# Survey of Deep Learning-Based Methods for FMCW Radar Odometry and Ego-Localization
## 5 Deep Learning Approaches
### Odometry Estimation
[85] also utilized a convolutional neural network (CNN) to predict a mask for spinning radar scans. This model learns to filter out all non-essential detections from the radar scan. To determine the relative pose between two scans specifically, a mask is learned for a reference scan denoted as S1 and for another subsequent scan S2. Each mask is then multiplied with its respective scan. Scan S2 is then adjusted using possible pose offsets \(\Delta t=[\Delta x,\Delta y,\Delta z]\). Finally, [PERSON] et al. employed a brute force correlative matching technique to identify the most suitable transformation. The process involved calculating the discrete cross-correlation between the FFT of S1 and the FFT of S2, which was adjusted using the aforementioned mask and pose offsets. Extending the foundation laid by [85], the study conducted by [PERSON] et al. [86] takes a step forward by disentangling the search process for the rotation and translation components. This strategic decoupling serves to alleviate the computational complexity inherent in the correlative scan matching technique. Initially, the optimal angle is identified by assessing the cross-correlation of the masked scans in polar coordinates. This angle then serves as a pivotal factor in the subsequent correlative scan matching approach. By segregating the search for the rotation angle from the search for the translation component, the computational load is significantly reduced. This improvement in computational efficiency is achieved with only a minimal decline in performance when compared to the method proposed by [85]. An alternative approach to generating ego-motion predictions involves directly extracting keypoints from the data. [PERSON] et al. [87] implemented a U-Net encoder-decoder architecture with two decoder branches to gain insights into keypoints, weights, and descriptors. These components collectively contribute to determining a transformation matrix between two frames. The architectural design is adept at generating keypoints along with corresponding weights and descriptors for each of these keypoints. Subsequently, a matching process is applied to identify the keypoints that exhibit the most pronounced similarity. From these matched keypoints, a transformation is deduced using the Singular Value Decomposition (SVD) technique. A noteworthy aspect of their approach is the embedded differentiability within the keypoint matching and pose estimation processes. This design choice ensures that the parameters of the model remain differentiable, facilitating seamless integration with optimization processes. Much like the approach taken in [87], [PERSON] et al. [88] also harnessed the capabilities of a U-Net architecture. This architecture was utilized to extract keypoints, weights, and descriptors from a spinning radar scan, ultimately facilitating the prediction of odometry across successive scans via an unsupervised methodology. The authors integrated a General Expectation-Maximization (GEM) scheme into their approach, with the primary aim of maximizing the evidence lower bound (ELBO). This combined strategy enables them to enhance the efficiency and effectiveness of their unsupervised odometry prediction process. \[\mathcal{L}=\underbrace{\int_{-\infty}^{\infty}q(\mathbf{x})\ln\biggl{(} \frac{p(\mathbf{x}|\mathbf{z},\theta)}{q(\mathbf{x})}\biggr{)}d\mathbf{x}}_{ \leq 0}-\underbrace{\int_{-\infty}^{\infty}q(\mathbf{x})\ln\biggl{(}\frac{p( \mathbf{x},\mathbf{z}|\theta)}{q(\mathbf{x})}\biggr{)}d\mathbf{x}}_{\text{upper bound}} \tag{5}\]When finding update rules for the parameters, only the upper bound from Equation (5) is optimized. When assuming a multivariate Gaussian probability distribution for the posterior approximation (\(q(\mathbf{x})=\mathcal{N}(\mu,\Sigma)\)), it results in a new loss.