# An Algorithm to Assist the Robust Filter for Tightly Coupled RTK/INS Navigation System
## 4 Results
### The Performance of the TC RTK/INS Integration with the Improved Outlier Resistance  
#### 4.4.1 Further Analysis of the Shinjuku Dataset  
As excessive robustness is more evident when we process the Shinjuku dataset, we further analyze the positioning results of the Shinjuku dataset. The measurements, along with a lot of noise or multipath error, usually provide low CNR. As the multipath effect generally depends on the environment around the receiver, the fault caused by the multipath effect can persist for some epochs. As mentioned in Section 2.3.3, we only inflate the range-related components in \(R\). Figure 12 illustrates the excluded pseudo-range measurements and the corresponding CNR. If the test statistic exceeds the second threshold of the IGG-III model, which means a significant gross error happens, IGG-III-based RKF will exclude the corresponding measurement. Notably, the exclusion only happens at the current epoch. When it comes to the next epoch, the test statistic should be calculated again to decide whether the gross error still contaminates the corresponding measurement. In Figure 12, the symbols with different colors and shapes represent different satellites. The specific symbol at an epoch means the corresponding satellite is excluded at this epoch. The Y-axis value corresponding to this symbol indicates the CNR of that satellite for that epoch. A line in a specific color at an epoch means the corresponding satellite contributes to the TC RTK/INS integration. Figure 12 shows the CNR of the excluded pseudo-range measurements fluctuates over a wide range. Some pseudo-range measurements with high CNR are directly excluded as outliers. Excessive robustness can happen when RKF incorrectly excludes the measurements that should be retained. The CNR can help RKF detect the fault more reliably. Figure 13 shows the positioning error from the 1720 th epoch to the 1770 th epoch. Excessive robustness happens as the positioning error given by the IGG-based integration can be larger than that given by the integration without the outlier resistance. The turning points are the 1731 st epoch and the 1732 nd epoch, which are marked with two rectangles. Figure 14 illustrates the excluded pseudo-range measurements and the corresponding CNR from the 1720 th epoch to the 1755 th epoch. We use two red rectangles to highlight the excluded measurements at the 1731 st epoch and the 1732 nd epoch corresponding to the turning points in Figure 13. If a symbol with a specific shape appears in the rectangle, the corresponding measurements will be discarded and not contribute to positioning at a certain epoch. In contrast, a line in a certain color in the rectangular means the corresponding measurement is retained for positioning. Figure 14a shows that conventional RKF excludes some potential outlying GPS pseudo-range measurements at both the 1731 st epoch and the 1732 nd epoch. Meanwhile, no BDS pseudo-range measurements are treated as outliers. Figure 12: The excluded pseudo-range measurements and the corresponding CNR. The pseudo range of the 24 th GPS satellites is detected to be faulty for only two epochs, whereas the CNR is around 42 dBHz, which means the signal quality is quite good. Notably, RKF excludes all the pseudo-range measurements at the 1731 st epoch and only excludes the pseudo range of the 24 th GPS satellites at the 1732 nd epoch. We manually control the operation of the outlier exclusion following our proposed algorithm at the 1731 st epoch and the 1732 nd epoch to see the influence. Specifically, we exclude all the pseudo-range measurements at the 1731 st epoch as traditional RKF does and retain the pseudo range of the 24 th GPS satellites at the 1732 nd epoch. Furthermore, we inflate the corresponding components in \(\mathbf{R}\). The results are presented in Figure 15. Figure 15 shows that the manual control based on our proposed algorithm reduces the positioning error when compared to conventional RKF.