## 1 Introduction  
Synthetic aperture radar has been widely applied in various fields such as ocean observation, cartography, and civilian remote sensing due to its imaging characteristics and all-day, all-weather, and high azimuth resolutions [1, 2]. Compared to microwave SAR, THz SAR offers a shorter wavelength, wider bandwidth, and distinct Doppler characteristics resulting from platform or target motion. This enables THz SAR to achieve a higher imaging resolution [3] and real-time detection capabilities at video frame rates [4], thus presenting broader application prospects. The integrated navigation system based on the Global Navigation Satellite System (GNSS) and Inertial Navigation System (INS) allows for real-time acquisition of the position and attitude information of radar platforms, finding effective application in synthetic aperture radar systems [5]. For vehicle-borne or airborne SAR systems, although an integrated navigation system can periodically record the position information of the radar, the non-uniform sampling characteristics in azimuth are inevitable due to the difficulty in maintaining an ideal constant linear motion during radar movement [6], which leads to a degradation in the imaging quality of the radar. Compared to microwave SAR, THz SAR requires a higher sampling rate in azimuth, resulting in more severe non-uniform sampling issues that significantly impact the image reconstruction. Traditional methods for addressing non-uniform sampling in the azimuth of microwave SAR primarily focus on hardware considerations. By utilizing an integrated navigation system to measure the real-time motion velocity of the radar platform, the PRF can be adjusted to achieve a more uniform azimuth sampling position [7]. However, for THz SAR systems with denser sampling points in azimuth, this hardware-based method of adjusting the PRF has certain limitations. The azimuth sampling positions still remain somewhat non-uniform to some extent, making it difficult to achieve the desired imaging results. In addition, a higher azimuth sampling rate also increases the hardware design requirements and incurs additional hardware costs. The issue of non-uniform sampling in the azimuth of SAR can also be addressed from a software perspective. The flight path error of the SAR platform can be divided into along-track motion errors and cross-track motion errors [8]. The along-track motion error is the azimuth non-uniform sampling problem studied in this paper. On the other hand, the cross-track motion error, caused by the deviation of the radar platform from the ideal motion trajectory, is typically compensated for after compensating for the along-track motion error. Based on the importance of the impact on imaging quality, there is a considerable amount of literature that has studied the problem of cross-track motion error compensation [5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15], while research on the problem of along-track motion error compensation is relatively limited, even though its impact on imaging quality should not be overlooked [16]. Currently, the predominant approach for addressing the issue is azimuth resampling [10], which involves interpolating the non-uniformly sampled data to obtain uniformly sampled echo data for processing. This method is straightforward in principle; however, when the influence of spectral aliasing cannot be neglected, it results in a degradation of the image focusing effect [17]. The BPA, being a time-domain imaging technique, is applicable to any imaging geometry and can also be used for imaging non-uniformly sampled echo data [8]. This method offers high imaging accuracy but requires significant computational resources. A phase compensation-based method was employed in [17] to compensate for along-track motion errors, which offers high computational efficiency. However, this method relies on certain approximations and lacks general applicability, particularly for imaging scenarios involving close-range distances.