An Equivariant Filter for Spacecraft Nonlinear Relative Navigation with Range and Bearing Measurements

Relative navigation is a fundamental task in space proximity operations and autonomous rendezvous. The nonlinear relative orbital dynamics are equivariant and admit a semidirect product Lie group symmetry. This property is used to design an Equivariant Filter (EqF). The filter estimates the relative position and velocity between a chaser spacecraft and a target by lifting the filter dynamics to the group, while respecting the underlying geometry of the problem. Simulations demonstrate the filter's performance and effectiveness.