# An Efficient Ground Moving Target Imaging Method for Airborne Circular Stripmap SAR
## 1 Introduction  
### Background of Airborne CSSAR and Ground Moving Target Imaging  
Airborne synthetic aperture radar (SAR) has been widely applied in both civilian and military fields due to its high-resolution observation capability and the ability to work regardless of weather and daylight [1, 2, 3, 4, 5]. The ground moving target imaging is a typical application of airborne SAR, which is of great value in air-to-ground surveillance and reconnaissance [6, 7, 8, 9, 10, 11].  
Airborne circular stripmap SAR (CSSAR) is a kind of SAR that travels along a horizonal circle with its antenna pointing to the outside of the horizonal circle [12, 13, 14, 15], as shown in Figure 1. Benefiting from the circular path and the outward-pointing antenna, airborne CSSAR possess the advantages of a short revisit time and large coverage, and thus is an attractive tool for air-to-ground wide-area reconnaissance and time-sensitive targets surveillance [15].  
SAR time-sensitive targets surveillance usually involves ground moving target imaging, and it has been a hot research topic in recent years. A key parameter in SAR imaging is the range equation of the target (i.e., the instantaneous range between the radar and the target), which determines the azimuth phase characteristics and the range cell migration (RCM) of the target [16]. The second-order Taylor approximated range equation model is a commonly used range model in SAR ground moving target imaging [9, 10, 17, 18, 19, 20, 21]. It enables the derivation of an accurate analytical two-dimensional (2-D) spectrum of the target and thus can simplify the design of imaging method. However, its accuracy willbe insufficient when the azimuth resolution is relatively high or the target moves with accelerations [22; 23; 24]. Although the higher order Taylor approximated range equation has higher accuracy, the derivation of the accurate 2-D spectrum is challenging and thus would complicate the design of imaging methods [25]. To address this problem, in [26; 27; 28], an equivalent hyperbola range model was proposed. This range model is much more precise than the second-order Taylor approximated range model. Besides, based on this range model, the analytical expression of the target's 2-D spectrum can be easily derived. However, it is only applicable to the constant-moving target in the case of straight path SAR.  
Due to the unknown motion of the target, SAR ground moving target imaging usually involves the searching of the target's motion parameters or other equivalent parameters (e.g., the Doppler parameters), the coefficients of the target's range equation, and the coefficients of the target's phase history [18; 19; 20; 21; 29; 30; 31]. For instance, for the imaging method proposed in [29], the two velocity parameters and two acceleration parameters of the target need to be searched. As for the imaging method proposed in [30], the coefficients of the phase history's second-order and third-order terms also require to be searched. These searches result in a huge computational load since the inefficient ergodic search method  
Figure 1: Geometry of airborne CSSAR. (**a**) 3-D view and (**b**) top view.  
is usually used. Several papers proposed to utilize the second-order keystone transform and time-frequency techniques to replace the searching of the target's parameters [22; 23; 24]. However, the interpolation required by the second-order keystone transform and the searching involved in the time-frequency techniques make these methods still suffer from the problem of large computation load.