Spacecraft to Spacecraft Absolute Tracking for Autonomous Navigation of a Distributed Space System from Relative Sensors

Abstract Navigation for a distributed space system can be fully and autonomously provided by relative measurements between vehicles under non-linear dynamics, thereby removing any need for external observation. This paper derives the observability of a generic distributed system using relative measurements through an investigation of non-linear dynamical moments. The absolute state becomes observable due to second and higher dynamical moments that produce differential motion between vehicles, while the relative state observability is a function of the full system motion as traditionally expected. The results from observability analysis are leveraged to instantiate simulations which demonstrate observability for a distributed space system with relative optical measurements. The simulations assess uncertainty via a linearized covariance analysis in various settings including Keplerian, perturbed Keplerian, and cislunar dynamics. This navigation method excels when targets have highly differential motion and falters as the difference subsides. Therefore, highly perturbed environments with multiple targets generate the best results.