Geometry Optimization for Range-based Localization with Minimum Number of Sensors

We consider the geometry optimization problem for 2D range-based localization under some deployment constraints with minimum number of sensors,
$N=3$
. These constraints, imposed by circular area and minimum safety distance, allow the sensors to be placed only in some irregular area. We establish the geometry optimization problem as a constrained optimization problem by using the maximum feasible angle and separation angles. The discussions are based on different minimum safety distances, i.e., different maximum feasible angles.