## 5 Results
### SLAM Trajectory Experiment
#### 5.2.2 Experimental Environment Configuration and Parameter Setting  
The hardware configuration for the experiment is as follows: AMD Ryzen 7 5800H processor (USA), NVIDIA GeForce 3060 6 GB GPU, 16 GB RAM, and 64-bit Ubuntu 18.04 operating system. The experimental parameters are set according to the TUM1.yaml file of ORB-SLAM2. The PE-match parameters are mostly consistent with the settings in Section 5.1.2, with the number of coarse matching point pairs involved in fitness calculation (denoted as \"_j_\") adjusted to 50. The iteration stops and outputs the optimal fundamental matrix when there is no significant change in \(Gbest_{i}\) within 6 iterations. Such parameter adjustments are made with the consideration of reducing the time consumption of PE-match in the PE-SLAM system to free up time for backend optimization, meaning that PE-SLAM aims to improve the accuracy of the motion model while minimizing any negative impact on the effectiveness of the backend optimization.  
The TUM dataset provides real camera motion trajectory information, which is used to evaluate the trajectory information obtained by algorithms against the ground truth trajectory. The evaluation metrics include absolute trajectory error (ATE) and relative pose error (RPE). ATE represents the direct difference between estimated and ground truth poses, reflecting the trajectory consistency at a global level. RPE measures the local accuracy of the trajectory within fixed time intervals, corresponding to trajectory drift.  
The root mean square error (RMSE) is used to reflect ATE, with \(trans(F_{i})\) representing the translation part, written as follows:  
\[RMSE(F_{1:n}):=\left(\frac{1}{n}\sum_{i=1}^{n}trans(F_{i})^{2}\right)^{\frac{ 1}{2}} \tag{12}\]  
\[F_{i}:=Q_{i}^{-1}SP_{i} \tag{13}\]  
In the formula, \(Q_{i}\) represents the estimated pose of the \(i\)-th frame, \(P_{i}\) represents the real pose of the \(i\)-th frame, \(F_{i}\) represents the absolute trajectory error of the \(i\)-th frame, and \(S\) is the scale conversion matrix.  
Given the known time interval \(\triangle\) and the total number of image frames \(n\), it is possible to calculate \(m=n-\triangle\) RPEs, with the RMSE defined as follows:  
\[RMSE(E_{1:n},\triangle):=\left(\frac{1}{m}\sum_{i=1}^{m}trans(E_{i})^{2}\right) ^{\frac{1}{2}} \tag{14}\]  
\[E_{i}:=\left(Q_{i}^{-1}Q_{i+\triangle}\right)^{-1}\left(P_{i}^{-1}P_{i+ \triangle}\right) \tag{15}\]  
In the formula: \(Q_{i}\) represents the estimated pose of the \(i\)-th frame, \(P_{i}\) represents the true pose of the \(i\)-th frame, and \(E_{i}\) represents the relative pose error of the \(i\)-th frame.  
Due to the fact that various modules of ORB-SLAM2 and PE-SLAM, such as target detection, tracking, backend optimization, and mapping are independent threads, the most time-consuming among them is the tracking thread. The speed of the tracking thread determines the system processing speed. Additionally, since the backend optimization occurs between the tracking and the arrival of the next frame, its effectiveness is not only dependent on the tracking thread's performance but also on tracking time consumption. Moreover, PE-SLAM has made improvements to the motion model of ORB-SLAM2. Considering these factors, a tracking time evaluation algorithm is adopted to assess the real-time performance comprehensively.