A Minimal Representation for Dead‐Reckoning Navigation: Updating the Homing Vector

A number of organisms are capable of traveling directly back to the origin of locomotion after following a circuitous outbound path, using dead-reckoning navigation. We describe a minimal representation that could be used for such navigation. It involves keeping track of only the polar coordinates of the origin of locomotion with respect to the observer's current location. An exact solution is provided first, followed by a simplified solution, then a solution involving linearization of trigonometric functions. The paper also examines performance attainable with these solutions and briefly considers ways in which the model might be modified to account for human navigation without reference to landmarks.