## 2 Related Work  
There are multiple solutions for the GPS-denied problem, divided mainly into two approaches. The first approach is based on information from other agents, such as another vehicle [27; 26; 28], Unattended Ground Sensors (UGSs) [29], or other types of packet transmission devices that serve as reference points for the UAV [30; 31; 32; 33]. However, these techniques require the prior installation of these agents along the flight path, which can be unfeasible, especially if the agents are antennas that are difficult to transport or if passage to certain areas of the trajectory is restricted. Not relying on other agents adds an additional level of autonomy to the system. Other approaches to addressing the GPS-denied problem are based on visual information. Some approaches use Simultaneous Localization And Mapping (SLAM), which is a technique used to locate the UAV in unknown environments [34; 35; 36]. However, depending on the altitude and the range, achieving visual SLAM techniques may not be feasible. Most of these works, however, are only reliable when the problem of localization is at a low altitude and low range [23]. The main problem with using the previous approach for high-altitude UAVs (>1000 m) is the estimation of the scale. That is, the transformation between distances in the image (pixel units) and distances in the terrain (meters). Moreover, the nonlinear transformation between meters and latitude/longitude coordinates necessitates the prior setting of the Universal Transverse Mercator (UTM) zone. This scale could be computed based on IMU information and any other altitude sensor, such as LIDAR or barometer. However, the limitation of the LIDAR lies in its range, while the limitation of the barometer lies in its resolution. In this work, we do not consider the use of LiDAR, as, although there are some solutions available on the market capable of working at high altitudes (e.g., Riegl LMS-Q1560, with a range of up to 4700 m) [37], these either have a high cost or exceed the payload capacity of the UAV. In these cases, we must rely on the barometer to calculate the sea-level altitude. Then, with the help of an elevation map, we can calculate the difference between the altitude above sea level and terrain elevation, thus determining a scale. However, limitations in barometer resolution and accuracy [38; 39] result in an incorrect conversion from the pixel displacement to meters, leading subsequent readings to start from an incorrect latitude/longitude coordinate, thereby resulting in a misleading of the elevation map. Without assistance or prior knowledge (landmarks) of the area we are flying in, errors will accumulate over time. Recently, new studies based on artificial intelligence have been carried out. In [40], a Recurrent Neural Network (RNN) is used. Specifically, it uses Long Short-Term Memory (LSTM) and the IMU and GPS coordinates as inputs. These kinds of predictors based on RNNs can predict the coordinates a few steps ahead but it is not suitable for GPS-denied zones. Other techniques are based on visual information and landmarks. In [23], the authors start from a previously created map. The helicopter flies over the area of interest to collect image data and construct a feature map for localization. The area is divided into a set of discrete regions (nodes), which are related to each other. The problem with this approach is that the UAV needs to have previously flown over the area, and this would not be possible if the GPS signal was corrupted since the beginning of the flight. Our work is more similar to that in [24]. In this study, the authors start with geo-referenced satellite or aerial images and then search for landmarks. However, one disadvantage is that the range is limited, and they assume that the relationship between pixels and meters remains constant.