# An Effective Sensor Architecture for Full-Attitude Determination in the HERMES Nano-Satellites
## 4 Full-Attitude Determination Performance  
The full-attitude determination accuracy is strongly dependent on the sensor performance. In fact, the quality of the available measurements sets a physical limit to the lowest determination error that can be achieved. For these reasons, a credible attitude \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Specification** & **Value** & **Units** & **Notes** \\ \hline \hline \multicolumn{1}{l}{Bias Instability} & 2.2652 & \(\mu\)g & Worst Axis Value \\ \multicolumn{1}{l}{Velocity Random Walk} & 0.00783 & \((\mathrm{m/s})/\sqrt{\mathrm{h}}\) & Worst Axis Value \\ \multicolumn{1}{l}{Scale Factor Error} & \(1157\) & ppm & Worst Axis Value \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Memsense MS3025M accelerometer specifications. Figure 13: Allan variance, \(\sigma_{A}(\tau)\), for Memsense MS3025M accelerometer. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Specification** & **Value** & **Units** & **Notes** \\ \hline \hline \multicolumn{1}{l}{Position Accuracy} & 1.5 & \(\mathrm{m}\) & Datasheet Declared \\ \multicolumn{1}{l}{Velocity Accuracy} & 0.03 & \(\mathrm{m/s}\) & Datasheet Declared \\ \multicolumn{1}{l}{Time Accuracy} & 20 & \(\mathrm{ns}\) & Datasheet Declared \\ \multicolumn{1}{l}{Time to First Fix} & 39 & \(\mathrm{s}\) & Cold Start; Datasheet Declared \\ \multicolumn{1}{l}{Mass} & 33.2 & \(\mathrm{g}\) & \\ \multicolumn{1}{l}{Sampling Power} & 1.32 & \(\mathrm{W}\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Novatel OEM719 GNSS receiver specifications. determination design has to be founded on HIL testing results with the available sensors. Then, even if the attitude determination functions are going to be verified with MIL tests, or software-/processor-in-the-loop (SIL/PIL) analyses, the supporting system and dynamical simulators shall be calibrated with respect to real hardware performance. The attitude determination performance was verified by means of numerical simulations composing a model-in-the-loop testing campaign, exploiting a functional engineering simulator (FES) developed for small satellite applications in Earth orbits. The HERMES nano-satellite dynamics accounts for realistic system characteristics, such as the measured inertia properties and dimensions. The nominal orbital environment is described according to international standards [30] accounting for the nominal orbit of the spacecraft: an equatorial LEO with an altitude of 550 km. The simulation was run for four orbital periods, starting from a random attitude state. The nominal attitude mode was a nadir pointing mode, which is ideally tracked by an ideal controller (i.e., the pointing error was 0 deg). The FES contains detailed functional models of all the sensors composing the discussed architecture, whose parameters and performance were those discussed in the previous sections, retrieved from HIL testing activities. The full-attitude determination functions were executed at 10 Hz, and the sensor models were sampled at the same frequencies as the real hardware components. The output results were analyzed in terms of three-axis attitude determination error angle and three-axis orbit determination error position. The FES runs of MATLAB/Simulink with a fixed step numerical integrator with a sample time of 0.01 s. The numerical calculations of the attitude and orbit determination functions were executed with 32 bit floating numbers, to be representative of the numerical computations to be executed by the on-board processor. Table 9 summarizes the main simulation parameters used in the presented analyses. The attitude determination performance was assessed in several pointing modes, with random initial states and with realistic control performance. Moreover, the closed-loop determination and control functions were also verified together. However, to show and present the available attitude determination accuracy, an ideal attitude pointing control was exploited.