# Improving the Design of MEMS INS-Aided PLLs for GNSS Carrier Phase Measurement under High Dynamics
## 4 Testing and Verification
### Signal Tracking Results Comparison  
Taking satellite No.14 with an elevation of 60\({}^{\circ}\), and satellite No.26 with an elevation of 30\({}^{\circ}\) as examples, tracking errors of second-order PLLs, third-order PLLs, and MEMS INS-aided second-order PLLs were tested.  
Figure 11 shows carrier phase tracking errors of second-order PLLs with an integration time of 1 ms and a bandwidth of 18 Hz. With the increase of the platform acceleration, tracking errors enlarged obviously. The maximum tracking errors of satellite No.14 and satellite No.26 both exceeded the tracking threshold of 45\({}^{\circ}\). That is, the second-order PLLs lost lock under the maximum platform acceleration. In addition, the tracking error of the satellite No.26 was larger than that of the satellite No.14. This is because, compared to the high elevation satellite, the line of sight (LOS) acceleration between the antenna and the low elevation satellite was larger.  
Figure 12 shows carrier phase tracking errors of third-order PLLs. Comparing Figure 12a to Figure 11, with the same integration time and bandwidth, carrier phase tracking errors of third-order PLLs were smaller than that of second-order PLLs under dynamics. To reduce the tracking error caused by thermal noise, the integration time should be lengthened, and the bandwidth should be  
Figure 11: Carrier phase tracking errors of second-order PLLs. (**a**) Tracking errors of satellite No.14 and (**b**) tracking errors of satellite No.26.  
Figure 10: Antenna movement trajectory and the IMU raw output. (**a**) Antenna movement trajectory and (**b**) the IMU raw output.  
narrowed. Tracking errors of third-order PLLs with an integration time of 10 ms and a bandwidth of 10 Hz are shown in Figure 12b. Compared to Figure 12a, though tracking errors reduced under statics, tracking errors increased greatly, and caused PLLs to lose lock under dynamics. Therefore, to tolerate dynamic stress, stand-alone PLLs should use short integration time and wide bandwidth, which increases carrier phase noise, especially for weak GNSS signals.  
Figure 13 shows carrier phase tracking errors of improved INS-aided second-order PLLs. As is seen in Figure 13a, with the Doppler aiding of a MEMS INS, tracking errors of second-order PLLs, with an integration time of 1 ms and a bandwidth of 18 Hz, had no increase under dynamics. This illustrates that INS aiding could reduce the impact of dynamics on PLLs. The test results of MEMS INS-aided second-order PLLs with an integration time of 10 ms and a bandwidth of 10 Hz are shown in Figure 13b. On the one hand, tracking errors caused by thermal noise were suppressed. On the other hand, tracking errors did not increase obviously under dynamics. The results are consistent with the simulation. Therefore, the improved MEMS INS-aided PLLs can suppress tracking errors by thermal noise and dynamics simultaneously, and improve carrier phase measurement accuracy under dynamic environments.  
Figure 12: Carrier phase tracking errors of third-order PLLs. (**a**) PLL with an integration time of 1 ms and a bandwidth of 18 Hz and (**b**) PLL with an integration time of 10 ms and a bandwidth of 10 Hz.  
Figure 13: Carrier phase tracking errors of improved INS-aided second-order PLLs. (**a**) PLL with an integration time of 1 ms and a bandwidth of 18 Hz and (**b**) PLL with an integration time of 10 ms and a bandwidth of 10 Hz.