# Improving the Design of MEMS INS-Aided PLLs for GNSS Carrier Phase Measurement under High Dynamics
## 3 Improvement of INS-Aided PLLs  
The testing results showed that the tracking error caused by the aiding information was proportional to the step change of the INS velocity error at each integer second. This phenomenon can be explained from the theory of the INS-aided PLL. Due to the inertial sensor error, the INS velocity error was diverging over time. And with the dynamics increasing, the INS velocity error caused by the inertial sensor error became larger. When the GNSS observations were updated at each integer second, the INS velocity error was corrected by the coupled filter output [26]. As we see in Figure 1, the PLL NCO input is the sum of the filter 2 output and the aiding information. While the aiding information provides the estimated Doppler between satellite and vehicle, the filter outputs the residuals of the Doppler estimation. Due to the INS error divergence before the GNSS updates, the aiding information error accumulates, shown in Figure 6. To keep the NCO synchronous to the input signal, the filter would output a value to cancel the aiding information error. That means the change of the filter output  
Figure 4: INS velocity error and PLL tracking error.  
Figure 5: Zoomed-in INS velocity error and PLL tracking error. (**a**) Zoomed-in error under low dynamics and (**b**) zoomed-in error under high dynamics.  
is opposite to the aiding information error. When the GNSS data updated at each integer second, the INS error was modified. Hence, the aiding information appeared as a step change, sent to the NCO. But the filter could not percept the step change before the loop updates. Therefore, the step change in the NCO caused the tracking error increase, which was consistent with the testing results.  
The improved structure of INS-aided PLLs is shown in Figure 7. There is a frequency step \(\Delta f_{\text{aid}}\) in the aiding information \(\Delta f_{\text{aid}}\) at each integer second, caused by the modification of INS velocity. To eliminate the impact of the frequency step on PLL tracking, \(\Delta f_{\text{aid}}\) was compensated before the aiding information is sent into the NCO of the PLL. Since the modification of INS velocity is output from the coupled Kalman filter, we can obtain the negative value of the frequency step. Therefore, a negative frequency step \(-\Delta f_{\text{aid}}\) was compensated to the aiding information to eliminate the impact of the frequency step.  
Improved MEMS INS-aided PLLs were realized in our deeply-coupled system and were tested using the scenario in Section 2. Figure 8 shows the tracking errors of original INS-aided PLL and improved INS-aided PLL. Compared to the original INS-aided PLL, the tracking error caused by the INS velocity step was eliminated in the improved INS-aided PLL. Under low dynamics, the tracking error caused by the optimized aiding information was almost equal to zero, which can be ignored. Even when the acceleration was 1000 m/s\({}^{2}\), the tracking error caused by the optimized aiding information was no more than 3\({}^{\circ}\). Therefore, with the MEMS INS aiding, the PLL bandwidth did not need to be widened, and the carrier phase error had little increase under high dynamics.  
Figure 6: The principle of the step change impact on the PLL  
Figure 7: Improved structure of INS-aided PLL.