## 3 Preliminary Sampling and Analysis  
With aforementioned subsystem modules, the ReCon simulation for agile Earth observation may now be used in combination with optimization algorithms, as depicted in Figure 8. Optimization algorithms are located at a feedback loop to evaluate the current objectives vector and to decide the next design vector. Latin hypercube sampling (LHS) is a technique that can reduce the number of sampling while maintaining overall coverage. LHS divides the design space into \(l\) divisions (levels of value) for each of \(n\) factors (variables), combining them randomly. A square grid containing samples is called a Latin square if and only if there is only one sample in each row and each column (Figure 9). In ReCon, five factors were used because the sixth variable, propellant type, had been fixed as a monopropellant. Table 8 shows the factors and levels used for the experiment: Four levels for \(n/k\) ratio  
Figure 8: ReCon optimization framework. Figure 9: Latin hypercubes: (**a**) Two factors (A, B) and four levels; (**b**) three factors (A, B, C) and four levels. (\(N\)), number of planes (\(P\)), and number of satellites per plane (\(S\)); eight levels for the Walker altitude difference (\(A\)) and FoR (\(R\)). A Latin hypercube sample of 100 design points was created using a MATLAB built-in function, _Ilsdesign_. At each point, the following four figures of merit are compared to their corresponding 100-point average: ROM revisit time, GOM revisit time, constellation mass, and reconfiguration time. LHS reduced the total of 4096 combinations down to 100 design points via LHS to evaluate the following figures of merit: ROM revisit time, GOM revisit time, constellation mass, and reconfiguration time. Table 9 shows the main effects of the levels of each factor, where blue boxes and red boxes indicate the level of a given factor that has the greatest effect in a positive direction and in a negative direction, respectively. Note that all metrics are better if their values are smaller. The following trends can be observed from the LHS results:  
* As the RGT ratio decreases, the mass of the entire constellation increases because more propellant is required (i) to raise the altitude of satellites from the parking orbit to higher altitudes at the beginning of life and (ii) to lower the altitude to the disposal orbit. Reconfiguration time also increases with the RGT ratio because there are fewer locations where reconfiguration can occur. * High altitude difference increases both ROM revisit time and GOM revisit time because a satellite has to orbit along a longer trajectory with a lower orbit velocity, which leads to a longer orbit period. The constellation mass decreases as altitude difference increases, mainly, due to lower atmospheric drag and subsequent reduction in propellant mass. The reconfiguration time decreases as the absolute value of altitude difference increases because a greater deviation from the Walker altitude makes the orbit plane drift faster. * Both ROM revisit time and GOM revisit time (to a lesser extent) decrease when the number of planes decreases and the number of satellites per plane increases. * Increasing the FoR decreases the constellation mass. From which the following is recommended regarding a starting point for optimization algorithms:  
* The number of revolutions per day should be large. * The altitude difference from the Walker constellation should be large. * The satellites should be distributed in a small number of orbit planes. * The FoR should be large. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Design** & **Description** & **Factor** & **\#Levels** & **Units** \\
**Variable** & & & & \\ \hline _nk_ & RGT ratio & N & 4 & - \\ _delta\_alt_ & Altitude difference between Walker and RGT & A & 8 & km \\ _n\_planes_ & Number of orbit planes & P & 4 & - \\ _n\_sats_ & Number of satellites per plane & S & 4 & - \\ _regard_ & Field of regard & R & 8 & \(\circ\) \\ \hline \hline \end{tabular}
\end{table}