A Static Estimation Method for Autonomous Navigation of Relativistic Spacecraft

In-situ space exploration beyond our solar system is an inevitable next step for science. Such spacecraft will travel much faster, with speeds that are a significant fraction of the speed of light, to realize extrasolar exploration in a human lifetime. However, existing navigation technologies are not up to the task because they are generally Earth-based, exploiting the Deep Space Network for tracking. They lack the resolution to estimate the state of a high-speed spacecraft in the interstellar medium, and the long light-travel times likely preclude sharing state information with the spacecraft for active trajectory control. Moreover, all rely on reference-frame-independent physical laws and treat relativistic effects as perturbations of classical theories of orbital mechanics. Given the unprecedented uncertainty that interstellar environment can introduce in the trajectory of such a spacecraft, on-board navigation is likely the only feasible approach. This paper describes autonomous navigation for spacecraft traveling at relativistic speeds. The special theory of relativity is central to its flight-dynamics model. The proposed method assumes that the spacecraft has access to a state-of-the-art star catalog describing the relative positions and colors of a number of stars and can detect relative directions and apparent colors of the corresponding stars onboard with a star tracker and a spectrometer. By relating the motion of the spacecraft to these observations in the spacecraft's reference frame, the algorithm estimates its instantaneous position and velocity. The paper includes the results of simulations of the linearized equations for a spacecraft having a generic star tracker and a spectrometer as a sensor, traveling from Earth to Proxima Centauri at 20 percent of the speed of light. Results show that the algorithm can estimate the position and velocity of the spacecraft with less than 0.5 percent error. Assuming the key relativistic effects are apparent in the sensors, this approach provides a universal navigation algorithm that can be used by any space vehicle traveling at arbitrarily high speed. This work represents an enabling step toward relativistic spaceflight.