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.