To achieve high range resolution profile (HRRP), the geometric theory of diffraction (GTD) parametric model is widely used in stepped-frequency radar system. In the paper, a fast synthetic range profile algorithm, called orthogonal matching pursuit with sensing dictionary (OMP-SD), is proposed. It formulates the traditional HRRP synthetic to be a sparse approximation problem over redundant dictionary. As it employs a priori information that targets are sparsely distributed in the range space, the synthetic range profile (SRP) can be accomplished even in presence of data lost. Besides, the computational complexity is reduced by introducing sensing dictionary (SD) and it mitigates the model mismatch at the same time. The computation complexity decreases from O(MNDK) flops for OMP to O(M(N +D)K) flops for OMP-SD. Simulation experiments illustrate its advantages both in additive white Gaussian noise (AWGN) and noiseless situation, respectively.
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