## 1 Introduction  
Synthetic Aperture Radar (SAR) is widely used in military and civilian fields due to its high-resolution imaging of a target, its large coverage, and its all-weather capability [1, 2, 3]. Ground moving-target detection based on multi-channel SAR plays an increasingly important role in battlefield surveillance, traffic surveillance and other applications [4, 5, 6]. The conventional SAR imaging algorithm is designed for stationary targets in the observation scene, which uses motion parameters and the slant range history between the platform and the target to obtain focused imaging. Because the motion parameters of the target are not known, the moving target is defocused in SAR images and deviates from its real position, which makes it difficult to detect, identify and locate the target. Therefore, in order to obtain a well-focused image of a moving target, the motion parameters of the target must be accurately estimated. In high-resolution SAR images, moving-target refocusing can not only improve the signal-to-noise ratio of the target, but also the focused target can reflect its structure and attitude to a certain extent, which is conducive to target recognition and classification. Therefore, moving-target imaging has become one of the hotspots of SAR-GMTI research. With the improvement of SAR resolution and the continuous increase of synthetic aperture time, the high-order range migration caused by target motion cannot be ignored, which will increase the difficulty of range cell migration correction (RCMC) and parameter estimation. There are two problems in the existing moving-target parameter estimation. (1) Ignoring the range migration caused by high-order terms leads to poor parameter estimation accuracy [7,8]. For high-resolution SAR systems, ignoring the high-order terms of range migration will cause residual range migration, resulting in a large parameter estimation error. For example, reference [7] did not consider the third-order term when performing the instantaneous slant-range expansion. Although reference [8,9] constructed a third-order slant range model, the influence of the third-order range migration on the cross-correlation function was ignored in the parameter estimation; as a result, the energy of DCCF could not be gathered into the same range cell. (2) In order to pursue the accuracy of parameter estimation, the method of parameter traversal is used to search for the optimal value, which increases the computational complexity [10, 11, 12]. For example, reference [13] uses the Chirp Scaling Algorithm (CSA) to image moving targets, and reference [8] uses SOKT, Radon, Fourier transform and parameter search to obtain focused moving targets. Reference [14] traverses all range frequency points in the range frequency-azimuth-time domain and takes the average value as the estimation result. Reference [15] uses the convolutional neural network for moving-target imaging, which requires a large number of training data sets. Reference [9] proposed an algorithm called keystone transform and coherently integrated cubic phase function (KT-CICPF). The DCCF of KT-CICPF is constructed before RCMC. In the DCCF constructed by KT-CICPF, the energy of the moving target is dispersed into multiple range cells, resulting in defocusing of the peak of the constructed parameter estimation plane. In addition, when the RCMC is performed, the movement amount of the third-order term is ignored, resulting in parameter estimation errors. Aiming at the above two problems, this paper proposes an improved moving-target imaging method based on high-order parameter estimation. Firstly, the Hough transform and the SOKT are used to correct the range migration to improve the coherent accumulation gain of the target. Secondly, the DCCF is constructed to reduce the order of the range migration phase response in the slow-time domain. Different from the existing methods [10,11,13,14,16,17], the proposed method constructs the DCCF after the RCMC and compensates the residual range migration with the estimated third-order terms.