Distributed Localization with Grid-based Representations on Digital Elevation Models

It has been demonstrated that grid cells in the brain are encoding physical locations using hexagonally spaced, periodic phase-space representations. We explore how such a representation may be computationally advantageous for related engineering applications. Theories of how the brain decodes from a phase-space representation have been developed based on neuroscience data. However, theories of how sensory information is encoded into this phase space are less certain. Here we show a method for how a navigationrelevant input space such as elevation trajectories may be mapped into a phase-space coordinate system that can be decoded using previously developed theories. We also consider how such an algorithm may then also be mapped onto neuromrophic systems. Just as animals can tell where they are in a local region based on where they have been, our encoding algorithm enables the localization to a position in space by integrating measurements from a trajectory over a map. In this paper, we walk through our approach with simulations using a digital elevation model.