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针对无源雷达中时延估计辐射源信号未知的情况，构建了一种新的时延最大似然估计模型. 根据模型特点利用快速傅里叶变换（FFT）的计算方法实现时延估计. 为了提高估计的精度，采用马尔科夫链蒙特卡罗（MCMC）抽样的方法估计时延值. 该方法不需峰值检测，可直接给出时延估计结果. 并推导了该模型下的时延估计的克拉美罗界（CRLB）. 仿真实验表明，MCMC算法可适用于窄带和宽带信号的时延估计；在样本相同的条件下，MCMC算法估计精度高于重要性采样（IS）算法和基于峰值检测的ML算法，计算复杂度低于IS算法，且MCMC算法可直接估计采样间隔非整数倍的时延.A novel maximum likelihood estimation model for time delay is constructed to estimate the passive time delay; the signal of emitter is unknown in this model. According to the model characteristics, the fast Fourier transformation (FFT) method is used to achieve time delay estimation (TDE). In order to improve the accuracy of estimator, the Markov Chain Monte Carlo (MCMC) sampling method is used to estimate the time delay value directly. Unlike traditional algorithms, MCMC method can obtain time delay without peak detection. Furthermore, the Cramer-Rao lower bound (CRLB) of this model is derived. Finally, simulations show that the proposed approach is suitable for both narrowband and broadband TDE, and the MCMC algorithm can achieve more precise time delay value with the same sample, and it has lower computational complexity than IS algorithm. The novel approach can estimate also the time delay of non-integer multiple of the sampling interval.
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Keywords:
- time delay estimation /
- maximum likelihood /
- Markov Chain Monte Carlo /
- computational complexity
[1] Hai-Peng R, Wen-Chao L, Ding L 2010 Chin. Phys. B 19 030511
[2] Carter G C 1981 IEEE Transactions on Acoustics, Speech and Signal Processing 29 463
[3] Bo-Wen L, Jian-Ji D, Yuan Y, Xin-Liang, Z 2013 Chin. Phys. B 22 023201
[4] Knapp C, Carter G C 1976 IEEE Trans. Acoust. Speech Signal Processing 24 320
[5] Nandi A K 1995 IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control. 42 993
[6] Cheng Z, Tjhung T T 2003 IEEE Transaction on Signal Processing 51 1859
[7] Liu W 2012 IEEE International Conference on Mechatronics and Automation Chengdu, China, August 5-8, 2012 p1451
[8] Wen F, Wan Q, Liu Y 2012 IEEE 10th International Symposium on ISETC Timisoara, Romania, Nov. 15-16, 2012 p243
[9] Dong-Hai D, Wei X, Jun S, Bing-Chang Z 2011 Chin. Phys. B 20 030501
[10] Xin-Chun Z, Cheng-Jun G 2013 Chin. Phys. B 22 128401
[11] Ng W, Reilly J P, Kirubarajan T, Larocque J R 2005 IEEE Transaction on Signal Processing 52 411
[12] Zheng S 2013 Chin. Phys. B 22 029302
[13] Cao X Q, Zhang W M, Song J Q, Zhu X Q, Wang S C 2009 Acta Phys. Sin. 58 6050 (in Chinese) [曹小群, 张卫民, 宋君强, 朱小谦, 王舒畅 2009 58 6050]
[14] Masmoudi A, Bellili F, Affes S, Stephenne A 2011 IEEE Transaction on Signal Processing 59 4505
[15] Masmoudi A, Bellili F, Affes S, Stephenne A 2013 IEEE Transaction on Signal Processing 61 182
[16] Li H W, Wang J 2012 IET Radar Sonar & Navigation 6 180
[17] Xiao-Feng Z, Si-Xun H, Jie X, Wei-Lai, S 2011 Chin. Phys. B 20 099201
[18] Li-Feng G, Xin L, Shan G 2008 Chin. Phys. B 17 4396
[19] Flores B C, Solis E A, Thomas G 2003 IEE Radar Sonar & Navigation 150 313
[20] Scarbrough K, Tremblay R, Carter G C 1983 IEEE Transactions on Acoustics, Speech, and Signal Processing 31 1191
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[1] Hai-Peng R, Wen-Chao L, Ding L 2010 Chin. Phys. B 19 030511
[2] Carter G C 1981 IEEE Transactions on Acoustics, Speech and Signal Processing 29 463
[3] Bo-Wen L, Jian-Ji D, Yuan Y, Xin-Liang, Z 2013 Chin. Phys. B 22 023201
[4] Knapp C, Carter G C 1976 IEEE Trans. Acoust. Speech Signal Processing 24 320
[5] Nandi A K 1995 IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control. 42 993
[6] Cheng Z, Tjhung T T 2003 IEEE Transaction on Signal Processing 51 1859
[7] Liu W 2012 IEEE International Conference on Mechatronics and Automation Chengdu, China, August 5-8, 2012 p1451
[8] Wen F, Wan Q, Liu Y 2012 IEEE 10th International Symposium on ISETC Timisoara, Romania, Nov. 15-16, 2012 p243
[9] Dong-Hai D, Wei X, Jun S, Bing-Chang Z 2011 Chin. Phys. B 20 030501
[10] Xin-Chun Z, Cheng-Jun G 2013 Chin. Phys. B 22 128401
[11] Ng W, Reilly J P, Kirubarajan T, Larocque J R 2005 IEEE Transaction on Signal Processing 52 411
[12] Zheng S 2013 Chin. Phys. B 22 029302
[13] Cao X Q, Zhang W M, Song J Q, Zhu X Q, Wang S C 2009 Acta Phys. Sin. 58 6050 (in Chinese) [曹小群, 张卫民, 宋君强, 朱小谦, 王舒畅 2009 58 6050]
[14] Masmoudi A, Bellili F, Affes S, Stephenne A 2011 IEEE Transaction on Signal Processing 59 4505
[15] Masmoudi A, Bellili F, Affes S, Stephenne A 2013 IEEE Transaction on Signal Processing 61 182
[16] Li H W, Wang J 2012 IET Radar Sonar & Navigation 6 180
[17] Xiao-Feng Z, Si-Xun H, Jie X, Wei-Lai, S 2011 Chin. Phys. B 20 099201
[18] Li-Feng G, Xin L, Shan G 2008 Chin. Phys. B 17 4396
[19] Flores B C, Solis E A, Thomas G 2003 IEE Radar Sonar & Navigation 150 313
[20] Scarbrough K, Tremblay R, Carter G C 1983 IEEE Transactions on Acoustics, Speech, and Signal Processing 31 1191
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