# Estimation of Antenna Pose in the Earth Frame Using Camera and IMU Data from Mobile Phones
## 2 Related Work
### Visual Pose Estimation  
The general problem of visual pose estimation has been a long-standing topic in computer vision (see [20] for an early review). By adopting an antenna geometry model, we are formulating the problem as one of a 2D-3D matching in which \"3D objects are observed in 2D images\" [20], the goal of which is \"to estimate the relative position and orientation of a 3D object to a reference camera system\" [20]. There are two major paradigms for approaching this problem, distinguished by how correspondences are established between the model and the imagery. One is the feature-based approach, in which an image is abstracted into a small number of key-point features. The other is the direct approach, in which image intensities are used directly to determine the desired quantities. The feature-based approach is typically the most popular solution. The core underlying idea is to compute a set of correspondences between 3D points and their 2D projections, from which the relative position and orientation between the camera and target can then be estimated using various algorithms, such as those for solving the perspective-n-point (PnP) problem [21]. Consequently, the performance of this approach hinges on whether enough features can be detected and correctly matched. Although numerous feature detection and tracking schemes [22; 23; 24; 25] have been developed, these methods are unsuitable for textureless objects. Recently, line features, such as the bunch of lines descriptor (BOLD) [26], have been proposed for handling textureless objects, but on very simple shapes with too few line segments and little informative content, they are still prone to failure. Furthermore, the question of how to build stable 2D-3D correspondences is a topic that is still under investigation. The direct pose estimation approach attempts to avoid issues of feature tracking and matching by matching model projections to 2D images as a whole. There exists a large class of methods based on template matching. [PERSON] et al. proposed a series of template-matching-based methods using inputs based on the distance transform [27], dominant gradient orientations [28] and the recently developed concept of gradient response maps (GRM) [29]; [PERSON] et al. [30] used edge images and included edge orientations in templates in their fast directional chamfer matching (FDCM). GRM and FDCM are state-of-the-art template matching methods. Once an object is registered using a pre-built template, a refinement process, which is usually based on the iterative closest point (ICP) algorithm [31], is performed to refine the object's pose, such as in FDCM. In 2015, [PERSON] and [PERSON] proposed the direct directional chamfer optimization (D2 CO) [32] for pose estimation, in which a non-linear optimization procedure (the Levenberg-Marquardt algorithm) is applied in the refinement stage instead of an ICP-based method, and in a comparison with four ICP-based refinement methods (including FDCM), D2 CO demonstrated an advantage in terms of the correct model registration rate. The idea of optimizing the pose parameters has also been pursued in tracking [33] and simultaneous localization and mapping (SLAM) applications [34]. As an alternative to the template matching framework, [PERSON] and [PERSON] [35] introduced a level-set-based modeling method based on a cost function describing the fitness between the estimated pose and the foreground/background models, and they solved the optimization problem using a simple gradient descent approach given an initial pose. Their Pixel-Wise Posteriors for 3D tracking and segmentation (PWP3D) method has been widely used in tasks of simultaneous segmentation and pose estimation, and as a subsequent improvement to PWP3D, [PERSON] et al. [36] proposed a boundary term to PWP3D (BPWP3D), which offers finer boundary constraints for more challenging detection environments. However, these (local) optimization-based methods depend on the initial parameters and may become trapped in local optima.