# An Algorithm to Assist the Robust Filter for Tightly Coupled RTK/INS Navigation System
## 4 Results
### The Performance of the TC RTK/INS Integration without the Outlier Resistance  
This section introduces the performance of the TC RTK/INS integration without the outlier resistance. Firstly, we present the availability of GNSS measurements. We compare the DD measurements with the INS-based DD ranges to calculate the residuals in our implementation. The corresponding DD measurement will be discarded if the residuals exceed the empirical threshold. Both RTKLIB and GINAV adopt the same strategy to preprocess the measurements. Figure 6 illustrates the number of preprocessed DD measurements, which equals the dimension of the measurement vector of EKF. As a time-dependent plot over 1000 epochs does not reveal much, we use a histogram to visualize the statistical data. Figure 6 is a histogram that shows the distribution of the occurrence of the measurement number over two datasets. The X-axis in Figure 6 reflects the number of measurements, whereas the Y-axis reflects the number of epochs when the same number of measurements is valid. Figure 6 shows that the number of valid DD measurements in both datasets can be small or even zero. In such cases, RTK can occasionally fail to provide positioning results, which means a GNSS outage can happen. The TC RTK/INS integration can help bridge the outage. The INS drift can be suppressed in TC integration as long as the number of measurements is not zero. Otherwise, the INS solution can be output as the positioning results. As a result, the TC RTK/INS integration can provide more continuous positioning results when compared to RTK. Furthermore, as we mentioned in the Introduction part, the fixed rate and the positioning accuracy can benefit from the TC integration. However, the bullying measurements can degrade the performance of the TC integration. The datasets are collected in harsh urban areas, which means gross errors frequently occur in GNSS measurements. Figures 7 and 8 show the performance comparison between RTK and the integration without the outlier resistance. Figures 7a,b show the epochs when valid positioning results are provided. In Figures 7a,b, a cycle with a specific color means the specific algorithm can provide a valid positioning result at the corresponding epoch. The local results in the red rectangles are highlighted in the subfigures. In the subfigures, the circles associated with RTK are sparser compared to those associated with the TC RTK/INS integration. Figures 7c,d illustrate the number of epochs in which each algorithm can provide valid positioning results and the number of epochs in which each algorithm cannot provide valid positioning results. Accordingly, Figure 7 demonstrates that the TC RTK/INS integration can provide valid positioning results at every epoch whereas RTK fails to output  
Figure 5: The solution visualization. positioning results from time to time, which means the integration's positioning continuity is improved. Figure 8 shows the positioning error in meters. In Figure 8, the \"TC/EKF\" legend denotes the results provided by the TC RTK/INS integration without IGG-based outlier resistance. Figure 8a,b show that the positioning results given by the TC RTK/INS integration are smoother than that given by RTK. There are some large jumps in RTK results, which means gross errors contaminate the measurements and lead to big positioning errors. The introduction of INS reduces the magnitude of the unnormal jumps, which means the integration suppresses the influence of outlying measurements. The integration benefits from the high short-term accuracy of INS, which mitigates the effects of some sudden gross errors. However, the positioning accuracy of the TC RTK/INS integration is not satisfying. At many epochs, the positioning errors provided by the integration are larger than those given by RTK. Figure 6: The number distribution of preprocessed DD measurements. Figure 7: _Cont_. In Figure 8a,b, the dots representing the positioning results are too dense, which causes some inconvenience to the visualization.