Autonomous Navigation of Relativistic Spacecraft in Interstellar Space

Abstract

This paper introduces a general autonomous navigation method for any spacecraft for which relativistic effects are significant. It builds on a relativistic observation model and represents the foundational step in the development of interstellar navigation. By comparing astrometric and spectrometric measurements obtained in two different reference frames, the method estimates instantaneous spacecraft position and velocity, and distances to observed stars. The paper first derives relativistic autonomous observation equations, which are more general than those provided in the existing literature. It then presents an autonomous navigation algorithm that compares favorably to a nonrelativistic approach. A case study investigates the method in the context of technological details of a mission, including certain sources of noise and disturbance in the interstellar medium. Specifically, a state-of-the-art spacecraft traveling to Proxima Centauri at can estimate its position and velocity with less than 0.001% error, and distances to stars it observes with less than 1% error. Measurement noise is the dominant source of this error; thus, the algorithm is highly sensitive to sensor performance. A simple running average reduces these errors by more than an order of magnitude, which suggests that this algorithm is suitable as a first step in a realistic, recursive navigation algorithm.