Navigation and Localization via Wave Interference Patterns: An approach inspired by Marshallese Stick Charts

Navigation and localization problems are challenging to solve when operating in ocean environments owing to inherent environmental dynamics and severe limitations on communication capabilities. This is compounded in coastal regions, precisely where the majority of the phenomena of interest occur, and the need for accurate navigation estimates is most critical. Existing navigation and localization techniques rely either on high-powered sensors (e.g., Doppler Velocity Loggers) resulting in decreased deployment time, or dead-reckoning (compass and IMU), with motion models resulting in poor navigational accuracy due to unbounded sensor drift combined with large environmental disturbances. Here we examine a low-cost, low-energy approach to navigation and localization in near-shore (<; 100 km) environments by considering non-metric instantiations of maps. Ocean navigation methods in the Marshall Islands up through the last century relied upon knowledge of charts made of sticks, shells, and engravings to aid seafarers in long sea voyages. These charts hold a wealth of information about the ocean in a seemingly simple representation of what we would call a map. In this paper, we examine the utility of a non-metric map representation that incorporates moving currents, wind directions, swell, and fluid-dynamic properties of refraction and reflection - data regarding the intrinsics of the ocean most germane where a geometric or absolute reference frame becomes less obviously the appropriate representation. We provide simulation results for both navigation and localization problems, and propose a simple control law for a practical navigation problem.