## 4 Discussion  
Quality estimation of LRNTS is based on three criteria:  
1. coverage of LRNTS navigation signals within the crater--viewsheds (Table 1 and Figure 6); \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Map** & **Number of** & **Number of** & **Number of** & **\% of Signal** \\  & **Points** & **Measurements** & **Unknowns** & **Availability** \\ \hline
**1** & **6** & **58** & **18** & **91.6** \\ \hline
2 & 8 & 102 & 24 & 95.7 \\
3 & 10 & 162 & 30 & 98.6 \\
4 & 6 & 52 & 18 & 84.0 \\ \hline
5 & 8 & 102 & 24 & 95.3 \\
6 & 10 & 152 & 30 & 96.3 \\
7 & 7 & 48 & 21 & 78.4 \\
8 & 7 & 60 & 21 & 86.8 \\
9 & 8 & 82 & 24 & 92.8 \\
10 & 7 & 64 & 21 & 91.2 \\
11 & 9 & 134 & 27 & 95.5 \\
12 & 11 & 188 & 33 & 96.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: LRNTS configuration setups. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Map** & **(3D)** & **(3D)** & **(2D)** & **(2D)** & **(1D)** & **(1D)** \\
**Model** & \(\sigma_{\text{xyz (Min)}}\) & \(\sigma_{\text{xyz (Max)}}\) & \(\sigma_{\text{xy (Min)}}\) & \(\sigma_{\text{xy (Max)}}\) & \(\sigma_{\text{z (Min)}}\) & \(\sigma_{\text{z (Max)}}\) \\ \hline (N\({}^{\circ}\)) & (mm) & (mm) & (mm) & (mm) & (mm) & (mm) \\
1 & 20.1 & 38.0 & 3.9 & 7.4 & 19.7 & 37.4 \\
2 & 17.1 & 44.0 & 3.5 & 7.2 & 16.6 & 43.4 \\
3 & 22.1 & 41.3 & 3.6 & 6.5 & 21.8 & 40.8 \\
4 & 41.3 & 283.3 & 15.7 & 151.1 & 38.2 & 239.6 \\
5 & 22.9 & 5* (2) accuracy expressed as positional standard errors of the points (Table 2, Figures 7-9); (3) efficiency expressed as the number of points and measurements (Table 1). Figure 8: LRNTS vertical standard deviations. Figure 7: LRNTS horizontal standard deviations. Figure 9: LRNTS spatial (3D) standard deviations. Regarding the coverage of the crater area with transceiver signals, none of the configurations assure 100% signal availability within the crater. Table 1 displays the number of the transceivers in each configuration setup with the percentage of signal coverage within the crater. Among the 12 tested models, half of them (grey-shaded in Table 1) provide less than 95% signal availability, which limits their possible utilization. Inspecting 3D position accuracies in Table 2, one can observe that the maximal standard deviations of the tested configuration setups are between 17.5 cm and 336.8 mm. Detailed analysis shows that the vertical component (z values) results in much larger standard deviations due to the adjustment linear model. Partial derivatives for the pseudo-distance Pij (connecting transceivers \(i\) and \(j\)) over the unknown coordinate zi of the design matrix A follow the form \(\frac{\partial p_{i}}{\partial z_{i}}=\frac{z_{j}-z_{i}}{D}\). Derivation over \(y_{i}\) and \(x_{i}\) gives analogue forms, replacing \(z\) with \(y\) and \(x\), respectively. Since the transceiver height spans are smaller, in some cases, up to an order of value compared to horizontal components, the corresponding elements of **A** referring to the vertical component are proportionally smaller. Therefore, the cofactor matrix \(\textbf{Q}_{\textbf{x}}=\textbf{N}^{+}=\left(\textbf{A}^{\textrm{T}}\textbf{ PA}\right)^{-1}\) produces elements related to the \(z\) coordinate much larger than for the \(x\) and y axes. Bearing that in mind, the 3D problem is split into 2D + 1D. The calculated standard deviations of the horizontal positions and related vertical accuracies are given in columns 4-7 of Table 2. There are three models with extremely high standard deviations (shaded grey in Table 2). They are not taken into account with further processing. Graphical representations of the other nine models that fulfill the accuracy requirements, sorted with respect to their performance, are given in Figures 7-9. The abscise holds the numbers of selected models (from Tables 1 and 2), while the results (minimum and maximum standard deviations) are given in mm and presented as short red vertical lines. The average standard deviation values for each model are connected with the green line.