# Satellite-Based Localization of IoT Devices Using Joint Doppler and Angle-of-Arrival Estimation
## 2 Related Works  
IoT over NTN is gradually becoming a viable solution due to market newcomers and cheaper access to space. This is gradually covering the gap left by terrestrial networks, due to both technical and financial limitations. Figure 1 illustrates the overview of the NTN category, which includes (i) airborne platforms that are deployed in the troposphere, such as unmanned aerial vehicles (UAVs), or stratosphere, like high-altitude platforms (HAPs), and (ii) spaceborne platforms such as satellites at various altitudes. The satellite altitude ranges from low Earth orbits (180-2000 km) to geosynchronous equatorial orbits (GEOs) at around 35,786 km [20]. A spaceborne LEO NTN is able to provide a wider coverage with a beam footprint of approximately 100-1000 km in diameter compared to that of the airborne NTN with a diameter of only around 5-50 km [21]. However, the spaceborne link is more susceptible to losses, such as the atmospheric effect, and free space path loss due to its high altitude. Having location information is advantageous, or even vital, in some IoT applications such as mining, agriculture, and environmental monitoring. The GNSS is often the established solution for localization problems given its ubiquity and high accuracy. However, for some IoT use cases, especially in low-cost and energy-limited IoT devices, the GNSS could be substituted by direct localization performed by the satellite itself on the uplink communication signal from the IoT device. One of the suitable satellite-based localization methods is the use of Doppler measurements [22], which only works for non-geostationary satellites. Two available algorithms can be used in previously mentioned ARGOS systems: least-squares and Kalman filtering [5]. The least-squares method has not been changed since 2007 [23], in this scheme the localization algorithm needs at least four uplink transmissions of the ARGOS message that contains several Doppler measurements during the initialization procedure [5]. After the initialization, it requires at least two uplink transmissions per satellite pass to find the intersection of the Doppler solution, which provides both the actual and mirror positions. The Kalman filter algorithm also requires four transmissions during initialization, but it only needs a single uplink transmission per satellite pass, where it uses the interactive multiple models (IMMs) of the unscented Kalman filters (UKFs) to handle multiple hypotheses when combining measurements with multiple behaviors [6]. Other than Doppler measurements, angle-of-arrival (AoA) measurements can also be used to localize ground devices using satellites. One of the common methods for localization using AoA measurements is triangulation. Typically, the angle estimation is approximated with an assumption of a flat Earth surface for a low altitude observer such as an unmanned aerial vehicle (UAV), since the altitude is insignificant compared to the Earth's radius. For a low-Earth-orbit (LEO) satellite observer, the work in [10] utilizes spherical trigonometry and singular value decomposition (SVD) to localize a ground target when more than two AoA measurement points are available. The analysis shows that the higher the number of AoA measurement points, the lower the root mean squared localization error. Furthermore, it is crucial to consider the geolocation bias in the target position estimate due to high non-linearity in the AoA measurements [24]. To account for the bias error, several compensation methods have been presented in [11; 25; 26]. For example, a reduced-bias pseudolinear estimator in [26] can decrease the bias by acquiring sufficient measurements where the bias is dependent on the correlation vector of the measurement matrix. Moreover, both works in [11; 25] apply a Taylor-series expansion to estimate the  
Figure 1: Overview of the non-terrestrial network (NTN): spaceborne and airborne. bias; where [11] applies it directly to the target position estimate, Ref.