# In-Orbit Attitude Determination of the UVSQ-SAT CubeSat Using TRIAD and MEKF Methods
## 4 Results
### Discussion and Perspectives
Using large numbers of values corresponding to large numbers of different configurations helps us to quantify the ability of the methods to recover the Sun LOS in the body frame. \begin{table}
\begin{tabular}{l l l l} \hline \hline \multirow{2}{*}{**Definition**} & \multicolumn{3}{c}{**Attitude Determination**} \\ \cline{2-4}  & & **Facing the Sun** & **Not Facing the Sun** \\ \hline
**UVS** & \begin{tabular}{l} Facing the Sun \\ Not facing the Sun \\ \end{tabular} & \
\begin{tabular}{l} _True Positive (TP)_ \\ _False Positive (FP)_ \\ \end{tabular} &
\begin{tabular}{l} _False Negative (FN)_ \\ _True Negative (TN)_ \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Definition of the true positive, false negative, false positive, and true negative. Figure 11: Precision (**a**) and accuracy (**b**) of the TRIAD method based on the UVS indicator. The methods can be compared by computing the difference between the indicators for MEKF and TRIAD. The results are presented in Figure 13. The MEKF method allows us to increase the precision by about 20% and the accuracy by a few percent. The last indicator used to compare the methods is the absolute uncertainty of the two methods developed above. To do this, we choose to use the Monte Carlo method to perform the propagation of uncertainties. The uncertainties of the instruments are quantified from the specifications and empirically. They are represented as a Gaussian probability density function. We then seek to quantify the uncertainty propagated on the angle to the Sun and the angle to the nadir as the flux computation depends on those parameters. The uncertainty is estimated in two different cases. The plot at the top of Figure 14 shows the evolution of the uncertainty for TRIAD and MEKF methods in the case of the data received almost continuously over the whole selected period. The sampling rate is thus almost constant and regular. This represents the ideal case where all the data are retrieved, and the only limitation is the sampling rate. The plot at the bottom of Figure 14 represents the same evolution for a longer period equivalent to more than 22 orbits including phases with missing data. It is thus possible to obtain the restitution of attitude with a 3\({}^{\circ}\) uncertainty (at 1\(\sigma\)) in sunlight for both methods. In eclipse, for long periods of time (including missing data), the uncertainty reaches 14\({}^{\circ}\) for TRIAD while it converges to about 10\({}^{\circ}\) for the MEKF method. In general, we see an improvement of about 4\({}^{\circ}\). Eclipse phases appear in gray and sunlight in white. The determination of the uncertainty in time is pertinent as the attitude will be time-dependent for the MEKF method. This is apparent in Figure 14 as the uncertainty for the MEKF method converges with time. We also see that sunlight and eclipse phases have totally different results in terms of uncertainty as the data provided come from different instruments. Figure 12: Precision (**a**) and accuracy (**b**) of the MEKF method based on the UVS indicator. The accuracy of the MEKF method can be compared to validation with in-orbit data from [3]. It appears that the uncertainty is much lower for the Radio Aurora Explorer satellites with a 1 Hz sampling rate (below 1\({}^{\circ}\)). A 1 Hz sampling rate was not enough to capture the spacecraft motion, and a slowing down of the satellite rotation was therefore undertaken and allowed to improve the results. In our case, the sampling period of 30 s does not allow us to reach such accuracy. This is nevertheless important to note as feedback. It is possible to estimate the uncertainties on the incident flux from the uncertainties on the angles to the source. Indeed, fluxes are corrected using the cosine of the angle for the Sun and the view factor in the case of terrestrial flux. Those uncertainties are based only on the attitude determination uncertainties. Therefore, for the solar flux, the uncertainty is estimated at 4% (1\(\sigma\)) for both methods.