5.3.2. EKF- and RTSS-estimated results

The EKF-estimated PIG navigation system result is shown in Figure 11 by the blue trajectory. It only utilizes the forward velocity provided by the odometers and also the PIG NHCs updates to reduce the system error. The maximum position error of the blue trajectory is 18.93 m in the eighth landmark, and meanwhile, the corresponding mean error is 10.86 m. Meanwhile, the azimuth and pitch errors correction in each SPS of the PIG navigation system is provided by the PJ detection result. And the EKF/PJ-estimated PIG navigation system is shown in Figure 11 with yellow trajectory. The maximum position error of yellow trajectory is 8.75 m in the eighth landmark, and the corresponding mean error is 4.96 m. So, the mean error of PIG navigation system improves 54.328% at all eight landmarks after adding the azimuth and pitch errors correction by EKF/PJ estimation. However, the position precision of EKF estimation technique on micro-inertial sensors still cannot fulfill the precision requirements of PIG navigation system when the azimuth and pitch errors correction are added in SPS. Fortunately, the RTSS offline estimation technology can be used to improve the position precision of the PIG navigation system once after the EKF estimated result.

In Figure 12, the blue curve denotes the trajectory of EKF- and RTSS-estimated PIG navigation system with 3D continuous velocity error and 3D coordinate correction at the starting point. The maximum position error of blue trajectory at the fifth landmark is 6.62 m, and the corresponding mean error is 3.73 m. In addition, the PJ-identified azimuth and pitch errors correction at the SPS is also utilized to improve the position precision of PIG navigation

Figure 11. The trajectories of EKF-estimated PIG navigation system.

system. The yellow trajectory is the result of the EKF/PJ/RTSS-estimated PIG navigation system. The maximum position error of blue trajectory is 3.08 m at the fifth landmark, and the corresponding mean error is 1.70 m. Therefore, the mean error of PIG navigation system at the overall eight landmarks improves 54.42% after adding azimuth and pitch errors correction with EKF/RTSS estimation technology.

Subsequently, the statistic results of PIG navigation system errors at all eight landmarks that are optimized by EKF, EKF/PJ, EKF/RTSS, and EKF/PJ/RTSS are listed in Table 1. Specifically, the second column is position errors of PIG navigation system estimated by EKF when it is compared with the referenced eight landmarks. The position errors are increased with the PIG traveling distance from 1.96 m at first landmark to 18.93 m at last landmark. Then, the third

Figure 12. The trajectories of EKF/RTSS-estimated PIG navigation system.


Table 1. The statistic result of PIG navigation system error.

Figure 13. The errors of PIG navigation system by various optimization methods.

column is position errors of PIG navigation system that is estimated by EKF/PJ when it is compared with the referenced eight landmarks. The position errors are increased with the PIG traveling distance from 0.76 m at first landmark to 8.75 m at last landmark. In addition, the fourth and fifth columns of Table 1 denote position errors of PIG navigation system when it is referenced to all eight landmarks that are estimated by EKF/RTSS and EKF/RTSS/PJ techniques. The maximum errors estimated by EKF/RTSS and EKF/RTSS/PJ are 6.62 and 3.08 m at the fifth landmark that has the longest distance from the start point or coordinate update point. This is mainly because of the inverse correction by RTSS, which reduces the position error of PIG navigation system when the trajectory is close to the coordinate update points. Therefore, both the maximum error and mean error are improved by the RTSS estimation technique.

More intuitively, both the maximum and mean errors of the PIG navigation system estimated by EKF, EKF/PJ, EKF/RTSS, and EKF/PJ/RTSS are shown by column chart in Figure 13. Both maximum and mean errors are improved greatly when adding the PJ detection result and the RTSS estimation technique.

### 6. Conclusions

This chapter presents a micro-inertial-aided high-precision positioning method for smalldiameter PIG navigation, which is based on the micro-inertial/AGM/odometer/PJ PIG navigation system. Apart from the previous 3D continuous velocity updates from odometers and NHCs and the 3D sporadic coordinate updates from AGMs, the proposed micro-inertial/ AGM/odometer/PJ-based PIG navigation system also adds continuous azimuth and pitch error correction in each SPS to reduce the divergent SINS-error-induced PIG navigation error. Furthermore, an indoor-Husky-robot-simulated PIG experiment is implemented to testify the performance of the PJ detection result on PIG navigation system, and the mean error of PIG navigation system improved 54.42% after adding azimuth and pitch errors correction by EKF/ RTSS estimation technique.
