# A Femto-Satellite Localization Method Based on TDOA and AOA Using Two CubeSats
## 4 Discussion and Conclusions
Figure 6 shows that improving the accuracy of the used attitude determination and control systems improves the accuracy of the location estimation. However, the relation is not linear. For instance, the location estimation accuracy obtained with [\(\sigma_{ADS}=0.01^{\circ}\), \(\sigma_{ACS}=0.01^{\circ}\)] is the same than that reached with [\(\sigma_{ADS}=0.01^{\circ}\), \(\sigma_{ACS}=0.03^{\circ}\)], and the difference in the location estimation accuracy when using [\(\sigma_{ADS}=0.03^{\circ}\), \(\sigma_{ACS}=0.03^{\circ}\)] is a few meters less than the accuracy achieved when using [\(\sigma_{ADS}=0.03^{\circ}\), \(\sigma_{ACS}=0.01^{\circ}\)]. It tells us that for certain attitude control accuracy, there is a point where improving the attitude determination accuracy has a negligible impact on the accuracy of source location estimation. Then, by using \(\sigma_{ADS}=0.01^{\circ}\) and \(\sigma_{ACS}=0.06^{\circ}\), we studied how the accuracy of the on-board GNSS receivers affected the performance of the localization system. The simulations show that when the accuracy of the GNSS receivers is better than 50 m, the RMSE remains more or less constant (see Figure 7). Since several GNSS receivers offer \(\sigma_{GNSS}=10\) m of accuracy, we selected this value. After selecting the deployment direction and the ADCS and GNSS accuracies, we ran a final simulation to evaluate the localization accuracy achievable with the TDOA-AOA method. This system achieved a root CRB below 30 m and an RMSE near this value for most of the orbit. The only exception is when the three satellites align with each other. These alignments between the satellites generate geometries detrimental to the AOA method. Having a third CubeSat not aligned with the rest of the satellites allows the Time Difference Of Arrival (TDOA) method to solve this issue. However, we wanted to know if we could estimate the location using only two CubeSats, not only because the number of stations is lower but also because we have only two CubeSats in our mission [9]. These results show the feasibility of performing the remote geo-location of femto-satellites by using a communication link with patch antenna arrays to estimate the AOA, while estimating the TDOA of the signal using a GNSS clock signal. This approach will be tested in space by the SUCHAI-2 and -3 mission. The SUCHAI-3 will carry and deploy two femto-satellites once in space. The femto-satellites will carry PNI magnetometers for magnetospheric studies [5; 7] and single-frequency GPS receivers to contrast the results of the method presented in this work. This approach, which includes the method and the deployment strategy, might be relevant to reduce the size, cost, and power consumption of femto-satellites while maintaining accuracy in their location estimation. This method could also be useful for missions at very low altitudes (below 350 km) or missions developed for other celestial bodies. In addition, this technique might help estimate the orbits of other satellites in LEO (satellite tracking) by using a small number of CubeSats. The accuracy of the geo-location method might be improved, especially in this 20% of the orbit where the satellites are aligned, by taking advantage of the a priori knowledge that the source follows an orbital trajectory. Conceptualization, M.G.V.-V. and M.A.D. ; methodology, M.G.V.-V. and M.A.D. ; software, M.G.V.-V.; validation, M.G.V.-V.; formal analysis, M.G.V.-V.; investigation, M.G.V.-V.; resources, M.G.V.-V. and M.A.D. ; data curation, M.G.V.-V.; writing--original draft preparation, M.G.V.-V. and M.A.D. ; writing--review and editing, M.G.V.-V. and M.A.D. ; visualization, M.G.V.-V.; supervision, M.G.V.-V. and M.A.D. ; project administration, M.G.V.-V. and M.A.D. ; funding acquisition, M.A.D. All authors have read and agreed to the published version of the manuscript. This research was funded by the Air Force Office of Scientific Research (AFOSR) under award number FA9550-18-1-0249.