Continuous basis compressive time-delay estimation in overlapped echoes

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.