# An Effective Sensor Architecture for Full-Attitude Determination in the HERMES Nano-Satellites
## 3 Sensor Selection
### Gyroscopes  
Gyroscopes are needed to guarantee good propagation performance during the eclipse period, and they also provide continuous data for feedback action on the desired reference velocity. Given the dimensions of nano-satellites, MEMS gyroscopes are mandatory and shall be compliant with the power budget. The proposed architecture requires two redundant gyroscopes, with accuracy levels of tactical-grade sensors. In fact, the eclipse propagation of \(\sim\)30 min shall not accumulate more than 3 deg of error to comply with the maximum 3\(\sigma_{a}\) error requirement. Taking into account the on-board calibration, the parameter to focus on is the bias instability of the gyroscope. Thus, the sensor selection focused on components with a maximum bias instability of 5 deg/h, which are fully compliant with the tactical-grade limits [27]. Moreover, the mass and volume constraints suggest searching for a combined IMU with three-axis gyroscopes, magnetometers, and accelerometers. The selection identified the Memsense MS3025M IMU as a good choice as primary gyroscope for this sensor architecture. This component provides about 1 deg/h of gyro bias instability and sub-seven micro-g accelerometer bias instability. This is performed with less than 18 g of mass and 1 W of power. The package dimensions are fully compatible with nano-satellite specifications, the size of the sensor being \(28\times 28\times 11.5\) mm. The sensor component under testing is shown in Figure 4, and the measured performance is reported in the specification matrix in Table 2. The gyroscope's stochastic processes' analysis was performed with the Allan variance method, whose results are shown in Figure 5. The noise performance test was performed sampling the zero-rate outputs of the IMU at a 25 Hz sampling rate through the RS-422 serial interface. The IMU was configured with a full-scalerange of 75 deg/s, and the steady-state component temperature was at 38 \({}^{\circ}\)C. The Allan variance data were sampled over a time span of 6 h.  
The hot redundancy with an identical MS3025M component is not possible in the HERMES spacecraft, and in general, it is not easy to accomplish with the imposed system constraints. Thus, gyroscope hot redundancy was performed with another MEMS gyroscope with a lower mass and consumed power. In this case, the same performance cannot be achieved, but good industrial-grade gyroscopes are available as qualified COTS components. The Invensense MPU3300 three-axis gyroscope provides around 5 deg/h of bias instability in a mass of less than 1 g, consuming \(\sim\)12 mW and with dimensions of \(4\times 4\times 0.9\) mm. In this case also, the component performance is listed in Table 3, stating that it was tested sampling the component at 25 Hz through an I2C interface. The component temperature is not directly available, but the room temperature during the test was at 23 \({}^{\circ}\)C. Figure 6 shows the gyroscope integrated into one of the spacecraft's electronic boards. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Specification** & **Value** & **Units** & **Notes** \\ \hline Bias Instability & 1.0662 & deg/h & Worst Axis Value \\ Angle Random Walk & 0.1296 & deg/\(\sqrt{\mathrm{h}}\) & Worst Axis Value \\ Scale Factor Error & 1785 & ppm & Worst Axis Value \\ Mass & 17.8 & g & \\ Sampling Power & 0.92 & W & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Memsense MS3025M gyroscope specifications. Figure 4: Memsense MS3025M IMU. Figure 5: Allan variance, \(\sigma_{\omega}(\tau)\), for Memsense MS3025M gyroscope. It can be noted that, despite the lower accuracy grade, this component has good performance and allows maintaining the imposed requirements, even in the case of a failure of the primary gyroscope. The low bias instability allows maximum propagation errors along the eclipse periods lower than 3 deg at 3\(\sigma_{a}\). Moreover, the low noise level of this industrial-grade miniaturized component makes it an excellent choice as a secondary redundant gyroscope.