## 4 Carrier Phase Accuracy Tests
### Tests and Analysis Based on Signal Simulator  
A GNSS/inertial hardware signal simulator can generate typical scenarios with strict repeatability, flexible parameter set, less external disturbance and, most importantly, with perfect true values for error analysis. It is an effect method to test the performance of PLLs under strong earthquake dynamics. According to the amplitude-frequency characteristics of the strong earthquake signal, a simulated strong earthquake dynamic trajectory was set on the signal simulator. And the GNSS/MEMS accelerometer raw date was processed in our deeply coupled software system to test PLL performance. The typical strong earthquake signal characteristics showed that the maximum acceleration was more than 2 g and its power spectral density was in the range of 0 to 10 Hz. Therefore, a motion case with sinusoidal acceleration was set on the simulator with a frequency of 2 Hz, and a magnitude of 2 g. In this motion case, the receiver was initially static for some time, and then did circular motion with only translational movement, and no angular movement in the horizontal plane for 100 s. The accelerometer parameters set was based on STIM300. The GNSS signal strength was set as 45 dB-Hz, and the GNSS satellite distribution was shown in Figure 9. Since the elevation of satellite G10 was low, the dynamic between receiver and G10 was large, which was about 1.7 g. Figure 10 showed the recorded accelerometer raw data, which was consistent with simulator set. Figure 9: Satellite sky distribution in signal simulator tests. Taking satellite G10 as an instance, the stand-alone PLL and MEMS accelerometer-aided PLL were tested and analyzed on our deeply coupled software system. Since the output of PLL discriminator can reflect the carrier phase accuracy of the PLL, it was used to evaluate the PLL performance. Stand-alone second-order PLLs with bandwidths of 15 Hz and 20 Hz were tested. Their discriminator outputs were shown in Figure 11. When the receiver was static, the discriminator outputs were less than 10\({}^{\circ}\), mainly caused by thermal noise and oscillator. When the movement happened, the maximum discriminator output of PLL with a bandwidth of 15 Hz was about 40\({}^{\circ}\). When the loop bandwidth was increased to 20 Hz, the maximum discriminator output reduced to 24\({}^{\circ}\). These results were consistent with the theoretical values calculated by Equation (5). Testing results showed that the phase errors of stand-alone PLLs had a significant increase under dynamics, and the phase errors caused by the dynamic stress could be reduced by widening the bandwidth. However, considering the impact of a weak satellite signal, discussed based on Figure 5, the stand-alone PLL bandwidth cannot be increased blindly. Since third-order PLLs can track higher order dynamics, most commercial receivers use third-order PLLs. Therefore, a third-order PLL with a bandwidth of 20 Hz was tested. Its discriminator output was shown in Figure 12. When the movement occurred, the maximum discriminator output exceeded 40\({}^{\circ}\), clearly higher than that of the second-order PLL with the same bandwidth. This is because the acceleration frequency is bigger than 1 Hz, which caused the amplitude of jerk to be larger than that of acceleration. Therefore, for a strong earthquake application, third-order PLLs have no advantage. Figure 11: Phase error of stand-alone second-order PLL. Figure 10: Recorded accelerometer raw data in signal simulator tests. MEMS accelerometer-aided second-order PLLs with bandwidths of 15 Hz and 5 Hz were tested. Their discriminator outputs were shown in Figure 13. When the loop bandwidth is 15 Hz, the phase error almost had no increase under dynamics. Compared with Figures 11 and 12, the phase error caused by dynamics was almost eliminated with accelerometer aiding. When the loop bandwidth was compressed to 5 Hz, the static error was not significantly reduced.