Autonomous driving vehicles have strong path planning and obstacle avoidance capabilities, which provide great support to avoid traffic accidents. Autonomous driving has become a research hotspot worldwide. Depth estimation is a key technology in autonomous driving as it provides an important basis for accurately detecting traffic objects and avoiding collisions in advance. However, the current difficulties in depth estimation include insufficient estimation accuracy, difficulty in acquiring depth information using monocular vision, and an important challenge of fusing multiple sensors for depth estimation. To enhance depth estimation performance in complex traffic environments, this study proposes a depth estimation method in which point clouds and images obtained from MMwave radar and cameras are fused. Firstly, a residual network is established to extract the multi-scale features of the MMwave radar point clouds and the corresponding image obtained simultaneously from the same location. Correlations between the radar points and the image are established by fusing the extracted multi-scale features. A semi-dense depth estimation is achieved by assigning the depth value of the radar point to the most relevant image region. Secondly, a bidirectional feature fusion structure with additional fusion branches is designed to enhance the richness of the feature information. The information loss during the feature fusion process is reduced, and the robustness of the model is enhanced. Finally, parallel channel and position attention mechanisms are used to enhance the feature representation of the key areas in the fused feature map, the interference of irrelevant areas is suppressed, and the depth estimation accuracy is enhanced. The experimental results on the public dataset nuScenes show that, compared with the baseline model, the proposed method reduces the average absolute error (MAE) by 4.7–6.3% and the root mean square error (RMSE) by 4.2–5.2%.

The transport process is an important part of the research of fluid dynamics, especially when it comes to tracer advection in the atmosphere or ocean dynamics. In this paper, a series of high-order semi-Lagrangian methods for the transport process on the sphere are considered. The methods are formulated entirely in three-dimensional Cartesian coordinates, thus avoiding any apparent artificial singularities associated with surface-based coordinate systems. The underlying idea of the semi-Lagrangian method is to find the value of the field/tracer at the departure point through interpolating the values of its surrounding grid points to the departure point. The implementation of the semi-Lagrangian method is divided into the following two main procedures: finding the departure point by integrating the characteristic equation backward and then interpolate on the departure point. In the first procedure, three methods are utilized to solve the characteristic equation for the locations of departure points, including the commonly used midpoint-rule method and two explicit high-order Runge–Kutta (RK) methods. In the second one, for interpolation, four new methods are presented, including (1) linear interpolation; (2) polynomial fitting based on the least square method; (3) global radial basis function stencils (RBFs), and (4) local RBFs. For the latter two interpolation methods, we find that it is crucial to select an optimal value for the shape parameter of the basis function. A Gauss hill advection case is used to compare and contrast the methods in terms of their accuracy, and conservation properties. In addition, the proposed method is applied to standard test cases, which include solid body rotation, shear deformation of twin slotted cylinders, and the evolution of a moving vortex. It demonstrates that the proposed method could simulate all test cases with reasonable accuracy and efficiency.

Depth estimation is a key technology in autonomous driving, as it provides an important basis for accurately detecting traffic objects and avoiding collisions in advance. To enhance depth estimation performance in complex traffic environments, this study proposes a depth estimation method in which point clouds and images obtained from MMwave radar and cameras are fused. Firstly, a residual network is established to extract the multi-scale features of the MMwave radar point clouds and the corresponding image obtained simultaneously from the same location. Correlations between the radar points and the image are established by fusing the extracted multi-scale features. A semi-dense depth estimation is achieved by assigning the depth value of the radar point to the most relevant image region. Secondly, a bidirectional feature fusion structure with additional fusion branches is designed to enhance the richness of feature information. The information loss during the feature fusion process is reduced, and the robustness of the model is enhanced. Finally, parallel channel and position attention mechanisms are used to enhance the feature representation of key areas in the fused feature map; the interference of irrelevant areas are suppressed, and the depth estimation accuracy is enhanced. Experimental results on the public dataset nuScenes show that, compared with the baseline model, the proposed method reduces the average absolute error (MAE) by 4.7%-6.3% and the root mean square error (RMSE) by 4.2%-5.2%.