Time-Delay Estimation of Ground-Penetrating Radar Using Co-Prime Sampling Strategy via Atomic Norm Minimization

Time-delay estimation (TDE) of pavement using ground-penetrating radar (GPR) is an important task in the field of civil engineering. However, when dealing with GPR waves at the centimeter scale, there are challenges in real-time processing of the coherent, overlapping backscattered echoes within limited bandwidth. To address these problems, this article proposes a TDE method for GPR signals using a co-prime sampling strategy via atomic norm minimization (ANM). The conventional uniform frequency sampling strategy requires lengthy data acquisition time and large data storage in the GPR system. In this case, the co-prime sampling strategy is adopted in this article to lower the sampling rate and lighten the hardware burden. The “holes” in co-prime sampling are filled by solving the ANM problem, where the reconstructed Hermitian–Toeplitz matrix can be used for decorrelation without loss of degrees of freedom (DoFs). By selecting multiple-measurement vectors (MMVs) directly from the second statistics of the co-prime sampling signal, the scale of the semidefinite programing (SDP) of ANM is reduced. Moreover, we propose a two-level ANM by recovering two Hermitian–Toeplitz matrices instead of one Toeplitz matrix and one Hermitian matrix, reducing further the complexity of the proposed method. Numerical and experimental results show the superiority of the proposed method in terms of temporal resolution, estimation accuracy, and computational complexity.