# Underwater SLAM Meets Deep Learning: Challenges, Multi-Sensor Integration, and Future Directions
## 8 Underwater SLAM Systems Evaluation and Comparison
### Localization Evaluation
#### 8.2.1 Traditional SLAM Metrics  
Standard metrics used to evaluate SLAM performance include absolute pose error (APE) [155], which measures the difference between the estimated position and the ground truth; relative pose error (RPE), which evaluates the error relative to the actual position [156]; root mean squared error (RMSE) [155], which provides an aggregate measure of the errors over all \(N\) instances; and absolute trajectory error (ATE) [156]. All position vectors are measured in meters unless otherwise specified. Traditional SLAM metrics provide quantitative insights into system performance, enabling: accuracy assessment, error propagation analysis, and comparative evaluation.  
**Absolute Pose Error:**  
\[APE=\left\|\mathbf{p}_{\text{Pred}}-\mathbf{p}_{\text{true}}\right\| \tag{3}\]  
where  
- \(\mathbf{p}_{\text{pred}}\) is the predicted position vector;  
- \(\mathbf{p}_{\text{true}}\) is the true position vector;  
- \(\|\cdot\|\) denotes the Euclidean norm.  
This metric provides direct insight into the accuracy of the SLAM system's instantaneous pose estimates.  
**Relative Pose Error:**  
\[RPE=\frac{\left\|\mathbf{p}_{\text{Pred}}-\mathbf{p}_{\text{true}}\right\|}{ \left\|\mathbf{p}_{\text{true}}\right\|} \tag{4}\]  
This metric calculates the error relative to the magnitude of the actual position, providing a normalized measure of performance that is dimensionless.  
**Root Mean Squared Error:**  
\[RMSE=\sqrt{\frac{1}{N}\sum_{i=1}^{N}\left\|\mathbf{p}_{\text{pred}}^{(i)}- \mathbf{p}_{\text{true}}^{(i)}\right\|^{2}} \tag{5}\]  
where  
- \(N\) is the total number of samples;  
- \(\mathbf{p}_{\text{pred}}^{(i)}\) and \(\mathbf{p}_{\text{true}}^{(i)}\) are the predicted and true positions at instance \(i\).  
RMSE provides an aggregate measure of the errors over all instances, with larger errors having a more significant impact due to the squaring operation.  
**Absolute Trajectory Error:**  
\[ATE_{RMSE}=\sqrt{\frac{1}{N}\sum_{i=1}^{N}\left\|\mathbf{T}_{\text{pred}}^{(i)}- \mathbf{T}_{\text{true}}^{(i)}\right\|^{2}} \tag{6}\]  
where  
- \(\mathbf{T}_{\text{pred}}^{(i)}\) and \(\mathbf{T}_{\text{true}}^{(i)}\) are the predicted and actual poses (including both position and orientation) at instance \(i\).  
ATE measures the difference between the estimated and ground truth trajectories over time, providing a global sense of the SLAM system's accuracy.  
**Sampling Rate:** The frequency at which sensor data are collected influences the resolution and responsiveness of the SLAM system. For example, a higher sampling rate (e.g., \(30\) Hz) can capture rapid movements more effectively but may increase the computational load.  
**Trajectory Length:** The total distance or duration over which the SLAM system is evaluated. Longer trajectories can help assess the accumulation of errors over time, which is critical for understanding long-term navigation performance.  
**Environmental Conditions:** Parameters such as water turbidity, lighting conditions, and dynamic obstacles affect sensor measurements and, consequently, the performance of SLAM. For example, higher turbidity levels can degrade visual sensor data, increasing positional errors.  
**Sensor Specifications:** The characteristics of the sensors (e.g., camera resolution, IMU accuracy) impact the quality of the data and the SLAM system's ability to estimate poses accurately. For instance, a high-resolution camera can provide more detailed visual information, improving feature detection and matching.