## 1 Introduction  
Sonar is an essential technology for underwater sensing. However, its spatial resolution depends on a combination of transducers to (roughly) approximate a sampling beam via interferences. A larger number of transducers placed on a larger area accordingly provides a higher resolution. However, the number of transducers in a sonar sensor is limited by many factors like sensor size, power consumption and costs. A popular approach is hence the use of a synthetic aperture, i.e., the sonar with its \(N\) transducers is positioned at \(k\) places to generate a virtual sensor with \(kN\) transducers [1; 2; 3]. So, the core idea of Synthetic Aperture Imaging in general is to use a sequence of measurements that are combined to form improved 2D or 3D representations of the sampled environment. The motion of the sensor, respectively of its carrier platform, generates a synthetic aperture that leads to higher resolution images. The related methodology of Synthetic Aperture Radar (SAR) has been for multiple decades a standard technique for remote sensing [4]. A general optical counterpart is camera arrays [5; 6] to improve imaging performance. For sonar, the same fundamental principles apply, but there are specific challenges related to the propagation properties of sound including its slow speed, the medium water, the available technologies for transducers, etc. An introduction to Synthetic Aperture Sonar (SAS) and discussions of related research can be found in [2; 3]. The state of the art for synthetic aperture sonar (SAS) is strongly coupled to constraints on the way it can be used [1; 2; 3]. For example, the \(k\) sensor poses often have to be equidistantly placed on a virtual line perpendicular to the sensor. This is motivated by the intention to ease the signal processing as well as by practical aspects: a vehicle, for example, a surface vessel or an Autonomous Underwater Vehicle (AUV), with a sonar facing down to the seafloor is only required to use its navigation sensors to travel with constant speed on a straight line. However, it also significantly limits the scope of the vehicle's mission. A core element in conventional SAR/SAS systems is in general the precise localization of the sensor poses, which is achieved through navigation sensors. This is a less critical issue for SAR, i.e., for remote sensing satellites, which need extremely precise navigation for control anyway. Nevertheless, SAR autofocus is still in the interest of research where sensors cannot provide the required accuracy, for example, for ultra-high resolution imaging [7; 8]. In [9], it is shown that extracted phase information can be used for the additional detection of moving targets. In [10], a novel SAR application for near-field microwave imaging is presented. A treatment of trajectory inaccuracies by a constrained least squares approach is presented in [11]. In conventional SAS systems, two methods exist to alleviate motion errors. One method is the Displaced Phase Center Antenna (DPCA) [12] that exploits the spatial coherence of the seafloor backscatter in a multiple receiver array configuration. It uses a ping to ping correlation of single sensor elements. The second line of methods are phase-only autofocus algorithms, of which the phase gradient autofocus (PGA) is the most popular one. It extracts the phase error by detecting a common peak in each range cut. In [13], PGA is extended to a generalized phase gradient autofocus, which works for reconstruction methods including the polar format algorithm (PFA), range migration, and backprojection (BPA). The idea presented in this article is to use scans without navigation data for the extended aperture of a standard antenna. In conventional SAS systems, the area coverage is generally limited by the propagation speed in water [14]; this restriction is usually remedied by employing multi-receiver configurations [2].