An improved shooting and bouncing ray (SBR) method based on the Blend-Tree structure is presented for solving the scattering from multiple complex movement targets. Since the positions and attitudes of targets change with time, the spatial distribution of facets is variable. Hence, quickly finding illuminated areas and tracing high-order rays are two main bottlenecks. A Blend-Tree structure consisting of the ray aggregation transport layer (RATL) and the multiple octree layer (MOL) is proposed for the above problems. RATL assigns a conversion interface (CI) and target-seeking interface (TSI) to each target. MOL stores each octree which is built at the initial moment and connected to CI. In shadow elimination, targets are rotated and translated for virtual display by CIs, and the scanline algorithm is used for acceleration. In high-order raytracing, the ray which enters and exits the target is transformed quickly by quaternions in CIs. The TSI determines the next target for the exiting ray. Therefore, the raytracing area is extremely limited within each bounding box and time-invariant. Furthermore, the ray marching algorithm is improved to accelerate ray tracing in octrees. Numerical results demonstrate the computational accuracy and efficiency of this method. Moreover, echo characteristics of multiple moving targets are analyzed.

This paper proposes a shooting and bouncing ray (SBR) method based on a dynamic octree structure to accelerate the solution of scattering from a moving target. In this algorithm, three coordinate systems are established: the world coordinate system (WCS), the local coordinate system (LCS), and the perspective projection coordinate system (PPCS). Firstly, an octree structure is created to store the target facets in the LCS that moves with the target in the WCS. The octree remains relatively stationary with the target, which avoids rebuilding the structure at every moment. Secondly, to accelerate the shadow elimination, the scan line algorithm is used to convert the three-dimensional processing into a two-dimensional graphic display in the PPCS. Thirdly, high-order ray tracing is completed in the LCS. A forward-backward ray tracing technology is adopted to guarantee the precision of the illuminated facet identification. Finally, the information of illuminated facets is transferred from the LCS to the WCS, and the scattering of target is calculated in the WCS. Meanwhile, some numerical simulations of our method are compared with those of the FEKO-MLFMM and the traditional Octree-SBR method. The results show that the proposed method greatly reduces the computation time while maintaining satisfactory accuracy.

This letter proposes an improved shooting and bouncing ray (SBR) method to efficiently predict the radar cross (RCS) of electrically large targets. First, the scan line algorithm is used to convert three-dimensional (3-D) processing to the 2-D graphic display, which expedites the elimination of shadows. Then, the ray tracing process is accelerated by the ray-marching technique which greatly decreases the intersection test. The validity of the proposed method is verified by comparing the simulation results with those of the multilevel fast multipole method. The runtime performance contrast of the traditional Octree-SBR method and ours indicates that the accelerated algorithm is more computationally efficient. Therefore, the presented algorithm has an excellent performance in the RCS prediction of electrically large targets.

For fast solving the electromagnetic scattering of multiple moving targets above or on a rough surface, the multi-dynamic-octrees-based SBR algorithm is proposed in the paper. Firstly, a local coordinate system (LCS) for each object is established that moves with targets in the geodetic coordinate system (GCS). The dynamic octree structure based on LCS is applied to keep the affiliation between facets and leaf nodes unchanged during target motion, which omits the reconstruction of the octree. Secondly, the emission plane determined by the incident direction is used for object projection. The scan line algorithm is improved and utilized to accelerate the elimination of shadows. Moreover, the ray-marching technique is employed to reduce the traversal of octree nodes for the high-order ray tracing on each object. For the ray tracing between different objects, the ray information is converted by the transformation matrix. Thirdly, the scattering fields from targets and the surface (including the couple scattering between each other) are computed in LCS according to the illuminated facets. Then the scattering fields are transformed to GCS and the phase change caused by target movement is compensated. Finally, the total scattering of the composite model is acquired. Numerical results show the scattering of stationary and moving targets above/on the surface. The accuracy and efficiency of the proposed method are verified by comparing it with FEKO-MLFMM and the traditional SBR method. Moreover, the electromagnetic scattering of multiple moving targets on the rough surface under different parameters is analyzed.

In this paper, we present a tailored shooting and bouncing ray (SBR) method for the fast solution of electromagnetic (EM) scattering from a moving target. And, the micro-Doppler features of the moving target are investigated using a time-frequency analysis technique. In our method, a dynamic spatial division technique is employed to accelerate facet information processing and ray-tracing progress of the moving target. At first, the two coordinate systems are established, which are the geodetic coordinate system (GCS) and the local coordinate system (LCS). In GCS, the target is moving with translation and rotation. The dynamic spatial division is established in LCS to store the facet information and remain relatively stationary to the target. In comparison with the traditional SBR method, this technique avoids repetitive spatial division at each moment in the GCS. Then, ray tracing is performed to find the illuminated facets in the LCS. Finally, the scattering field and the phase compensation are computed in the GCS. In numerical simulations, the verification and computation efficiency comparison are provided using our method and other solutions (MLFMM, RL-GO, and traditional SBR). Moreover, the micro-Doppler features are extracted and analyzed using the time-frequency analysis technique, which includes the precession and spin of the missile, and the rotation of the aircraft. Meanwhile, the micro-Doppler spectra of the target is also compared with the theoretical Doppler of equivalent strong scattering points, which are obtained using the instantaneous high-resolution range profile (HRRP).

In this paper, an accelerated hybrid method of physical optics (PO) shooting and bouncing ray (SBR)–physical theory of diffraction (PTD) is proposed to deal with the electromagnetic scattering of a complex target on rough ground. To accelerate the ray tracing progress, the ray marching technique based on octree structure is employed. In this technique, only the nodes passed by the ray are detected successively until the first facet intersected by ray is found or the ray passes through the bounding box, which greatly decreases the intersection test. Then, based on the accelerated PO-SBR-PTD method, the spotlight synthetic aperture radar (SAR) echo data of the composite target–ground model is obtained by the vector superposition of the echo on each meshed patch. Furthermore, the spotlight SAR image of the composite model is simulated by the polar format algorithm (PFA). In numerical simulations, both the EM scattering of the target and composite model are calculated and evaluated by comparing with the multilevel fast multipole method (MLFMM) in FEKO software. Meanwhile the spotlight SAR image of the composite target–ground model is also compared with the real image in MSTAR data, and a satisfactory similarity between them is obtained. In addition, the SAR images of two targets on rough ground for different pose angles are also presented and analyzed.