Station Arrangement Optimization of Photoelectric Theodolites Based on Efficient Traversing Discrete Points

Abstract

Station arrangement optimization of photoelectric theodolites in shooting ranges presents a non-convex and non-linear problem, and the method required to seek the global optimal solution remains an open question. This paper proposes an efficient traversal algorithm that could solve this problem by utilizing discretization of regions with a finite length of mesh, in which both the terrain of the station arrangement region and the observation airspace region are discretized through triangulation. To enhance the computational efficiency of the traversal algorithm, two strategies are employed to speed up the calculation: reducing the dimension of the observation airspace and using the Euclidean distance matrix to compute the intersection angle. After the global optimal solution with discrete finite precision was obtained through the traversal algorithm, it was then used as the initial points for local mesh refinement and to implement gradient-based optimization in order to further improve the precision of the solution. The proposed approach is demonstrated to be practical through application to numerical examples used for the optimization of station arrangements that involve two to four stations.