# Opportunistic In-Flight INS Alignment Using LEO Satellites and a Rotatory IMU Platform
## 6 Conclusions  
LEO-SOPs with a wide-carrier frequency rage, a number of satellites, and an orbit time are somehow known as free infrastructures for augmenting the outdoor navigation systems in non-GNSS environments. The use of pseudorange rate measurements of downlink signals propagated from Iridium-Next and Orbcomn constellations are popularly investigated in many previous works, although most of them showed the navigation performance in short-term experiments. In this study, a regular LEO-based Doppler positioning method was used as a slave EKF estimator to calibrate the INS system. The error state space model of the INS was presented as a master system. In parallel, two EKFs were presented in the proposed method. At first, the slave EKF estimates the position of the vehicle by fusing the pseudorange rate measurements obtained from the receiver. By comparing the positions of the master and the slave systems, the error measurements were provided for the INS  
Figure 17: (**a**) Estimated accelerometer bias, and (**b**) Estimated gyroscope bias with \(\pm 3\sigma\) bound.  
Figure 18: Estimated attitude of the aircraft with \(\pm 3\sigma\) bound.  
alignment model. This system calculated all the errors of the INS system including IMU biases and errors of the position, the velocity, and the attitude. As the alignment model was not completely observable, the observability rank of the system was increased by rotation of the IMU in a special sequence. The observability rank of the calibration model was enhanced to 14 out of 15 states.  
Two experiments were planned to examine the proposed method. The receiver, antenna, front-ends, IMU, and other equipment were installed one time on the ground and the next time on a flight vehicle. A special 2-min trajectory for the ground experiment and a 10-min air path for the flight test were selected. The final accuracy of the ground test reached 12.234 m, which showed a significant improvement compared to the stand-alone INS. The results of the flight test were demonstrated in different time periods. It helped us to track the accuracy of the proposed method by time. It could also measure the robustness of each algorithm. The accuracy of the alignment method in the first 150 s increased by around 60% compared to the Doppler positioning method. The method showed a RMSE of around 197 m, which advanced around 180% for the entire trajectory.  
Conceptualization, F.F. and H.B.; methodology, F.F.; software, F.F. and H.B.; validation, F.F.; formal analysis, F.F.; investigation, F.F. and H.B.; resources, F.F. and H.B.; data curation, F.F.; writing--original draft preparation, F.F.; writing--review and editing, F.F.; visualization, F.F.; supervision, R.L.J.; project administration, R.L.J. and H.B.; funding acquisition, R.L.J. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
We appreciate all the LASSENA team members who supported this project by gathering data and assisting during the outdoor experiments. We also offer special thanks to [PERSON], the manager and supervisor of the LASSENA laboratory, for his kind support and encouragement.  
The authors declare no conflict of interest.