Optimization of Observer Trajectory for Coordinated Bearing-Only Localization in Constrained Three-Dimensional Scenarios
Liraz Mudrik, Alfonso Sciacchitano, Sean P. Kragelund, Justin Kang, Isaac I. Kaminer · 2025
A coordinated localization problem is considered between an unmanned aerial vehicle (UAV) and a cooperative unmanned surface vessel (USV) when data from the global positioning system (GPS) is unavailable. The UAV’s task is to gather information about the unknown locations of both cooperative and adversarial USVs. The cooperative USV then uses this information to engage the target, which is the adversarial USV. The UAV is equipped with a strapped-down vision system with limited field-of-view (FOV), which produces bearing-only measurements about the USV and the target only when they are within the camera’s FOV. We use the Cramér–Rao lower bound to measure the acquired information at each time step. Specifically, we use its trace, as it resembles position dilution of precision, a well-known measure in GPS-based localization problems. This formulation yields an infinite-dimensional trajectory optimization problem for the UAV, whose solution is generally intractable. We approximate the optimal solution using Bernstein polynomials, which have been shown to be asymptotically optimal. Using the Bernstein polynomial-based solution yields an optimal solution as the order of the approximant increases. Finally, we demonstrate the performance of the proposed solution via numeric simulations.