## 7 Conclusions  
In this paper, a table-based adaptive DPLL algorithm for GNSS receivers operating in Moon exploration missions was proposed. The algorithm continually adjusts the noise bandwidth of the loop filter by measuring the current C/N\({}_{0}\) and dynamic stress and extracting the noise bandwidth value from the optimal bandwidth table. The structure of the algorithm, as well as the method which calculates the proper integration time to maintain the normalized bandwidth to constant, was proposed. The generation method and the result example of the optimal bandwidth table were presented in consideration of the thermal noise, Allan deviation oscillator phase noise, vibration-induced oscillator phase noise, and dynamic stress error. Each noise bandwidth value was selected optimally to minimize the DPLL RMSE. The numerical simulation scenario was configured using the mission trajectory analysis results of the Moon exploration. During the simulation scenario, the C/N\({}_{0}\) has a range of 5.4-57 dB-Hz, and the maximum jerk dynamic stress is 411 g/s. The proposed algorithm operated stably throughout the simulation, while a conventional fixed-bandwidth loop lost its lock. For the low SNR region, the noise bandwidth was narrowed to 0.7 Hz, and the integration time was increased to 420 ms to track the noisy signal. The noise bandwidth was widened to 213.3 Hz at the high dynamics region to track the fast variation in the signal components. Most of the time, the normalized bandwidth, which is a product of the noise bandwidth and the integration time, was maintained below the target normalized bandwidth value, so the stability of the loop filter was maintained. The proposed algorithm was evaluated by comparing it with the existing adaptive DPLL algorithms (FAB, FL, LBCA) in terms of the phase jitter performance and the execution time. Since the noise bandwidth values in the table were generated in consideration of the optimality, the proposed algorithm has a similar phase jitter performance to the FAB  
Figure 18: Execution time measurement results of each adaptive DPLL algorithm. The proposed algorithm has approximately 2.4–5.4 times faster execution time compared to the other adaptive DPLL algorithms. \begin{table}
\begin{tabular}{c c c c c} \hline
**Algorithm** & **Addition (Subtraction)** & **Multiplication** & **Division** & **Remarks** \\ \hline Table-based (proposed) & \(5\) & 4 & 1 & Floor(\(\cdot\)) \\ FAB & \(1\) & 16 & 5 & Seventh-root \\ FL & \(15\) & 20 & 3 & - \\ LBCA & \(8\) & 5 & 2 & Exp(\(\cdot\)) \\ \hline \end{tabular}
\end{table} 
Table 3: Theoretical computational complexities of each adaptive DPLL algorithm. and a slightly degraded performance to the FL and LBCA. However, due to the simple calculation procedure of the proposed algorithm, it has an approximately 2.4-5.4 times faster execution time compared to the other algorithms. This paper uses the proposed algorithm for a specific scenario, the Moon exploration mission. It is suitable for the proposed algorithm because the mission has significant variations in signal power and dynamic stress during the trajectory, but they change slowly. So, adaptivity may be more important than the estimation performance of current C/N\({}_{0}\) and dynamic stress. Moreover, the trajectory during the mission is fixed, so the receiver can know its approximate C/N\({}_{0}\) and/or dynamic stress. Nevertheless, the proposed algorithm can be applied to any condition using a regenerated optimal bandwidth table with modified parameters. However, in the case of a situation where the signal power and dynamic stress change rapidly, sophisticated algorithms estimating C/N\({}_{0}\) and dynamic stress would be needed. Conceptualization, J.-H.W. ; methodology, [PERSON]-J.S. and [PERSON]-H.W. ; software, Y.-J.S. ; validation, [PERSON]-J.S. and [PERSON]-H.W. ; formal analysis, Y.-J.S. ; investigation, Y.-J.S. ; resources, J.-H.W. ; data curation, [PERSON]-[PERSON]; writing--original draft preparation, [PERSON]-[PERSON]; writing--review and editing, [PERSON]-H.W.