## 2 Materials and Methods  
The role of the image processing module is the segmentation of each image forming the sequence of images acquired by the fisheye camera, indicating if a pixel belongs to the sky or to an object (obstacle) which disrupts the LoS towards a satellite. In order to increase the viability of the information extracted by the image processing module, our choice of output is the probability map of a pixel corresponding to a satellite in LoS. The image processing module needs also to compute the correspondence between an image pixel and a couple of elevation and azimuth angles. Having the sky/non-sky segmentation and the correspondence elevation, azimuth-image pixel, the localization module will be able to decide if a satellite (also named Space Vehicle, SV), having the elevation and azimuth known, is in LoS or NLoS, and hence adopt a proper localization approach. The correspondence between elevation, azimuth and an image pixel is obtained by performing camera calibration [5; 6]. An example of computed correspondence using the toolbox provided by the authors of [5; 6] is given in Figure 1. The calibration process performs the projection of the image on a hemisphere. Once this projection is known, we have the azimuth and elevation for each pixel. The elevation is given by the z-coordinate of the pixel and the azimuth is the angle between the x-axis and the projection on the (x,y) plane of the pixel. Thus, the azimuth is computed based on x and y coordinates. All these computations are made with respect to the optical center found in the calibration process. Next, the proposed algorithm produces the probability map, which represents the output of the image processing module. Using the information provided by the GNSS receiver, the surrounding satellites are marked on the probability map. A three-levels discretization of LoS probability map has been considered. Its result is the rejection of the satellites in NLoS and the weighting of satellites with small probabilities. Next, the GNSS data corresponding to remaining satellites go through the Kalman filter (belonging to the GNSS receiver) correction step, which provides the final Position, Velocity, Time (PVT) solution. The Horizontal Protection Level (HPL) can be computedKalman filter, facilitating the computation of the Horizontal Positioning Error (HPE) and Miss-Integrity (MI), which is selected as a QoS indicator. The HPL is defined as the radius of a circle in the horizontal plane, with its center being at the true position, which describes the region assured to contain the indicated horizontal position. The horizontal positioning errors are computed based on the position error in the north (parallel with the ordinates' axis) and the east (parallel with the abscissas' axis) components. These errors are computed based on the difference between measured positions and referenced true positions:  
\[E_{pos}=X_{measured}-X_{ref}, \tag{1}\]  
where:  
\[E_{pos}=\left[ \begin{array}{c}E_{east}\\ E_{north}\end{array} \right], \tag{2}\]  
due to the bi-dimensional nature of the horizontal error. The HPE can be represented as a radial error:  
\[HPE=\sqrt{E_{east}^{2}+E_{north}^{2}}. \tag{3}\]  
The effect of the DOP on the horizontal position value is evaluated with the aid of the Horizontal DOP (HDOP) indicator. Navigation system integrity refers to the ability of the system to provide timely warnings to users when the system should not be used for navigation. The evaluation of integrity is achieved by means of the concepts of Alert Limit, Integrity Risk, Protection Level and Time to Alert, explained in the following. * Alert Limit (AL): The alert limit for a given parameter measurement is the error tolerance not to be exceeded without issuing an alert. The horizontal alert limit is the maximum allowable horizontal positioning error beyond which the system should be declared unavailable for the intended application. Figure 1: Examples of correspondence between spherical coordinates and image pixels.