# 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
#### 4.4.2 The Performance of MRKF  
This section introduces the performance of the TC RTK/INS integration with improved outlier resistance. We use MRKF to denote our proposed CNR-assisting algorithm to distinguish it from the traditional IGG-based RKF. As mentioned in Section 2.6, MRKF can be divided into the CNR-based classification and the constraints. The CNR-based classification aims to suppress excessive robustness, whereas the constraints reduce the probability of incorrectly retaining true outliers. Figure 16 illustrates the performance of MRKF with and without the constraints. Figure 16a,b both show that the positioning accuracy is improved around the 1500 th epoch and the 1730 th epoch. The CNR-based classification maintains some measurements that are incorrectly identified as outliers, which reduces the effects of excessive robustness and provides more accurate positioning results. In Figure 16a, there are two time periods when the positioning errors given by MRKF without the constraints are larger than those given by RKF, which means some outliers are retained incorrectly because of high CNR. Figure 16b shows that the constraints eliminate improper maintenance. As the dots denoting positioning results in Figure 16 are too dense, we use a box plot to visualize the distribution of the positioning error to compare TC/EKF, TC/RKF, and TC/MRKF, as shown in Figure 17. In Figure 17, each group contains 200 results. The boxes of Group 8 and Group 9 are related to the positioning error results from the 1400 th epoch to the 1800 th epoch in Figure 16b. The boxes of Group 8 and Group 9 show that MRKF significantly reduces the first quartile, median, and third quartile values compared to RKF, which shows MRKF generally provides more accurate positioning results when compared to RKF during the corresponding period. Overall, RKF either outperforms or performs comparably to RKF for all the groups. Figure 18 shows the positioning error in three dimensions. Notably, Figure 18 shows the positioning error and not the absolute value of the error as in Figure 16. Figures 16 and 18 qualitatively show the combination of the CNR-based classification and the constraints can improve the positioning accuracy reliably. We calculate the RMSE of RKF and MRKF in three dimensions and total. The statistics are presented in Table 6. Table 6 and Figure 18 also contain the results given by RTK and the TC RTK/INS integra  
Figure 15: The comparison between the performances with and without the manual control. Figure 10 shows that evident excessive robustness happens in the Shinjuku dataset, whereas no apparent excessive robustness happens in the Odaiba dataset. We test the performance of MRKF on the Odaiba dataset to see whether our proposed algorithm will degrade when processing datasets without evident excessive robustness. The results are based on the same CNR thresholds as those used when processing the Shinjuku dataset. Figure 19 illustrates the positioning error in three dimensions. Figure 20 compares the total positioning error given by three algorithms at each epoch. Figure 20 is a box plot that visualizes the distribution of the positioning error for each group. In Figure 20, each group contains 120 positioning results. Figure 20 shows the positioning error of RKF and MRKF is essentially the same at each epoch, whereas Figure 20 shows that the error distribution for each group is essentially the same. Figure 20 illustrates that MRKF performs comparably to RKF for the Odaiba dataset. Table 7 shows the quantitative analysis for the Odaiba dataset. Figures 19 and 20 and Table 7 show that the positioning accuracy is essentially the same for RKF and MRKF. These facts say that MRKF will not reduce positioning accuracy when processing datasets where no evident excessive robustness happens. Tests on the Shinjuku and Odaiba datasets verify our proposed algorithm's validity and feasibility in using CNR to assist traditional RKF. Figure 18: The position error in three dimensions (Shinjuku).