## 9 PCI for Enhancing KF Based Tightly-Coupled Navigation Solution  
For loosely coupled integration, a clear line-of-sight between the receiver and no less than four satellites is considered a prerequisite to provide position, velocity, and timing aiding. The signals transmitted by the GNSS satellites can suffer from frequent interference and signal blockage in urban canyons and thick foliage where an uninterrupted clear view of the sky for the receiver is not presumable. Tightly coupled integration using the 3D reduced inertial sensor system is a better choice in challenging GNSS scenarios, especially when the number of visible satellites is three or less, as it can provide GNSS aiding. However, errors of pseudoranges measured by the GNSS receiver used as aiding in the RISS/GNSS integrated solution will affect the overall positioning accuracy. This section of the paper explores the benefits of using PCI, a system identification technique for modeling residual pseudorange correlated errors that can be utilized by a KF-based tightly-coupled RISS/GNSS navigational solution. PCI can improve the overall navigation solution by modeling residual pseudorange correlated errors to be used by a KF-based tightly-coupled RISS/GNSS navigational solution, as shown in Figure 12.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Outage No.**} & \multirow{2}{*}{**Outage Dur. (s)**} & \multicolumn{2}{c}{**RMS Error in Position (Meter)**} \\ \cline{3-4}  & & **KF** & **KF-PCI** \\ \hline
1 & 120 & 20.3 & 11.1 \\ \hline
2 & 120 & 10.7 & 6.3 \\ \hline
3 & 120 & 17.6 & 8.8 \\ \hline
4 & 120 & 17.8 & 7.9 \\ \hline
5 & 120 & 35.9 & 10.9 \\ \hline
6 & 120 & 84.2 & 8.5 \\ \hline
7 & 120 & 62.9 & 16.5 \\ \hline
8 & 120 & 91.4 & 7.9 \\ \hline \multicolumn{4}{c}{Average} & 42.6 & 9.7 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Two-dimensional position rms-error comparison.  
Figure 12: Block diagram of non-linear system identification to model the pseudoranges during GNSS availability using tightly coupled KF.  
When less than four satellites are visible, the PCI model for the visible satellites is utilized to estimate the residual pseudorange errors for these satellites, and the corrected pseudorange value is provided to the KF, as shown in Figure 13.  
Around a 3000 s long trajectory was considered to check the validity of the proposed technique. It started at the Royal Military College of Canada, covering the major roads in the city of Kingston. Six 60 s GNSS outages were introduced in post-processing during good GNSS availability, as shown in Figure 14 on the map as blue circles.  
The trajectory was tested by partial outages having 3, 2, 1, and 0 visible satellites, respectively. The errors estimated by KF-PCI and KF-only solutions for RISS/GNSS integration were evaluated with respect to the NovAtel reference solution. Table 3 shows the average RMS position errors in meters.  
Figure 14: Road test trajectory and circles indicate the approximate locations of 60 s GNSS outages.  
Figure 13: Tightly coupled KF-PCI technique during partial GNSS outage.  
The most significant performance of the PCI build model for pseudoranges error corrections was observed when three satellites were available since three corrected ranges served the tightly coupled solution, offering the highest effect. For RMS position errors, the performance enhancement of the KF-PCI over KF-only solution was 38.68%. The contributions of pseudorange error corrections using PCI continue to diminish for the cases of two satellites and one satellite. For RMS position errors, the improvement using the proposed PCI model reduced to 16.48% for KF-PCI over KF-only for two-satellite cases. There was no improvement using the proposed PCI model for one-satellite cases. No corrections were available for the PCI build model for pseudorange errors in the case of zero satellites, and the solutions provided by KF-PCI and the traditional KF were equivalent.