Enhanced cooperative single-range underwater navigation based on optimal trajectories

This work addresses the observability analysis for a cooperative range-based navigation system based on the optimization of an index. A nonlinear model is first defined in order to describe the motion of the vehicle and a mobile beacon. Then, the Fisher Information Matrix is introduced to explain how it is related with the observability problem. A unconstrained optimization problem is formulated in order to find the best sequence of actions for the beacon to ensure observability in the system; the unconstrained problem does not take into account physical limitation of the vehicle and beacon. Then, four different scenarios are solved using different constraints; we show that, when the beacon is rotating with variable angular velocity we get a better strategy than rotating with constant velocity, despite that in both scenarios the system is observable. Finally, we show that increasing the energy provided to rotate the beacon does not improve further the observability of the system. These results are important from a theoretical and practical point of view, since they represent a strategy to plan the motion of the beacon to guarantee observability in the system.