## 1 Introduction  
Terahertz (THz) waves are the electromagnetic waves between 0.1 THz and 10 THz; they are in the gap between microwave and infrared. In terms of their energy, they are between electrons and photons [1, 2]. Therefore, THz waves have many unique advantages that microwaves and infrared do not have. For example, THz waves can generate a higher carrier frequency and larger absolute bandwidth than microwaves. At the same time, THz radiation can penetrate materials such as ceramics, fats, fabrics, plastics, etc., with very little attenuation. In addition, when it penetrates the human body, THz radiation is harmless due to its lower photon energy. These unique characteristics allow THz imaging to be used in many fields [3, 4, 5, 6, 7]. The concept of a synthetic aperture imaging technique in the microwave band has been introduced in the THz band [8, 9]. Compared to microwave synthetic aperture radar (SAR), THz-SAR can achieve higher two-dimensional image resolution. Additionally, with its shorter synthetic aperture time, THz-SAR imaging has a higher frame rate [10; 11]. Theoretically, the SAR principle requires uniform linear movement of the antenna phase center (APC). In practice, due to the influence of atmospheric turbulence and artificial control, APC always deviates from the ideal motion state, resulting in motion error. According to the variations of the motion error in the whole synthetic aperture, it can be divided into low-frequency motion error and high-frequency vibration error. The low-frequency motion error ranges from the centimeter level to the meter level, but now there are many compensation methods to eliminate its influence on SAR imaging. Meanwhile, the vibration amplitude of high-frequency vibration error is very small, usually at the millimeter level or even the sub-millimeter level, such that its influence can be ignored in microwave SAR imaging. However, since the wavelengths of THz waves are relatively short and comparable to the vibration amplitude of high-frequency vibration error, its influence has to be considered in THz-SAR imaging. Currently, there exist two kinds of high-frequency vibration-error compensation methods. Similar to motion-error compensation in microwave SAR, phase errors caused by high-frequency vibration error is estimate directly through extended phase gradient autofocus (PGA) [12; 13], where the specific vibration information is still ambiguous after phase-error compensation. Therefore, some researchers have focused on another class of methods based on parameter estimation, whose main idea is to estimate the vibration-signal parameters. Sinusoidal frequency modulation Fourier transform (SFMFT) and wavelet multi-resolution analysis are directly utilized to operate on the phase term of the vibration signal through phase unwrapping in [14; 15; 16]. However, these methods will fail when the phase ambiguity is serious. In [17], the discrete fractional Fourier transform (DFrFT) is used to reconstruct the vibration signal with the estimated instantaneous vibration accelerations and vibration frequency. In [18], the vibration parameters are estimated based on the wavelet transform. The adaptive chirplet decomposition and the short-time Fourier transform (STFT) are used in [19] and [20], respectively, and an estimation method considering the variation of vibration amplitude is proposed in [21]. However, the above methods may fail in dealing with multiple frequency component vibration. The discrete sinusoidal frequency modulation transforms (DSFMT) and the optimization method are combined to estimate the multi-component vibration parameters in [22; 23]. However, it inevitably results in large estimation errors because of the convergence to a local minimum. In [24], an improved DFrFT-based estimation method is proposed to estimate multi-component vibration parameters. However, there exists a great correlation between the method accuracy and the window width.