# LCNS Positioning of a Lunar Surface Rover Using a DEM-Based Altitude Constraint
## 5 Results
### Sensitivity Analysis Process Noise  
As previously discussed in Section 4.2, the selection of the process noise matrix \(Q\) has a large impact on the attainable position accuracy. Therefore, this section shows the results of the sensitivity analysis for these critical parameters. Table 12 shows three different scenarios for the selection of process noise. The first scenario is in line with the definition of the process noise provided in Table 6, which assumes a relatively low quality IMU. Note that this level of process noise is in line with [29; 32] assuming a tactical-grade IMU. However, the values used in the previous publications are considered conservative for a tactical-grade IMU. Therefore, in this paper, we aim to consider a more realistic process noise definition. The second and third scenario correspond to, respectively, a tactical- and navigation-grade IMU. Detailed characteristics of both types of IMU can be found in Table 4. The process noise for position and velocity is set to \(5\cdot 10^{-5}\) (note that these values are obtained from internal studies), characterizing the mismodeling of the kinematic filter. The process noise accounting for the IMU velocity random walk (defined in Table 4) is added to this value, leading to the values reported in Table 12, consistently with the definition of the process noise for a tightly coupled GNSS/INS filter [47]. \begin{table}
\begin{tabular}{l c c c} \hline
**Scenario** & **68 th Percentile [m]** & **95 th Percentile [m]** & **99.7 th Percentile [m]** \\ \hline
1. Baseline ODTS & 37.2 & 80.3 & 81.0 \\
2. Improved ODTS & 23.4 & 50.1 & 50.6 \\ \hline \end{tabular}
\end{table} 
Table 11: Statistics highlighting the improved position accuracy in case of an improved ODTS accuracy. The percentiles refer to the time series of the horizontal uncertainty (3-sigma). Figure 13: Performance of the LCNS position solution. (**a**) shows the horizontal (2D) covariance of both the LCNS-only as well as the LCNS and DEM solution, while (**b**) shows the 1-sigma uncertainty of the DEM measurement. Figure 14a shows the horizontal covariance (3-sigma) for the three scenarios introduced in Table 12. It can be observed that the difference in attainable position accuracy between scenario 1 (baseline) and scenario 3 (navigation grade IMU) is almost an order of magnitude for the periods in which only 3 satellites are visible (Figure 10a). For the epochs in which 4 satellites are visible, the impact is less pronounced but still significant (approximately 20 m). Figure 14b shows the uncertainty of the DEM measurement. Similar to the baseline scenario, the DEM uncertainty is primarily governed by the data component in case 4 satellites are available (as the horizontal uncertainty is within 5 m). However, contrary to the baseline scenario, scenarios 2 and 3 (tactical- and navigation-grade IMU) do not show the increase in the DEM uncertainty measurement during the periods in which only 3 satellites are visible, as its horizontal uncertainty is always below 2 m 1-sigma (except when initializing the EKF). Finally, Table 13 shows the statistics (in terms of the 68 th, 95 th and 99.7 th percentiles) of the three scenarios defined in Table 12. In line with Figure 14a, a substantial improvement is shown when using a higher-grade IMU (i.e., tactical- or navigation-grade). Figure 14: Performance of the LCNS position solution. (**a**) shows the horizontal (2D) covariance of for the different process noise scenarios identified in Table 12, while (**b**) shows the 1\(\sigma\) uncertainty of the DEM measurement for the different process noise scenarios identified in Table 12.