# A Femto-Satellite Localization Method Based on TDOA and AOA Using Two CubeSats
## 4 Discussion and Conclusions  
This work presents the adaptation of a method that allows us to geolocalize a source with only two stations in low earth orbit (LEO). We based our work on a methodology intended originally for fix stations located on the ground [22]. Our geo-localization method also relies on the radio link between the source and the stations and on a system to combine the time difference of arrival (TDOA) and the angle of arrival (AOA) methods. We evaluated the geo-localization accuracy of this method for several LEO scenarios. The simulated scenarios used two 3U CubeSats (stations) and one femto-satellite (source), which is assumed to be deployed by one of these CubeSats. In contrast to the work by [PERSON] et al. [22], our work allows the sources to go below \(0^{\circ}\) of elevation of the receiving stations due to the absence of ground and adds the complexity of having moving stations (the two CubeSats). Additionally, we studied the impact that different uncertainties in the location estimation of these CubeSats have on the source location estimation. We simulated the deployment of the femto-satellite from the CubeSat and studied the impact on the source location accuracy for different deployment directions and accuracy levels of the on-board attitude determination and control systems for CubeSats. We found in our analysis that with the current technology available for CubeSats, there are operational strategies that allow localization of the femto-satellite with an accuracy  
Figure 8: Source localization RMSE and bias for the first 100 min after deployment. The line \(||\mathbf{u}-\mathbf{s_{1}}||\) is the distance between the femto-satellite and the mother-CubeSat, displayed **in meters**. The line \(||\mathbf{u}-\mathbf{s_{2}}||\) is the distance **in kilometers** between the femto-satellite and the second CubeSat. The \(\alpha\) line represents the angle between the vector femto-satellite-CubeSat-1 and femto-satellite-CubeSat-2. as good as 30 m, \(\sim\)80% of the time per orbit. We accomplished this by using only two CubeSats as receiving stations, without the necessity of using GNSS receivers on the source satellite. We will test this in space with the SUCHAI-2 and SUCHAI-3 missions [9] developed by the Space and Planetary Exploration Laboratory (SPEL) at the University of Chile (see Figures 1 and 2). For the analysis, we developed a simulation tool available on the GitHub of the SPEL: [[https://github.com/spel-uchile/Pypredict](https://github.com/spel-uchile/Pypredict)]([https://github.com/spel-uchile/Pypredict](https://github.com/spel-uchile/Pypredict)) (last accessed on 15 December 2021). When one CubeSat is following another one, the simulations show that the performance is highly dependent on the direction of deployment (see Figure 4). The best scenario is when we deploy the femto-satellite towards the \(y\) axis, perpendicular to the nadir and the direction of movement of the mother-CubeSat (see the red and green curves in Figure 4). After choosing the direction of deployment, we studied the impact on the accuracy of the source location estimation depending on the point of the orbit where the deployment takes place. We found that these variations were negligible compared to the variations provoked by the deployment direction. Nevertheless, we obtain the lowest root CRB on average when deployment occurs 10 min after the apogee. Since the accuracy of the source location estimation is highly dependent on the deployment direction, we analyzed the current attitude and control system technology in their capacity to ensure that the geometry formed by the CubeSats with the femto-satellite is as close to the optimal as possible. By using the reported accuracy of an open-source star tracker [26], we simulated the localization procedure for different accuracies of the attitude determination systems and the attitude control systems, where the lowest simulated values were \(\sigma_{ADS}=0.01^{\circ}\) and \(\sigma_{ACS}=0.01^{\circ}\).