# Intelligent Environment-Adaptive GNSS/INS Integrated Positioning with Factor Graph Optimization
## 4 Performance Assessment and Validation
### Experiment Results  
#### 4.2.1 Deep Learning Results  
The training processes for all receivers show convergence, with the final loss being less than 0.1. The stochastic gradient descent method (SGDM) was used to search for optimal learnable parameters and biases that minimize the loss function [47]. The initial learning rate of SGDM was set to \(1\times 10^{-5}\), and after every 400 samples, the learning rate will drop by a factor of 0.5 as summarized in the following Table 3. The prediction and truth result of  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Gyroscope noise term [rad\({}^{2}\)] & \(2.5\times 10^{-5}\) \\ Gyroscope bias term [rad\({}^{2}\)/s\({}^{2}\)] & \(4\times 10^{-11}\) \\ Accelerometer noise term [m\({}^{2}\)/s\({}^{2}\)] & \(6.4\times 10^{-5}\) \\ Accelerometer bias term [m\({}^{2}\)/s\({}^{4}\)] & \(1\times 10^{-5}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: INS noise and bias parameters.  
Figure 5: The anticlockwise ground truth trajectory (green) in Kowloon Bay, Hong Kong. It is separated by breakpoints 1-5 (marked in red) and junctions A, B, and C (marked in yellow). The light, medium, and harsh urban areas are shaded in blue, orange, and purple backgrounds, respectively.  
the 2D error for the three GNSS receivers are shown in Figure 6. The prediction accuracy is indicated by the root mean square error (RMSE), defined by:  
\[RMSE=\sqrt{\frac{1}{N}\Sigma_{i}^{N}(x_{prediction}^{i}-x_{truth}^{i})^{2}}, \tag{28}\]  
where N stands for the total number of calculated epochs and i is the epoch index at which \(x_{prediction}^{i}\) and \(x_{truth}^{i}\) denote the predicted and true uncertainty values.  
The overall evaluation in RMSE has also been summarized in Table 4. The RMSE for Xiaomi data (52.71 m) is the highest, while NovAtel is the lowest (8.78 m) and U-Blox lies in the middle (13.50 m). The main reason may come from the different qualities of the three receivers. Xiaomi has the most and highest noise in the positioning, while NovAtel has the least and U-Blox has the middle level. The CNN model with limited training datasets can hardly generate precise extreme predictions in epochs with occasionally large positioning errors (higher than 100 m). Therefore, the overall RMSE will be elevated for the receiver with more significant noise, especially for the performance of Xiaomi. Nevertheless, the different performance of CNN prediction across the three receivers would differently impact the adaptation quality on solution uncertainty for GNSS/INS integration.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Metrics** & **U-Blox** & **Xiaomi** & **NovAtel** \\ \hline RMSE[m] & 13.50 & 52.71 & 8.78 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Training parameters in the CNN model.  
Figure 6: CNN predicted and true 2D positioning error for the three GNSS receivers. The subplot for the Xiaomi receiver has been zoomed in for better illustration. The highest 2D error for the Xiaomi receiver is around 170 m.  
It is noted that a different total number of epochs exists for the data of three receivers due to the different GNSS availability. This is defined by the ratio between the number of available GNSS epochs (\(N_{GNSS}\) ) and the number of all calculated epochs (\(N_{All}\)), as in the expression:  
\[GNSS\ Availability=\frac{N_{GNSS}}{N_{All}}. \tag{29}\]