# Survey of Deep Learning-Based Methods for FMCW Radar Odometry and Ego-Localization
## 5 Deep Learning Approaches
### Evaluation
#### 5.4.1 Odometry  
In point-matching or pose estimation evaluations, determining the translational and rotational components of the pose difference between predicted and true poses is a fundamental aspect. The Absolute Trajectory Error (ATE) serves as a common metric, representing the average error for both translation and rotation components. Typically measured in meters (\(m\)) for translation and degrees (\(deg\)) for rotation, the ATE is calculated as follows for a pair of poses:  
\[E_{tra}=||\hat{t}-t||_{2}\quad E_{rot}=||\hat{\mathsf{R}}R^{T}-\mathbf{I}||_{2} \tag{10}\]  
In Equation (10), \(\hat{t}\) and \(t\) are the predicted and true translational components, and \(\hat{R}\) and \(R\) are the predicted and true rotational components, respectively. The ATE combines these individual components into a single measure of translational and rotational error.  
However, in the context of odometry estimation, where the global drift over a certain spatial extent is often more critical than small pose differences between consecutive frames, the ATE may not be the most appropriate metric. If a network learns to predict the transformation between two scans, it is more relevant to know how wrong the network is after some spatial or temporal extent than to know how the network performs in between consecutive scans. This is relevant especially in slow-moving systems with high data generation frequencies. An example would be the Oxford radar dataset, which operates at 4 Hz. Small pose differences may not accurately capture the global drift over a significant range in such cases.  
To address this concern, the KITTI evaluation benchmark [135] introduces a metric that averages the relative position and rotation error over sub-sequences of various lengths (e.g., 100 m, 200 m,..., 800 m). The resulting translational and rotational ATE is reported as a percentage offset for the translational component and in degrees per 1000 m for the rotational component. This provides a more comprehensive evaluation metric, considering the performance of the system over the extended distances and offering a metric relevant for odometry tasks.  
The methods presented in Table 4 showcase four distinct approaches evaluated using the same data and same metric; the Oxford radar dataset using the KITTI metric on spinning radar. Fast-MbyM [86] demonstrates the fastest inference speed, achieving a notable speed-up compared to the MbyM method with only a marginal sacrifice in accuracy. Among the deep learning models, RaLL [102] stands out as the top performer, although it requires additional LiDAR data during training for effective conversion between radar and LiDAR representations using a GAN.  
Observing Table 4, it becomes evident that correlation models generally outperform keypoint extraction and matching methods. Notably, methods like [85; 86; 87; 88] and have the added advantage of using learned keypoints and weights for both odometry estimation and localization, rendering them more versatile in an end-to-end approach. However, it is worth mentioning that methods by [87; 88] exhibit higher inference times and require more substantial GPU support. Despite this, given the 4 Hz rotation frequency of the spinning radar in the Oxford robot dataset, all methods remain applicable in real-time scenarios.  
In comparison to CFEAR [90], deep learning methods demonstrate comparable performance in terms of accuracy and computational time. However, it is important to note that the CFEAR evaluation was conducted on an Intel i7-8700k CPU, while the other models required GPU support for evaluation.