In this paper, we consider the Unified Camera Model and its properties, as well as investigate and apply the improved Double-Spherical one (DS-model) in the task of restoring exterior and interior orientation elements for a set of images with ultra-wide-angle fisheye lens. The use of panoramic cameras in photogrammetry issues is a new trend, while the spherical model fully inherits the properties of the classical central-projection sample. The mathematical concept of using it is presented, as well as the solution of the optimization problem of calculating the elements of the internal and external orientation of the camera through the Gauss-Newton method, which is relevant for the tasks of reconstructing a three-dimensional scene and developing an optical SLAM based on a multi-camera system with ultra-wide-angle lenses, is implemented. In this work, epipolar geometry methods, digital image processing methods, statistical, numerical, and optimization ones were used. The results obtained enable evaluating the applicability of the DS-model for three-dimensional reconstruction of scenes during external and internal monitoring of buildings and structures, restoration of the motion trajectory and position in space for mobile systems with an installed camera, solving matters such as Perspective-n-Point for restoring the relative orientation between different active and passive sensors