# Opportunistic In-Flight INS Alignment Using LEO Satellites and a Rotatory IMU Platform
## 5 Experimental Evaluation and Results
### Experimental Results and Discussion  
#### 5.3.1 Ground Experiment  
The mentioned hardware and software equipment was installed on a ground vehicle, and the experiment was done in a pre-selected route with 166 s duration. The EKF-based slave model was injected using the pseudorange rate measurements of two satellites from the two different constellations (Orbcomm and Iridium-NEXT) given by the receiver. The slave system also utilized the position and velocity of both satellites obtained from the downloaded TLE files. Additionally, the GPS was used to initialize the system and record the reference position track. The true reference orientation was also recorded by the AHRS module of the VN100-Rugged IMU. The initial covariance matrices were defined as \(P_{X}(0|0)=diag\big{[}10^{-4}.I_{4\times 4},10^{-2}.I_{6\times 6},10,2 \big{]}\), for the slave EKF system, and \(P_{X}(0|0)=diag\big{[}10^{-10}.I_{3\times 3},10^{-6}.I_{6\times 6},10^{-2}.I_{3 \times 3},10^{-3}.I_{3\times 3}\big{]}\) for the KF alignment system, where, \(I\) is the identity matrix. In the receiver's model, a typical temperature-compensated crystal oscillator (TCXO) was considered, with coefficient values \(\{h_{0,r},h_{-2,r}\}=\{9.4\times 10^{-21},3.8\times 10^{-21}\}\).  
Figure 10 demonstrates the comparison of the reference and estimated AV's orientation obtained from the proposed alignment and positioning algorithm. The mean square error (MSE) for the roll, pitch, and heading angles during the experiment were obtained as \(2.0234^{\circ}\), \(1.9764^{\circ}\), and \(22.1529^{\circ}\), respectively. Furthermore, Figure 11 shows the attitude errors. It was obvious that the highest attitude error was for the heading angle, while it diverged gradually by time. In this case, cutting off the GNSS had a significant effect on the heading drift; moreover, attitude calibration using the proposed SOP-based method could  
Figure 9: (a) 3D Earth representation of the overhead Iridium-Next satellites. (b) Doppler shift curve tracked by the receiver.  
bound the roll and pitch errors with higher precision. Figure 12 represents the estimated velocity of the AV during the experiment, visualized in the local navigation frame.  
The receiver's clock errors were estimated for the typical TCXO using the slave system, as depicted in Figure 13. The clock error parameters were increased after a downward peak, which is caused by the satellite's pass. The clock bias reached its highest value, at about 300 m, and the clock drift culminated at around 1.5 m/s. Figure 14 shows the final 2-D position results plotted on the geographical map with latitude and longitude axes. The results prove that the proposed alignment method was able to bound the stand-alone INS. On the other hand, the INS was well-calibrated using the pseudorange rate measurements of the LEO satellites and the observability enhancement method based on the IMU rotation. The proposed method showed the root mean square (RMS) error of 12.234 m in the entire trajectory, which is a significant advance compared to the stand-alone INS mode. The end-to-end error in the INS mode was also about 245.23 m, while this error after performing the proposed alignment method decreased to a mere 9.2 m.  
Figure 11: The orientation error for (**a**) roll angle, (**b**) pitch angle, and (**c**) heading.  
Figure 12: The estimated velocity of the ground vehicle for the North and East axes.  
Figure 10: The estimated and reference orientation of the ground vehicle for (**a**) roll angle, (**b**) pitch angle, and (**c**) heading.