# Towards Deep Radar Perception for Autonomous Driving: Datasets, Methods, and Challenges
## 4 Radar Depth and Velocity Estimation
### Velocity Estimation  
For autonomous driving, velocity estimation is helpful for trajectory prediction and path planning. Radar can accurately measure the Doppler velocity, i.e., radial velocity in polar coordinates. If a vehicle moves parallel to the ego-vehicle at a distance, its actual velocity can be approximated by the measured Doppler velocity. However, this only applies in highway scenarios. On urban roads, it is possible for an object to move tangentially while crossing the road, then its Doppler velocity will be close to zero. Therefore, Doppler  
Figure 8: (**a**) Radar detection expansion techniques. (**b**) Extend radar detections in height. (**c**) Build a probabilistic map, where the dark/light blue indicates channel with high/low confidence threshold. (**d**) Apply a strict filtering according to the bounding box, where only detections corresponding to the frontal surface are retained. velocity cannot replace full velocity. Recovering full velocity from the Doppler velocity needs two steps: first, compensate the ego-motion, then estimate the tangential velocity. In the first step, the ego-motion can be estimated by visual-inertial odometry (VIO) and GPS. Radar-inertial odometry [119; 120] can also be used in visually degraded or GPS-denied environments. Then, the Doppler velocity is compensated by subtracting the ego-velocity. In the second step, the full velocity is estimated according to the geometric constraints. Suppose that the radar observes several detections of an object and that the object is in linear motion. As shown in Figure (a)a, the relationship between the predicted linear velocity \((v_{x},v_{y})\) and the measured Doppler velocity \(v_{r,i}\) is given by  
\[v_{r,i}=v_{x}\cos(\theta_{i})+v_{y}\sin(\theta_{i}) \tag{7}\]  
where the subscript \(i\) denotes the \(i\)-th detection and \(\theta_{i}\) is the measured azimuth angle. By observing \(N\) detections per object, we can solve the linear velocity using the least-squares method. However, the L2 loss is not robust to outliers, such as clutter and the micro-Doppler motion of wheels. [PERSON] et al. [121] applied RANSAC to remove outliers, then used orthogonal distance regression (ODR) to find the optimal velocity. Although the linear motion model is widely used for its simplicity, it will generate large position errors for motion with high curvature [122]. Alternatively, as shown in Figure (b)b, the curvilinear motion model is given by  
\[v_{r,i}=\omega(y_{c}-y^{S})\cos(\theta_{i})-\omega(x_{c}-x^{S})\sin(\theta_{i}) \tag{8}\]  
where \(\omega\) is the angular velocity, \(\theta\) is the angle of the detected point, \((x_{c},y_{c})\) represents the position of the instantaneous centre of rotation (ICR), and \((x^{S},y^{S})\) represents the known radar position. In order to decouple angular velocity and the position of the ICR, we need at least two radar sensors that observe the same object. Then, we can transform (8) into a linear form as  
\[y^{S}_{j}\cos(\theta_{ji})-x^{S}_{j}\sin(\theta_{ji})=y_{c}\cos(\theta_{ji})-x _{c}\sin(\theta_{ji})-v^{D}_{ji}\omega^{-1} \tag{9}\]  
where the subscript \(j\) denotes the \(j\)-th radar. Similarly, RANSAC and ODR can be used to find the unbiased solution of both the angular velocity and position of the ICR [123]. For the single radar setting, it is also possible to derive a unique solution of (8) if we can correctly estimate the vehicle shape. According to the Ackermann steering geometry, the position of the ICR should be located on a line extending from the rear axle. By adding this constraint to (8), the full velocity can be determined in closed form [124]. The above methods predict velocity at the object level under the assumption of rigid motion. However, the micro-motion of object parts, such as the swinging arms of pedestrians, are also useful for classification. Capturing these non-rigid motions requires velocity estimation at the point level. This can be achieved by fusing with other modalities or  
Figure 9: Radar motion model.