# A High-Resolution SAR Focusing Experiment Based on GF-3 Staring Data
## 1 Introduction  
Synthetic aperture radar (SAR) has developed rapidly over the past few decades as an effective means of Earth observation. The resolution of spaceborne SAR has evolved from tens of meters to meters to even decimeters. Sliding spotlight (SL) mode in which an antenna always aims at a point called the virtual rotation point (VRP), allows for a longer accumulating time [1, 2] and results in high-resolution images. Compared with the traditional stripmap mode, in which the VRP moves toward infinity, staring spotlight (ST) mode is another version of SL mode in which the VRP is just within the imaged scene on the ground [3, 4, 5, 6]. Considering the multiple observation angles of SL/ST mode, [PERSON] et al. treated SAR image focusing as a tomographic reconstruction problem of narrow-band computer-aided tomography (CAT) and proposed a tomography formulation [7]. [PERSON] et al. used spotlight SAR interferometry for terrain elevation mapping and interferometric change detection [8]. Based on the COSMO-SkyMed Spotlight-2 data, [PERSON] recovered partiallycorrupted SAR images by spectrum extrapolation [9]. In contrast to stripmap mode, both SL and ST modes have a wider Doppler bandwidth that is usually much larger than the pulse repeat frequency (PRF), which causes a Doppler aliasing phenomenon to occur in azimuth. One way to overcome this barrier to divide the azimuth echo data into small blocks that have a Doppler bandwidth that is smaller than the PRF, and a traditional stripmap mode imaging algorithm, such as the chirp scaling algorithm (CSA) [10] or the range Doppler algorithm (RDA) [11], handles each piece of data so that the processed blocks can be combined into a complete image [12; 13]. Another method is the two-step processing approach proposed by [PERSON] [2]. The key point of this approach is a filtering operation in azimuth, which implements a convolution between the raw data and a chirp signal whose rate is selected--this step is also called azimuth prefiltering. Then, a classical stripmap SAR imaging algorithm can focus the prefiltered data into a SAR image. In reality, most SAR imaging algorithms are based on the acquisition geometry of airborne SAR. But the same approach used in airborne SAR and this experiment could not achieve the same performance, and there are two main reasons for this. Firstly, the acquisition geometry of airborne SAR can be depicted by the hyperbolic range equivalent model (HREM) [14], which is only able to describe the first- and second-order items of the range history. However, the third- and higher-order items would introduce significant phase errors in the signal processing when the azimuth resolution is in decimeter level. To solve this problem, [PERSON] et al. added a linear term to the HREM to improve the model accuracy to the third-order, and the method for L-band SAR systems at altitudes from 1000 to 10,000 km could get an azimuth resolution around 3 m [15]. Having considered the effect of the Earth's rotation, [PERSON] introduced a fourth-order model and derived the fourth-order extended exact transfer function (EETF4) algorithm to get better SAR images [16; 17; 18]. [PERSON] et al. proposed a modified equivalent squint range model (MESRM), which introduces the equivalent acceleration of the platform into the HREM [14]. [PERSON] et al. described the sliding spotlight SAR imaging geometry by an Nth-order model [19]. But the complexity of the algorithm became more difficult as the order increased. Secondly, all of these approaches did not consider that the actual range history of the target varies with the target's position. In other words, different targets in the imaged scene have different range histories. Based on the theory of motion compensation for airborne SAR, [PERSON] et al. made use of the range error caused by the non-linear movement of the spaceborne SL SAR relative to the VRP and corrected this kind of variance with a cubic item [20].