# 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 Outlier Resistance  
Our implementation uses the IGG-III model to inflate the noise covariance matrix components, which can suppress the influence of the outlying measurements. As mentioned in Section 2.3.3, the outlying measurements will be discarded if the corresponding inflation factor is too large. This section introduces the performance of the TC RTK/INS integration with the IGG-III model. Firstly, we present the effects of the IGG-III model on the measurements involved in the TC RTK/INS integration. We use Figure 9 to show in which epochs the outlier exclusion happens and how many measurements are excluded. We subtract the number of measurements after the IGG-based outlier exclusion from that before the outlier exclusion and plot the results in Figure 9. A zero-value subtraction result at an epoch means no outlier exclusion happens at the epoch. In contrast, the outlier exclusion happens, and the value equals the number of the excluded measurements. Notably, the difference results will not fall below zero, as the number of measurements after the outlier exclusion cannot exceed that before the outlier exclusion. Figure 9 illustrates the number difference between valid DD measurements before and after the outlier exclusion. Figure 9 shows that some measurements are regarded as significant outliers and excluded at some epochs, which demonstrates that the IGG-III model plays a role in discarding some potential outlying measurements. Figure 9: The number of the excluded measurements. The integration based on the IGG-III model can provide more accurate positioning results when compared to the integration without the outlier resistance. Notably, the introduction of the IGG-III model will not degrade the positioning continuity, which means the integration based on the IGG-III model can provide positioning results during the RTK outage like the integration without the outlier resistance. So, we will not use a figure like Figure 7 to illustrate the positioning continuity of the IGG-based integration. Figure 10 shows the positioning performance comparison between the integration with and without the outlier resistance. Notably, we use RKF to denote the TC RTK/INS integration with the IGG-based outlier resistance. Figure 10 shows the positioning errors in meters. As Figure 10 can provide a qualitative description, we calculate the positioning deviations for the two datasets to quantitatively analyze the positioning performances. Every epoch, we calculate the difference between the positioning result given by different algorithms and the corresponding one given by the reference. Then, we sum up these differences to calculate the RMSE for a dataset. Tables 4 and 5 show the statistics. For each dataset, we count the total number of epochs between the completion of the initial alignment and termination. Then, we count the number of epochs for which the algorithm can provide positioning results. The ratio of the latter to the former demonstrates the continuity of the algorithm. Tables 4 and 5 show the TC RTK/INS integration can bridge the RTK outage. Furthermore, the fixed rate benefits from the introduction of INS obviously, whereas the adoption of the IGG-III model brings a slight increase. On the whole, the positioning accuracy of the integration without the outlier resistance is not significantly better than that of RTK or it is even worse. In contrast, the IGG-III model improves the positioning accuracy significantly. Figure 10 and the tables show that the positioning errors given by the IGG-based integration are smaller than those given by the integration without the outlier resistance in general. Comparing Figures 9 and 10, we can see that the epochs with significantly improved positioning accuracy correspond to those in which some potential outlying measurements are discarded, which proves the validity of the IGG-based integration.