**4. Experiment Results**

The road experiments were carried out on a vehicle platform using an INS/GNSS system, as shown in Figure 5. The INS system uses high-precision fiber optic gyroscope and quartz flexible accelerometer that was developed by our group. The GNSS receiver is Ublox NEO-M8T. The sampling frequency of the INS is set to 400 Hz, and the sampling frequency of the GNSS is 10 Hz. RTK GNSS provides the ground truth values. The specific parameters are shown in Table 1. Two typical road experiments were carried out. After the initial alignment, the INS/GNSS was started in a loosely coupled integrated navigation mode. The experimental locations were in Zhejiang Province, China:


**Figure 5.** Data acquisition vehicle platform.

**Table 1.** The parameters of the sensors.


**Figure 6.** The vehicle trajectory in Experiment 1.

In order to verify the performance of the CNN-GRU-CKF that is proposed in our paper, we selected two typical road experiments, Experiment 1 focuses on urban roads, simulating GNSS interruptions by artificially turning off GNSS, while RTK is still working normally and can provide the ground truth of the position for verifying the algorithm accuracy. The GNSS signals interruption duration is 1 min, 3 min, and 5 min, respectively. In order to better reflect the effectivity of the algorithm, the trajectory containing the turn is deliberately chosen. When the GNSS signals are unavailable, the position information that is obtained by CNN-GRU prediction is used instead of the true GNSS information, and the measurement update process of CKF is carried out. Meanwhile, the performance of pure INS, MLP, and GRU is compared.

Due to the short GNSS outage time in the first period, the INS that is based on high precision fiber optic gyro shows high accuracy, as shown in Figures 8 and 9, the position errors in the east and north direction during the 60 s GNSS outage are within 2 m. The horizontal direction error of 60 s outage is shown in Figure 10. It can be seen that when the horizontal error is at its maximum, its east and north errors are not necessarily the maximum. Due to the high accuracy of INS, the overall horizontal error is within 2 m, and the difference between the accuracy of different algorithms is not significant, and the turning point of error dispersion mainly occurs at the vehicle corners. The trajectories during this period are shown in the Figure 11, and it can be seen that the position errors are mainly generated at the corners. The maximum position errors are shown in Table 2. The proposed method in our paper reduces the maximum position error in the east direction by 58.61%, 67.05%, and 63.35% compared to pure INS, MLP, and GRU, respectively. The maximum position error in the north direction is similar, increasing by 4.44% and 12.74% compared

to pure INS and GRU, reducing by 46.34% compared to MLP, and the maximum position in the horizontal direction error is reduced by 16.86%, 45.29%, and 35.34% compared to pure INS, MLP, and GRU, respectively. It can be seen that the accuracy of the RNN is significantly better than that of the MLP.

**Figure 8.** The east position error result of 60 s outage of Experiment 1.

**Figure 9.** The north position error result of 60 s outage of Experiment 1.

**Figure 10.** The horizontal position error result of 60 s outage of Experiment 1.

**Figure 11.** The trajectories of 60 s outage of Experiment 1.


**Table 2.** Maximum position error of 60 s outage of Experiment 1.

Figures 12 and 13 show the position errors of the different algorithms in the east and north directions during the 120 s GNSS outage. It can be seen that the north position error of the pure INS has started to decrease. The horizontal direction error of 180 s outage is shown in Figure 14, and it can be seen that as the GNSS outage time increases to 3 min, the accuracy of the pure INS starts to dissipate, and the MLP method does not perform well, starting to dissipate from around 100 s. The trajectories during this period are shown in Figure 15. The maximum position errors are shown in Table 3. Compared to the pure INS, MLP, and GRU, the proposed method in this paper reduces the maximum position errors in the east direction by 92.00%, 89.95%, and 81.10%, in the north direction by 37.39%, 80.45%, and 56.96%, and in the horizontal direction by 86.66%, 86.08%, and 72.18%.

