## 8 PCI for Modeling Azimuth Errors  
While using the low-cost MEMS-based inertial sensors, the application of KF linear error models with stationary white Gaussian noise for error state estimation can lead to quick deterioration of the navigation solution during GNSS outages due to their composite  
Figure 8: Schematic diagram of the Kalman filter for RISS/GNSS Integration. Figure 7: Kalman filter cycle. error characteristics. For RISS, residual azimuth errors after KF prediction of the linear part of these errors were the principal cause for the deterioration of the solution. PCI, a system identification technique that can be utilized to model the residual azimuth errors, can overcome the limitation of Kalman for RISS/GNSS integration and can increase the performance. When GNSS is available, KF is employed to perform RISS/GNSS integration. In parallel, as a background routine, the prediction of the KF azimuth is used together with mechanization results and the GNSS aiding azimuth to derive the true non-linear residual error of the azimuth. The block diagram that shows RISS/GNSS integration and includes the identification of the non-linear azimuth error by PCI is shown in Figure 9. The training data provided the reference output to construct the azimuth residual non-linear error PCI model. Moreover, the KF sent azimuth predictions to PCI as the input to build the model. The input and output system dynamics help to identify non-linear errors, and the algorithm can then achieve a residual non-linear azimuth error model. When less than four satellites are visible, GNSS outage occurs, as a loosely coupled architecture is used. When there is a GNSS outage, the identified parallel cascade will be utilized to predict the azimuth errors (residual and non-linear) from the KF prediction for the linear azimuth error. After correction, the azimuth angle is passed to the new mechanization shown in Figure 10 to calculate the corrected position and velocity. A road test trajectory using ultra-low-cost ADI IMU and the low-cost Trimble Lassen SQ GNSS receiver was conducted in Kingston, ON, Canada, for nearly 2000 s. The NovAtel ProPak-G2-Plus combines a GNSS receiver, and the Honeywell HG1700 IMU via SPAN technology is used as a reference navigation solution. The specifications of the utilized IMUs can be found in Table 1.  
Figure 10: Loosely coupled KF-PCI technique during the GNSS outage. Figure 9: Loosely coupled KF-PCI technique during GNSS availability. The errors of KF-PCI and KF-only solutions were compared with respect to the NovAtel reference solution. The comparison of KF-PCI and KF-only solutions for RISS/GNSS integration is presented in Table 2. The system identification technique PCI, along with KF, was able to model and diminish the residual and non-linear errors in the azimuth and improved the results for eight simulated GNSS outages by 77.91%. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**IMUs** & **ADI** & **HG1700 IMU** & **IMU-CPT** \\  & **(100 HZ)** & **(100 HZ)** & **(100 HZ)** \\ \hline Size (cm\({}^{3}\)) & 7.62 \(\times\) 9.53 \(\times\) 3.2 & 19.3 \(\times\) 16.7 \(\times\) 100 & 15.2 \(\times\) 16.8\(\times\) 8.9 \\ Weight & 0.59 Kg & 3.4 Kg & 2.28 Kg \\ Max data rate & 100 Hz & 100 Hz & 100 Hz \\ Start-up time & \textless{}1 s & \textless{}5 s & \textless{}5 s \\ \hline Accelerometer & & & \\ \hline Range & \(\pm\)5 g & \(\pm\)50 g & \(\pm\)10 g \\ Bias instability & \(\pm\)6 mg & \(\pm\)1 mg & \(\pm\)0.75 mg \\ Scale factor & \textless{}0.2\%, 1 \(\sigma\) & 300 ppm, 1\(\sigma\) & 300 ppm, 1 \(\sigma\) \\ \hline Gyroscope & & & \\ \hline Range & \(\pm\)150 \({}^{\circ}\)/s & \(\pm\)1000 \({}^{\circ}\)/s & \(\pm\)375 \({}^{\circ}\)/s \\ Bias instability & \textless{}\(\pm\)0.5 \({}^{\circ}\)/s & 1.0 \({}^{\circ}\)/h & \(\pm\)1.0 \({}^{\circ}\)/h \\ Scale factor & \textless{}0.1 \%, 1\(\sigma\) & 150 ppm, 1\(\sigma\) & 1500 ppm, 1 \(\sigma\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Performance characteristics of imus.