Minimal sensor arrays for localizing objects using an electric sense

Weakly electric fish encode perturbations in a self-generated electric field to sense their environment. Localizing objects using this electric sense requires that distance be decoded from a two-dimensional \emph{electric image} of the field perturbations on their skin. Many studies of object localization by weakly electric fish, and by electric sensing in a generic context, have focused on extracting location information from different features of the electric image. Some of these studies have also considered the additional information gained from sampling the electric image at different times, and from different viewpoints. Here, we take a different perspective and instead consider the information available at a single point in space (i.e. a single sensor or receptor) at a single point in time (i.e. constant field). By combining the information from multiple receptors, we show that an object's distance can be unambiguously encoded by as few as four receptors at specific locations on a sensing surface in a manner that is relatively robust to environmental noise. This provides a lower bound on the information (i.e. receptor array size) required to decode the three-dimensional location of an object using an electric sense.