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The time delay estimation is widely used in wireless location field, and is the research emphasis in complex environment of this field. The current delay estimation algorithms can be classified as five methods of correlation, high-order statistics, self-adaption, maximum likelihood and subspace. However, the existing algorithms can hardly achieve an ideal performance in small sample（single snapshot) and low signal-to-noise ratio environment during wireless location. In order to solve the problem about the insufficiency of the current algorithms in the above conditions, many new methods have been introduced into the delay estimation problem. The compressed sensing sparse reconstruction method has been applied to the signal processing field as a newly-proposed algorithm in recent years. The delay estimation is realized by using the method of sparse reconstruction, in which the sparse representation of the signal is the premise. The rational construction of the measurement matrix and the design of the signal reconstruction algorithm are the core of correct estimation.The purpose of this article is to deal with the lack of measurement data in small sample（single snapshot) and low signal-to-noise ratio environment during wireless location. In the model of wireless location, the signal can be represented as a sparse matrix form by selecting suitable sparse representation matrix. The wireless multi-channel is measured in the time domain, the propagation delay varies with channel and the delay representation in the time domain is sparse, so that it can be directly constructed into the form of sparse signal. Since the necessary and the sufficient condition of the coefficient sparse matrix successfully reconstructed by the measurement matrix are the measurement matrix meeting the restricted isometry property（RIP). The orthogonal measurement matrix based on the steering vector by the method of Gram-Schmidt is proven to achieve the RIP. A novel sparse reconstruction algorithm based on backtracking filter is constructed to estimate the time delay. In order to guarantee that the first selection includes the optimal atom, several atoms are selected. And then the backtracking mechanism is introduced, and the selected atoms are approached by the method of the minimum square to sequence the obtained signals and select the optimal atom. Therefore, this method can be used to guarantee that the optimal atom is selected. The presented algorithm can achieve the delay estimation by using the corresponding relation between the time delay and the measurement matrix in a high precision. Furthermore, the Cramer-Rao bound（CRB) of this model is derived. Finally, simulations show that the proposed approach is suitable for small sample（single snapshot) and low signal-to-noise ratio environment. The proposed method can achieve a higher precision than Root-Music and improve performance at low complexity cost compared with OMP algorithm. The simulation result proves that the algorithm is stable and reliable.
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Keywords:
- sparse reconstruction /
- time delay estimation /
- backtracking filter /
- orthogonal measurement matrix
[1] Zhang M, Ma Y L, Li B Q 2013 Chin. Phys. B 22 030511
[2] Knapp C, Carter G 1976 IEEE Trans. Acoust. Speech Signal Process. 24 320
[3] Ma W, Huang J G 2001 Comput. Eng. Appl. 37 54(in Chinese)[马雯, 黄建国2001计算机工程与应用37 54]
[4] Cheng L, Chen G, Gao W Z, Zhang F, Li G 2014 IEEE Trans. Smart Grid 5 2957
[5] Champagne B, Eizenman M, Pasupathy S 1989 Acoustics, Speech, and Signal Processing Glasgow, UK, May 23-26, 1989 p2633
[6] Li X M, Tao R, Wang Y 2010 Radar Sci. Technol. 8 362(in Chinese)[李雪梅, 陶然, 王越2010雷达科学与技术8 362]
[7] Wang F Q, Zhang X F, Wang F 2014 J. Commun. 35 137(in Chinese)[王方秋, 张小飞, 汪飞2014通信学报35 137]
[8] Li J, Zhu J D, Feng Z H, Zhao Y J, Li D H 2015 Circ. Syst. Signal Process. 34 3897
[9] Donoho D L 2006 IEEE Trans. Inform. Theory 52 1289
[10] Wang H T, Wang J 2013 J. Electron. Inform. Technol. 35 877(in Chinese)[王海涛, 王俊2013电子与信息学报35 877]
[11] Lin B, Zhang Z H, Zhu J B 2014 J. Electron. Inform. Technol. 36 589(in Chinese)[林波, 张增辉, 朱炬波2014电子与信息学报36 589]
[12] Chen Y F, Huang J G, Su J J 2013 Torpedo Technol. 21 110(in Chinese)[陈玉凤, 黄建国, 苏建军2013鱼雷技术21 110]
[13] Wang F Q, Zhang X F 2014 ETRI J. 36 460
[14] Candès E J, Tao T 2005 IEEE Trans. Inform. Theory 51 4203
[15] Stoica P, Nehorai A 1989 IEEE Trans. Acoust. Speech Signal Process. 37 720
[16] Stoica P, Nehorai A 1990 IEEE Trans. Acoust. Speech Signal Process. 38 1783
[17] Gast M S(translated by O'Reilly Media, Inc.) 2007802.11 Wireless Networks:The Definitive Guide (2nd Ed.)(Nanjing:Publishing House of Southeast University) pp309-317(in Chinese)[加斯特M S著(O'Reilly公司译) 2007802.11 无线网络权威指南(第二版)(南京:东南大学出版社)第309-317页]
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[1] Zhang M, Ma Y L, Li B Q 2013 Chin. Phys. B 22 030511
[2] Knapp C, Carter G 1976 IEEE Trans. Acoust. Speech Signal Process. 24 320
[3] Ma W, Huang J G 2001 Comput. Eng. Appl. 37 54(in Chinese)[马雯, 黄建国2001计算机工程与应用37 54]
[4] Cheng L, Chen G, Gao W Z, Zhang F, Li G 2014 IEEE Trans. Smart Grid 5 2957
[5] Champagne B, Eizenman M, Pasupathy S 1989 Acoustics, Speech, and Signal Processing Glasgow, UK, May 23-26, 1989 p2633
[6] Li X M, Tao R, Wang Y 2010 Radar Sci. Technol. 8 362(in Chinese)[李雪梅, 陶然, 王越2010雷达科学与技术8 362]
[7] Wang F Q, Zhang X F, Wang F 2014 J. Commun. 35 137(in Chinese)[王方秋, 张小飞, 汪飞2014通信学报35 137]
[8] Li J, Zhu J D, Feng Z H, Zhao Y J, Li D H 2015 Circ. Syst. Signal Process. 34 3897
[9] Donoho D L 2006 IEEE Trans. Inform. Theory 52 1289
[10] Wang H T, Wang J 2013 J. Electron. Inform. Technol. 35 877(in Chinese)[王海涛, 王俊2013电子与信息学报35 877]
[11] Lin B, Zhang Z H, Zhu J B 2014 J. Electron. Inform. Technol. 36 589(in Chinese)[林波, 张增辉, 朱炬波2014电子与信息学报36 589]
[12] Chen Y F, Huang J G, Su J J 2013 Torpedo Technol. 21 110(in Chinese)[陈玉凤, 黄建国, 苏建军2013鱼雷技术21 110]
[13] Wang F Q, Zhang X F 2014 ETRI J. 36 460
[14] Candès E J, Tao T 2005 IEEE Trans. Inform. Theory 51 4203
[15] Stoica P, Nehorai A 1989 IEEE Trans. Acoust. Speech Signal Process. 37 720
[16] Stoica P, Nehorai A 1990 IEEE Trans. Acoust. Speech Signal Process. 38 1783
[17] Gast M S(translated by O'Reilly Media, Inc.) 2007802.11 Wireless Networks:The Definitive Guide (2nd Ed.)(Nanjing:Publishing House of Southeast University) pp309-317(in Chinese)[加斯特M S著(O'Reilly公司译) 2007802.11 无线网络权威指南(第二版)(南京:东南大学出版社)第309-317页]
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