## 3 Optimal Bandwidth Table
However, the minimum value of the C/N\({}_{0}\) is selected as 5.4 dB-Hz (not 1.48 dB-Hz, as can be observed in Figure 3) because it is the smallest C/N\({}_{0}\) that the receiver can track in a theoretical sense (i.e., the smallest C/N\({}_{0}\) where the theoretical measurement error is less than 30 degrees). The figure shows that the measurement error varies with the noise bandwidth value, and one optimal point at which the measurement error is minimized exists for each condition. As expected, the optimal bandwidth for the low SNR condition is very narrow (\(B_{n}=0.7\) Hz) to suppress the large noise effect due to the very low C/N\({}_{0}\) of 5.4 dB-Hz. Furthermore, the optimal bandwidth is very wide (\(B_{n}=213.3\) Hz) for the case of the high dynamics to track fast variations in the signal component. The algorithm that generates the optimal bandwidth table is presented in Algorithm 1. This algorithm starts with the initialization of setting the required parameters for the calculation of the DPLL measurement error. Then, the optimal bandwidth and the minimum RMSE at the optimal point are calculated for each C/N\({}_{0}\) and jerk value. If the minimum RMSE is less than 30 degrees, the optimal bandwidth is saved to the optimal bandwidth table; otherwise, the calculated value is discarded. A two-dimensional table is outputted by the algorithm and is used for the table-based adaptive DPLL algorithm. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline \(k_{g}\) & \(2\times 10^{-10}\) [parts/g] \\ \(G_{g}\) & \(0.05\) [g\({}^{2}\)/Hz] \\ \(\omega_{1}\) & \(25\times 2\pi\) [rad/s] \\ \(\omega_{2}\) & \(2500\times 2\pi\) [rad/s] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameter values for the vibration-induced oscillator phase noise calculation [26]. The generated optimal bandwidth table for the Moon exploration mission, as an example, is presented in Figure 6. Note that another table can be generated for another operating environment of the GNSS receiver with modified parameters. For the current scenario, the optimal bandwidth table was generated with the step of 0.1 dB-Hz and 1 g/s for the C/N\({}_{0}\) and the jerk, respectively. The target generation ranges for each bin were selected as the maximum expected values (i.e., 57 dB-Hz for C/N\({}_{0}\) and 411 g/s for jerk) for the operating environment. Figure 6a shows the overall shape of the calculated optimal bandwidth table in a three-dimensional view, as the optimal bandwidth for each bin is represented as a height in the figure. The same shape is presented in Figure 6b,c with respect to the C/N\({}_{0}\) and jerk, respectively. A top view of the optimal bandwidth table is illustrated in Figure 6d. Since the optimal bandwidth is not saved to the optimal bandwidth table if the minimum RMSE exceeds 30 degrees, empty spaces can be observed in Figure 6d. Therefore, the empty space means the receiver cannot operate in that condition in a theoretical sense. Figure 5: Example of the measurement error calculation results with respect to the noise bandwidth variation for low signal-to-noise ratio (SNR) and high dynamics conditions. The optimal bandwidth table utilizes the thermal noise, Allan deviation, vibration-induced oscillator-phase noise, and dynamic stress error for the bandwidth calculations as these are well-known error sources of DPLL. Parameter values for each error source, especially for the oscillator, are fixed to the expected values in the operating environment of the receiver. Since the environment is the Moon exploration mission in this study, these values are set as the OCXO values suffering a moderate amount of vibration with assumptions as presented in Tables 1 and 2. However, in real conditions, they cannot be the same as the expected ones and would be changed as the environment changes. Thus, the optimality can only be assured when the environment is similar to the expected one, and if it deviates greatly, an additional estimator for the oscillator phase noise is required.