# An Effective Sensor Architecture for Full-Attitude Determination in the HERMES Nano-Satellites
## 3 Sensor Selection
### Sun Sensors
#### 3.2.1 Fine Sun Sensors  
The fine Sun sensors selected for the presented nano-satellite application are based on quadrant photodiode technology, which is capable of measuring the Sun vector direction by detecting the differential signals on the quadrant that are generated by the sunlight passing through a hole in the sensor's casing. Then, the signals are sampled, filtered, and processed with an analog-to-digital converter (ADC) integrated with a micro-controller. The measurements are finally made available for the attitude determination functions through an I2C communication interface. In the HERMES nano-satellites, the selected COTS \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Specification** & **Value** & **Units** & **Notes** \\ \hline Bias Instability & 5.3245 & deg/h & Worst Axis Value \\ Angle Random Walk & 0.7454 & deg/\(\sqrt{h}\) & Worst Axis Value \\ Scale Factor Error & 5534 & ppm & Worst Axis Value \\ Mass & \(\leq\)1 & g & \\ Sampling Power & 0.0119 & W & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Invensense MPU3300 gyroscope specifications. Figure 6: Invensense MPU3300 gyroscope. sensors with qualified space operations are produced by GOMSpace and commercialized as the NanoSense fine Sun sensors (FSSs). Each Sun sensor has a theoretical field of view of 60 deg at a half angle. Thus, each sensor covers a solid angle of \(\tau\)sr, and six sensors can cover the full sphere around the spacecraft. However, for many nano-satellites such as HERMES, the Sun direction will be contained in the spherical segment facing the solar wings and a lower number of fine sensors can be employed. Indeed, in HERMES, four FSSs are mounted on the faces aligned with the \(\pm x\) and \(\pm y\) axes, with reference to Figure 2. Despite their inclined mounting angle of 6 deg shown in Figure 3, they cover the complete spherical segment of half angle 60 deg cut by two planes parallel to the \(x-y\) plane. With this configuration, at least one Sun sensor has the Sun in view during nominal operations. With a random attitude, the Sun direction is contained in the covered spherical segment with a probability of \(\sim\)85 %. The remaining conditions are fully supported by the presence of the photodiode coarse Sun sensors. The inclined mounting angle allows having no portion of the FSS's field of view obstructed by the solar wings, and it reduces the incidence angle of the Sun with respect to the sensor's line of sight when the Sun is perpendicular to the solar arrays. Indeed, when the Solar arrays generate their maximum power, the Sun has an incidence angle with respect to the sensor of 39 deg. The best performance would have been available with the Sun directly perpendicular over the sensor, but in nominal conditions, this would have required mounting the sensor on the solar wing. However, the flexibility and the oscillations of the deployable surface would have reduced the determination accuracy of the sensor architecture. Then, the FSSs were solidly attached to the body-mounted solar panels, as shown in Figure 7.  
In this configuration, with the nominal Sun incidence angle in the range from \(\sim\)35 deg to \(\sim\)45 deg, the mean calibrated measurement error was in the order of 0.5 deg in the worst conditions around 1 deg. These values were retrieved by testing the fine Sun sensor with variable incident light, as shown in Figure 8. This clearly shows the performance of the sensors, which were sampled at 10 Hz with an artificial light source in dark laboratory conditions. These results were obtained by sweeping a light source for an arc of 120 deg from the positive to the negative direction. Then, the raw data measurements were converted into the Sun angle, geometrically calibrated, and directly compared with the reference values. The geometrical calibration exploited a look-up table filled with 81 calibration points associated with the azimuth and elevation of the light source with respect to the sensor's focal plane and line of sight.