We present an analytical model of a sensor for the navigation of underwater vehicles by the electric sense. This model is inspired from the electroreception structure of the electric fish. In our model, that we call the poly-spherical model (PSM), the sensor is composed of n spherical electrodes. Some electrodes play the role of current-emitters whereas others play the role of current-receivers. By imposing values of the electrical potential on each electrode we create an electric field in the vicinity of the sensor. The region where the electric field is created is considered as the bubble of perception of the sensor. Each object that enters this bubble is electrically polarized and creates in return a perturbation. This perturbation induces a variation of the measured current by the sensor. The model is tested on objects for which the expression of the polarizability is known. A unique off-line calibration of the poly-spherical model permits to predict the measured current of a real immersed sensor in an aquarium. Comparisons in a basic scene between the predicted current given by the poly-spherical model and the measured current given by our test bed show a very good agreement, which confirms the interest of using such fast analytical models for the purpose of navigation.