## 5 Simulation
The integration time variation during the simulation is illustrated in Figure 11. This variation has an almost inversely proportional shape with the noise bandwidth of Figure 10 to maintain a constant normalized bandwidth value, varying with a step of \(\Delta T\) (20 ms for this study). The integration time increases to 420 ms for 300-450 s because the noise bandwidth is narrowed to 0.7 Hz in that region. For the high dynamics region (after 500 s), the integration time reduces to 1 ms, which is a lower bound for the GPS L5 signal when the jerk dynamic stress exists. In fact, tracking loops with a long integration time, such as a few hundred milliseconds, are vulnerable to the instability of the oscillator, because the low-quality oscillator fluctuates during the long integration period. Therefore, to extend the integration time, a feasibility  
Figure 11: Integration time variation during the simulation varied with a step of \(\Delta T\) (20 ms for this study). It increases to 420 ms for the C/N\({}_{0}\) of 5.4 dB-Hz and reduces to the lower bound value in the high dynamics region. Figure 10: Optimal bandwidth variation during the simulation. The noise bandwidth is narrowed to 0.7 Hz as the C/N\({}_{0}\) is lowered to 5.4 dB-Hz and widened to 213.3 Hz as the jerk dynamic stress increases to 411 g/s. analysis for the target integration time and the oscillator quality should be done. It is assumed that the GNSS receiver uses high-quality OCXO for the current simulation scenario. The resulting normalized bandwidth variation during the simulation is shown in Figure 12. Most of the time, the normalized bandwidth is kept below the target normalized bandwidth, which is a predefined constant value that is set to 0.3 for this paper. However, it exceeds the target value for the high dynamics region because the integration time is limited to the lower bound while the noise bandwidth is widened. The maximum value of the normalized bandwidth is approximately 0.69, which is still less than one. Therefore, despite the exceeded normalized bandwidth value, the loop filter does not lose stability. The carrier tracking results of the proposed table-based adaptive DPLL algorithm are presented in Figure 13. The true and estimated values, including the errors between them, of the carrier phase, the Doppler frequency, and the Doppler rate are illustrated. Figure 13 shows that the proposed algorithm tracks the signal components well without the loss of lock for the whole simulation scenario. The carrier phase jitter is increased when the C/N\({}_{0}\) is low. The errors in the Doppler frequency and Doppler rate increase temporally for the high dynamics region and converge to zero after the jerk dynamic stress disappears. To compare the performance of the proposed algorithm with the conventional tracking loop, the carrier tracking results of a fixed bandwidth for the same simulation scenario are presented and compared with the results of the proposed algorithm. The parameters for the fixed-bandwidth loop are fixed at a noise bandwidth of 15 Hz and an integration time of 20 ms, which are typical values. Each carrier tracking error at the low SNR region (210-270 s) for the proposed algorithm and the fixed-bandwidth loop are illustrated in Figure 14. The fixed-bandwidth loop loses lock at approximately 253 s due to the low signal power (C/N\({}_{0}\) = 17 dB-Hz), while the proposed algorithm maintains its lock. The carrier tracking errors for the high dynamics region (500-550 s) are presented in Figure 15. The proposed algorithm continues the tracking during the high dynamics region with the temporally increased tracking error in the existence of the jerk dynamic stress. However, the fixed-bandwidth loop loses lock immediately after the first jerk dynamic stress occurs and cannot be recovered. Figures 14 and 15 show that the proposed algorithm operates stably in harsh environments where the conventional fixed-bandwidth tracking loop loses lock. Figure 10.0 Normalized bandwidth variation during the simulation.