A discrete dipole approximation approach to underwater active electrosense problems

Weakly electric fish use self-established electric field to sense the underwater environment that may be cluttered and turbid. Previous works on building artificial counterparts are limited to simplest cases, as no analytical solutions exist under complex boundary conditions. Universal numerical approaches like Finite Element Method (FEM) and Boundary Element Method (BEM) suffer from lengthy meshing process and heavily computational burden. In this paper, discrete dipole approximation (DDA), which is widely used in light scattering and absorption problems, was for the first time proposed to be applied for underwater electrosense. This approach is lightweight, flexible and computationally efficient compared with FEM. It was simulated in electric fields excited by parallel-plate electrodes and spherical electrodes of a simplified robotic model. A constrained unscented Kalman filter (CUKF) was further utilized to localize the position and identify the size of an invading cube. Results comparison with FEM indicate the differences of a cuboidal object in two orthogonal positions were 7.10% and 10.46% respectively, and the difference in size was 11.82%. These results were achieved at a cost of less than 1% of the computational effort of the FEM. The proposed approach proved effective from the simulation results and laid a solid foundation for real-time underwater active electrosense in a more general environment.