**Figure 12.** The east position error result of 180 s outage of Experiment 1.

**Figure 13.** The north position error result of 180 s outage of Experiment 1.

**Figure 14.** The horizontal position error result of 180 s outage of Experiment 1.

**Figure 15.** The trajectories of 180 s outage of Experiment 1.


**Table 3.** Maximum position error of 180 s outage of Experiment 1.

Since the GNSS outage time reached 300 s, the model was switched to the fine model when the GNSS outage time increase to more than two minutes. Figures 16 and 17 show the position errors of the different algorithms in the east and north directions during the 300 s GNSS outage. It can be seen that the prediction performance of MLP for the north position error was unsatisfactory, while the effect of the direction that was proposed in our paper is obvious. Horizontal direction error of 300 s outage is shown in Figure 18. It can be seen that as the GNSS outage time increases to 5 min, the accuracy of both the pure INS and the MLP method begin to diverge, while the GRU and CNN-GRU accuracy is better maintained. The trajectories during this period are shown in the Figure 19. The trajectory that is predicted by the method that is proposed in our paper is close to the real trajectory. The maximum position errors are shown in Table 4. Compared to the pure INS, MLP, and GRU, the proposed method in our paper reduces the maximum position errors in the east direction by 93.96%, 77.60%, and 61.27%, in the north direction by 86.34%, 82.87%, and 57.67%, and in the horizontal direction by 93.36%, 84.58%, and 66.81%.

**Figure 16.** The east position error result of 300 s outage of Experiment 1.

**Figure 17.** The north position error result of 300 s outage of Experiment 1.

**Figure 18.** The horizontal position error result of 300 s outage of Experiment 1.

**Figure 19.** The trajectories of 300 s outage of Experiment 1.


**Table 4.** Maximum position error of 300 s outage of Experiment 1.

As shown in Figure 20, Experiment 2 contains five tunnels, with lengths of 1.3 km, 1.7 km, 3.2 km, 5.2 km, and 1.7 km, respectively. The first three sections of the tunnel are closely spaced which is specifically designed to more accurately show the algorithms' effectiveness. As shown in Figure 21, the compensation effect of different algorithms for the first three tunnel sections can be seen. Since RTK cannot obtain position information in the tunnel, we choose the horizontal position error at the end of the tunnel as the evaluation index, and the results are shown in Table 5. Compared with pure INS, MLP, and GRU, the method that was proposed in this paper reduces the average horizontal position error at the end of the tunnel by 66.07%, 59.85%, and 36.50%.

**Figure 20.** The trajectories of Experiment 2.

**Figure 21.** The trajectories of periods #1-3 of Experiment 2.


**Table 5.** Horizontal position error at the end of the different tunnels.

#### **5. Conclusions**

In order to improve the positioning accuracy of integrated INS/GNSS navigation during GNSS outage, our paper proposes a new AI-assisted method. The method consists of two parts: first, CKF is used to provide more accurate positioning results. Then, by building a CNN-GRU network we can predict the position increments during GNSS outage. In the process, the CNN is utilized to quickly extract the multi-dimensional sequence features, and GRU is used to model the time series. In addition, a new real-time training strategy is proposed for practical application scenarios, where the duration of the GNSS outage time and the motion state information of the vehicle are taken into account in the training strategy. The experimental results show that compared with pure INS, MLP, and GRU, the proposed method reduces the maximum position error in the horizontal direction by 93.36%, 84.58%, and 66.81% in the 5 min simulated GNSS disruption experiments compared to the pure INS, MLP, and GRU, respectively. In the real GNSS failure scenario, the average horizontal position error at the end of the tunnel using our method is reduced by 66.07%, 59.85%, and 36.50%. The algorithm can provide real-time high-precision navigation results with high efficiency and has a good reduction effect on the error dispersion that is caused by prolonged GNSS failure.

**Author Contributions:** Methodology, writing—original draft preparation, software, S.Z.; Investigation, writing—reviewing and editing, Y.Z.; Supervision, conceptualization, T.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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