© The Institution of Engineering and Technology
High-accuracy time-delay estimation is basically noted in several research areas. L1-minimisation is a compressive sensing (CS) approach which solves this problem with high resolution and accuracy in the case of spars signals. Band excluded orthogonal matching pursuit is another CS method which uses a greedy algorithm to retrieve time delays and has lower complexity compared with the L1-minimisation method; however, it is only applicable when the signals are well spaced or orthogonal. Moreover, both approaches are established on a discrete basis which inherently limits their accuracy for the constraint on the sampling rate of the system. To mitigate these challenges in this study, the authors first incorporate the L1-minimisation method in a greedy algorithm to achieve a high resolution in the discrete grid. In the next step, to overcome the limitation caused by the sampling rate and refine the obtained time delays, the algorithm is combined with a complex continuous basis pursuit (CCBP) by using a polar interpolation. Their simulation and experiment results show that the proposed combination of L1-minimisation-CCBP can recover time delays in very closely spaced echoes not only with high accuracy but also with low computational time and sampling rate.
References
-
-
1)
-
5. Donoho, D.L.: ‘Compressed sensing’, IEEE Trans. Inf. Theory, 2006, 52, (4), pp. 1289–1306.
-
2)
-
14. Grant, M., Boyd, S.. .
-
3)
-
8. Gedalyahu, K., Eldar, Y.C.: ‘Time-delay estimation from low-rate samples: a union of subspaces approach’, IEEE Trans. Signal Process., 2010, 58, pp. 3017–3031.
-
4)
-
13. Tropp, J.A., Laska, J.N., Duarte, M.F., et al: ‘Beyond Nyquist: efficient sampling of sparse band limited signals’, IEEE Trans. Inf. Theory, 2010, 56, (1), pp. 520–544.
-
5)
-
6. Cai, T.T., Wang, L.: ‘Orthogonal matching pursuit for sparse signal recovery with noise’, IEEE Trans. Inf. Theory, 2011, 57, (7), pp. 4680–4688.
-
6)
-
2. Fyhn, K., Duarte, M.F., Jensen, S.H.: ‘Compressive time delay estimation using interpolation’. IEEE Global Conf. on Signal and Information Processing (GlobalSIP), 2013, pp. 620–624.
-
7)
-
12. Bruckstein, A.M., Shan, T.J., Kailath, T.L.: ‘The resolution of overlapping echoes’, IEEE Trans. Acoust. Speech Signal Process., 1985, 33, pp. 1357–1367.
-
8)
-
11. Ramazan, J.S.: ‘Model-based estimation of ultrasonic echoes part I: analysis and algorithms’, IEEE Trans. Acoust. Speech Signal Process., 2012, 48, (3), pp. 787–802.
-
9)
-
1. Ekanadham, C., Tranchina, D., Simoncell, E.P.: ‘Recovery of sparse translation-invariant signals with continuous basis pursuit’, IEEE Trans. Signal Process., 2011, 59, (10), pp. 4735–4744.
-
10)
-
10. Chen, S.S., Donoho, D.L., Saunders, M.A.: ‘Atomic decomposition by basis pursuit’, SIAM J. Sci. Comput., 1998, 20, pp. 33–61.
-
11)
-
15. Fereidoony, F., Sebt, M.A., Chamaani, S., et al: ‘Model based super resolution time delay estimation with sample rate consideration’, IET Signal Process., 2016, 10, pp. 376–384.
-
12)
-
4. Candès, E.J., Romberg, J., Tao, T.: ‘Stable signal recovery from incomplete and inaccurate measurements’, Commun. Pure Appl. Math., 2005, 59, pp. 1207–1223.
-
13)
-
9. Zhang, L.: ‘Compressive sensing based high resolution time delay estimation for UWB system’, Int. J. Digit. Content Technol. Appl., 2012, 6, pp. 170–181.
-
14)
-
3. Fyhn, K., Duarte, M.F., Jensen, S.H.: ‘Compressive parameter estimation for sparse translation-invariant signals using polar interpolation’, IEEE Trans. Signal Process., 2015, 63, (4), pp. 870–881.
-
15)
-
7. Fannjiang, A., Liao, W.: ‘Coherence pattern-guided compressive sensing with unresolved grids’, SIAM J. Imaging Sci., 2012, 5, (1), pp. 179–202.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-spr.2016.0496
Related content
content/journals/10.1049/iet-spr.2016.0496
pub_keyword,iet_inspecKeyword,pub_concept
6
6