# Survey of Deep Learning-Based Methods for FMCW Radar Odometry and Ego-Localization
## 5 Deep Learning Approaches
### Odometry Estimation
\[V(q|\mathbf{\Theta})=\mathbb{E}_{q}[\phi(\mathbf{x},\mathbf{z}|\theta)]+\frac{1 }{2}\ln\left(\left|\Sigma^{-1}\right|\right) \tag{6}\]  
where \(\mathbf{x}\) is the latent trajectory, \(\mathbf{z}\) represents the data measurements, and \(\theta\) represents the network parameters. During EM training, the parameters over the joint factor \(\phi(\mathbf{x},\mathbf{z}|\theta)\) are split up into motion prior factors and measurement factors. For the motion prior factors, [PERSON] et al. apply a white-noise-on-acceleration prior presented by [PERSON] et al. [110], and the measurements factors are calculated using the learned keypoints, weights, and descriptors from the U-Net architecture. In the E-step of the GEM, the model parameters \(\theta\) are hold fixed while optimizing Equation (6) for the posterior distribution \(q(\mathbf{x})\), and during the M-step the posterior distribution is hold fixed while optimizing Equation (6) for the network parameters \(\theta\). A notable departure from the methodology proposed in [87] was the utilization of a moving window strategy. This approach involved incorporating more than just two consecutive radar scans into the analysis. Another method to perform odometry estimation using external sensors is through scene flow prediction, which involves predicting the three-dimensional motion field of dynamic scenes. Such a method captures both the spatial and temporal aspects of static and dynamic objects within a perception scan of the environment. This is usually performed using a cost volume layer [111] to aggregate information across disparities or disparities and optical flow, facilitating the refinement of predictions. This layer computes matching costs between points at different disparities, enabling any network to capture intricate details and improve the accuracy of scene flow predictions by considering the cost relationships across different dimensions. [PERSON] et al. [89] introduced RaFLOW, depicted in Figure 5, a deep learning network specifically crafted for estimating the flow scene of a vehicle through the use of 4D automotive radar detections. The method involves processing two consecutive point clouds within a Radar-Oriented Flow Estimation module. Subsequently, a Static Flow Refinement module, employing the Kabsch algorithm [108], is applied to estimate the vehicle's ego-motion. Leveraging the determined ego-motion, the model then determines the scene flow of dynamic detections. This method integrates the ego-motion as one loss where the objective is to determine the complete scene flow. [PERSON] et al. [90] presented 4 DRO-Net, a novel approach for predicting radar odometry from 4D radar data. This technique employs a coarse-to-fine hier  
Figure 5: Overview of RaFlow [89]. Two point clouds, \(\mathcal{P}\) and \(\mathcal{Q}\) are inserted and first encoded using a multi-scale encoder. A cost volume layer is used with the point cloud and its features to approximate the scene flow of the entire scene in a flow decoder module. An additional static mask generator is used to filter out dynamic objects that could impact the ego-motion estimation by generating a mask \(\mathcal{M}_{\delta}\). Finally, the Kabsch algorithm is applied to generate the ego-motion \(T_{r}\). This transformation is used to further fine-tune the rest of the scene by predicting the final scene flow \(\mathcal{S}\). Reproduced with permission from [89]. strategy based on a sliding window estimation approach. Extracting separate features using PointNet-style feature encoders [112] from 4D radar data enables the fusion of features to generate both point and global features for each scan. The global features are instrumental in generating an initial pose estimate, while the point features contribute to a pose regression module utilizing a velocity-aware attentive cost volume layer between consecutive scaled point features.