# Sample-Wise Aiding in GPS/INS Ultra-Tight Integration for High-Dynamic, High-Precision Tracking
## 4 Test Results and Discussion
### Aiding Effects on Code/Carrier Phase Errors with a C/N\({}_{0}\) of 80 dB-Hz  
The carrier tracking loop is usually the weak link in a receiver and the carrier phase error characterizes the receiver dynamic performance. For the traditionally-aided receiver tracking in high dynamic conditions, however, the code tracking loop may also become the dynamically weak part since the DLL has a narrower bandwidth and a longer integration time and sometimes a narrow correlator spacing for the sake of noise and interference suppression. Both the carrier phase error and the code phase error are concerned in this subsection. The signal C/N\({}_{0}\) is configured to be 80 dB-Hz in the test for the following two reasons: (1) the 1\(\sigma\) thermal noise code tracking jitter is about 0.0059 m under 80 dB-Hz and a narrow correlator spacing of 0.1 chip. If the C/N\({}_{0}\) is set too low, all the test results of the aided receiver will be buried in the thermal noise jitter; and (2) one job in the future is to experiment based on a RF (radio frequency) signal simulator and a RF signal collection device, where the 80 dB-Hz C/N\({}_{0}\) has already been achieved at RF level using a single-SV scenario [31].  
Figures 11-13 show the test results of the traditional aiding method and the sample-wise method with user dynamics of 5 g, 50 g and 500 g, respectively. Figure 14 summarizes the standard deviations of carrier tracking errors and code tracking errors of the two aiding methods in the test results. For comparison, Figure 14 also shows the theoretical values of the thermal noise floors at 80 dB-Hz and 45 dB-Hz (in normal signal conditions) as well as the theoretical values of the total 1\(\sigma\) errors at 80 dB-Hz (including contributions from both the dynamic stress and the thermal noise) for the traditional aiding method.  
Figure 11: Tracking errors with 5 g dynamics and 80 dB-Hz C/N\({}_{0}\). (**a**) Carrier phase error; (**b**) Code phase error.  
Figure 12: Tracking errors with 50 g dynamics and 80 dB-Hz C/N\({}_{0}\). (**a**) Carrier phase error; (**b**) Code phase error.  
It can be seen that: (1) under a high C/N\({}_{0}\) of 80 dB-Hz the dynamic stress error remains the main error source in all the traditional aiding results, and the total carrier phase errors becomes much closer to the test results in last subsection with the dynamics increasing; whereas all the sample-wise aiding results are dominated by the thermal noise jitters; and (2) although the dynamic stress errors can be significantly reduced by traditional Doppler aiding, they can still become dominant in carrier phase errors when the dynamics go higher than 3400 m/s\({}^{2}\), and dominant in code phase errors when the dynamics go higher than 390 m/s\({}^{2}\) under a normal C/N\({}_{0}\) of 45 dB-Hz. As a contrast, the tracking errors remain almost the same values near the noise floor with the increase of user dynamics when using sample-wise aiding, which indicates that the dynamic stress errors have been almost completely eliminated by the sample-wise Doppler-aided receiver.