# Estimation of Antenna Pose in the Earth Frame Using Camera and IMU Data from Mobile Phones
## 2 Related Work
### Camera-IMU Calibration  
To relate measurements in the camera frame to the Earth frame, the relative pose between the camera and the IMU (i.e., the rigid transformation between the two frames) should be known. The process of determining this transformation is usually referred to as camera-IMU calibration [37]. [PERSON] et al. [38] classified the existing approaches into two categories: approaches that require specialized measurement setups and facilitate closed-form solutions and filter-based approaches with approximate solutions. [PERSON] et al. [39] categorized the approaches into three classes: methods with closed-form solutions, Kalman-filter-based methods and methods that make use of optimization techniques. Here, we offer a review from another perspective, based on the hardware configurations used in the various calibration methods, leading to two groups. Methods in the first group rely on the gyroscope in an IMU. A prevalent practice is a filter-based approach in which the calibration parameters are integrated into the state vector of an IMU motion filter (e.g., [40; 41] (see [42] for an overview)) and are solved simultaneously with other motion states. However, as noted by [PERSON] et al. [43], a long state vector naturally imposes certain limitations on accuracy. Moreover, the filter-based framework is unnecessary for offline calibration; based on this insight, [PERSON] et al. [38] modeled the calibration problem in a non-linear optimization framework by modeling the sensors' trajectory. In these methods, the camera is in constant motion, and over-simplifying the model of a camera on a mobile phone by using a global-shuttered model instead of a rolling-shuttered model may cause problems, as revealed in more recent works [44; 45]. The methods belonging to the other group considered here are also suitable for use with gyroscope-free IMUs. These methods are closely related to hand-eye calibration, or, more concretely, eye-in-hand calibration, an approach used in the robotics community in which the relative pose between the camera and a rigid rig is sought. Since it was first proposed by [PERSON] in 1989 [46], hand-eye calibration has been largely considered a solved problem (see [47] for a review), and recent research has mainly focused on the development of more powerful solvers [48]. In camera-IMU calibration, the role of the \"hand\" is played by an accelerometer or an accelerometer-magnetometer pair. In the first complete camera-IMU calibration procedure, proposed by [PERSON] and colleagues [37], the authors estimated the rigid rotation between the camera and accelerometer as a standalone step in which the rotation was estimated by having both sensors observe the vertical direction in several poses. The camera relies on an ideally vertically placed checkerboard and the accelerometer on gravity to obtain a vertical reference. Their work was released as a [49] toolbox and is widely used. In [PERSON]'s work on a camera that knows its orientation (ORIENT-CAM) [50], a similar idea was applied. However, since the IMU used in ORIENT-CAM consists of an accelerometer and a magnetometer, the relative rotation is estimated by aligning observations of the Earth frame from the IMU and the camera by means of a checkerboard that is ideally laid out such that it is both perfectly horizontal and perfectly northward-oriented. This method requires a carefully placed reference, as in [37], and any error during setup directly introduces bias into the calibration results. Under the assumption of negligible camera translations during the calibration process, in their work on ego-motion [51], [PERSON] and [PERSON] solved for the rotation between the camera and accelerometer by relating gravity observations in IMU frames with the motion of the camera. By considering the relative rotations between different camera frames, they avoided the need for artificial references requiring a rigorous setup. Our calibration method belongs to the second category.