NUMERICAL INVESTIGATION OF THREE-DIMENSIONAL HAUSDORFF DERIVATIVE ANOMALOUS DIFFUSION MODEL

The Hausdorff derivative has been recognized as an efficient tool to characterize anomalous diffusion phenomena. This paper makes the first attempt to numerically investigate three-dimensional Hausdorff derivative diffusion equation by the method of fundamental solutions. The fundamental solution of the three-dimensional Hausdorff derivative diffusion equation is closely related to scaling transform and non-Euclidean Hausdorff fractal distance. The used method, as a meshless technique, is simple, accurate and efficient for solving the partial differential equations with fundamental solutions. Three numerical experiments have been conducted to reveal the effectiveness and rationality of Hausdorff derivative anomalous diffusion models with various temporal and spatial fractal orders, as well as the accuracy of the developed methodology.

A Bistatic Imaging Method for GEOSAR in the Strip Mode and UAVSAR in the Steering Beam Mode

The bistatic configuration with a geosynchronous orbital SAR (GEOSAR) transmitter and unmanned aerial vehicle SAR (UAVSAR) receiver can continuously image in any dangerous and interesting district. In this paper, the new imaging method in the case with the smaller orbital inclination of geosynchronous earth orbit and the steering beam working mode of UAVSAR was mainly studied and analyzed. GEOSAR can be approximately expressed as a static state, and only the receiver provides all the Doppler information. UAVSAR works in the steering beam modes, such as spotlight, sliding spotlight, and TOPS (Terrain Observation by Progressive Scan) mode. The azimuth bandwidth increased by the steering beam causes an aliasing situation in the azimuth frequency domain. To solve this problem, the proposed imaging method corrects the azimuth frequency aliasing using the scaling transform and the bulk azimuth compression. Compared with the traditional imaging method, the simulation validates perfectly the effectiveness of the bistatic imaging algorithm.