 2006, 34(6): 985-990.WANG Cheng, HU Weidong, DU Xiaoyong, et al. The super-resolution range imaging based on sparse band multiple frequency bands radars signal fusion[J]. Acta Electronica Sinica, 2006, 34(6): 985-990.
[9] MENDI U M D, SARKAR B K. Passive radar using multiple GSM transmitting stations[C]// 2006 International Radar Symposium. Krakow, Poland: IEEE Press, 2006: 1-4.
[10] TASDELEN A S, KOYMEN H. Range resolution improvement in passive coherent location radar systems using multiple FM radio channels[C]// 2006 IET Seminar on Waveform Diversity and Design in Communications, Radar and Sonar. London, UK: IEEE Press, 2006: 23-31.
[11] BONGIOANNI C, COLONE F, LOMBARDO P. Performance analysis of a multi-frequency FM based passive bistatic radar[C]// 2008 IEEE Radar Conference. Rome, Italy: IEEE Press, 2008: 1-6.
[12] STEIN S. Algorithms for ambiguity function processing[J]. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1981, 29(3): 588-599.
[13] 杨亦春, 马驰州, 李晓东, 等. 相关峰细化的精确时延估计快速算法研究[J]. 声学学报, 2003, 28(2): 159-166.YANG Yichun, MA Chizhou, LI Xiaodong, et al. Algorithm study of fast and time-delay estimation with fine interpolation of correlation peak[J]. Acta Acustica, 2003, 28(2): 159-166.
[14] 沈彩耀, 李红波, 张颋, 等. 带限信号时延估计快速算法研究[J]. 信息工程大学学报, 2007, 8(1): 77-80.SHEN Caiyao, LI Hongbo, ZHANG Ting, et al. Fast algorithm study on time dealy estimation of band-limited signal[J]. Journal of Information Engineering University, 2007, 8(1): 77-80.
[15] 郭莹, 邱天爽, 张艳丽. 基于共变谱的CZT多源时延估计新方法[J]. 大连理工大学学报, 2007, 47(5): 746-750.GUO Ying, QIU Tianshuang, ZHANG Yanli. A novel multi-source time delay estimation method based on CZT and covariation spectrum[J]. Journal of Dalian University of Technology, 2007, 47(5): 746-750.
[16] 吴瑛, 张莉, 张冬玲, 等. 数字信号处理[M]. 西安: 西安电子科技大学出版社, 2009.WU Ying, ZHANG Li, ZHANG Dongling, et al. Digital signal processing[M]. Xi′an: Xidian University Press, 2009.