# Estimation of Antenna Pose in the Earth Frame Using Camera and IMU Data from Mobile Phones
## 1 Introduction
Second, to improve the accuracy of pose estimation, we develop a coarse-to-fine strategy for antenna pose estimation, in which we first find an approximate pose automatically by exploiting the shape characteristics of the antenna and reduce the original unconstrained candidate pose search space to a constrained one, and we then seek an optimal solution in this reduced space using global optimization techniques. Moreover, to reduce the visual-inertial fusion error of mobile phones, we also propose a new camera-IMU calibration method for accurate calculation of the relative poses between the relevant sensors. Therefore, we are able to build up a non-contact antenna pose estimation pipeline after addressing these challenging problems. The pipeline consists of three major steps: first, we capture antenna photographs remotely using a mobile phone with an IMU including the magnetometer despite the fact that an IMU is indeed composed of only inertial sensors (i.e., accelerometers and gyroscopes) in a strict way; then, we estimate the pose of the antenna relative to the camera from the images with our coarse-to-fine visual pose estimation method, and we estimate the orientation of the IMU relative to the Earth from the IMU outputs; and finally, the downtilt and azimuth angles of the antenna are calculated by concatenating the two poses with the refined transformation between the camera and the IMU as a result of our camera-IMU calibration method. Accordingly, our major technical contributions include the following:  
1. We present an accurate solution to the downtilt and azimuth estimation problem for antennas based on multi-view antenna images and IMU data captured by a mobile phone. To the best of our knowledge, this is the first report of a non-contact method of measuring the pose of an antenna using a mobile phone. 2. We enhance existing camera-IMU calibration models by introducing additional degrees of freedom (DoFs) between the accelerometer and magnetometer, and we define a new error metric based on both the downtilt and azimuth errors instead of a single unified rotational error. This enables us to propose a new camera-IMU calibration method that permits simultaneous improvement of the estimation accuracy for both the downtilt and azimuth angles, making it suitable for tasks in which both types of error are crucial. 3. We propose an automatic method of determining an approximate pose from multi-view antenna contours for visual pose estimation, and we also provide bounds on the search space for pose refinement, thereby converting the underlying unconstrained optimization problem to a constrained one to allow solutions to be obtained with better accuracy. The paper proceeds with a review of related works in Section 2. A formal formulation of the problem and an overview of our estimation approach are presented in Section 3, and the details of the implementation are given in Sections 4 and 5. Section 6 describes evaluations of the proposed approach using both synthetic and real-world datasets. Section 7 discusses and concludes the paper with indications of our future work.