# An InSAR Interference Fringe-Matching Algorithm Based on Mountain Branch Points
## 1 Introduction  
As modern society continues to develop, the demand for precise aircraft navigation is increasing. Therefore, studying high-precision and highly autonomous navigation systems has become increasingly important [1]. An inertial navigation system (INS) is a vital component of combined navigation systems due to its short-term stability and the fact that is does not require an exchange of information with the outside world. Therefore, a combination of other navigation methods is needed to correct the accumulation of INS errors and achieve accurate navigation [2]. This is the case with the existing combined navigation systems. There are many problems with existing combined navigation systems: optical image-matching-based scene-aided navigation systems do not have all-weather capability and are heavily influenced by seasons [3]; synthetic aperture radar (SAR) scene-matching navigation systems cannot achieve accurate three-dimensional positioning [4]; terrain-matching navigation systems do not have cross-course resolution and have low navigation accuracy [5], and global positioning system (GPS)-aided navigation systems rely on satellite signals and cannot achieve autonomous navigation [6]. Interferometric synthetic aperture radar has an inherent advantage in both acquiring images of the observed area and inverting high-precision digital terrain due to its imaging mechanism [7]. The authors of [8] proposed the use of interference fringes that can begenerated in real time and with terrain information to achieve matched navigation, and others have performed further research [9; 10]. The InSAR interference fringe-matching navigation system is shown in Figure 1[10], where the airborne InSAR system first acquires echo data and the INS outputs navigation data for self-aligned imaging, which is used to generate interference fringes in real time; the DEM database then generates reference interference fringes in real time according to the reference trajectory and system parameters output by the system, and the actual acquired interference fringes are matched with the reference interference fringe to extract the position of the eponymous point. At the same time, the platform motion parameters are estimated based on the time-varying baseline, Doppler frequency, point-target phase history and other coherent data of the InSAR system. Finally, the unified InSAR observation and observation error equations are constructed by combining the results of motion parameter estimation with those of interference fringe-matching positioning, and combined filtering with INS is used to correct the accumulated drift errors and output the combined navigation parameters. Compared with matched navigation systems based on DEM data, interference fringe data are more sensitive to aircraft attitude [11; 12] and have greater potential. The entire system requires a high degree of accuracy in the interference fringe-matching algorithm, which directly impacts the accurate output of subsequent navigation parameters. However, the interference fringe-matching algorithm is a challenging area of research. Several researchers [8; 9; 10; 11] have made important contributions to the framework of matching navigation with interference fringes but have not conducted in-depth studies of the interference fringe-matching algorithm and only used traditional matching algorithms to complete the task of matching. SIFT [13], as a representative traditional matching algorithm, uses Gaussian pyramids to detect keypoints, uses gradient information around the keypoints for description, is invariant to both rotation and scale, and has good robustness to noise and changes in viewpoint and illumination. SURF [14] is an improvement of SIFT based on the use of integral maps and wavelet responses, which are faster and more robust. The ORB [15] algorithm is a method for extracting image features that is based on the features from the accelerated segment test (FAST) [16] keypoint detector and the binary robust independent elementary features (BRIEF) [17] descriptor.