The conventional methods including cross-ambiguity function (CAF) and least square (LS) methods have intensively studied for the estimation of the delay-Doppler parameters from moving linear frequency modulated (LFM) signals. Due to the characteristic of underwater acoustic multipath propagation in shallow water and the mobility of sound source, the traditional methods provide limited resolutions for the lack of sparsity exploitation. This study aims to jointly estimate the multipath delay-Doppler parameters based on a sparse representation model, which leads to a large scale and computational complexity of the dictionary matrix in delay-Doppler framework. To solve the above problems, we propose an orthonormal operation via the Gram-Schmidt method for the delay-Doppler solution during the matching pursuit iterations. The obvious advantage of the proposed approach is to avoid inverse matrix computation, which improves the robustness and effectiveness for the estimation of the delay-Doppler parameters. The simulation and experimental results indicate that the proposed method outperforms the traditional CAF and LS methods both in terms of resolution and accuracy. Furthermore, the proposed method, compared with the ROMP and CoSaMP methods, provides superior performance in terms of mean square error (MSE).