Improved analytical solutions for relative motion of Lorentz spacecraft with application to relative navigation in low Earth orbit

Abstract

Electrostatically charged spacecraft accelerates when orbiting a central body with magnetic field due to the induced Lorentz force. This Lorentz force could be used as propellantless propulsion for orbital maneuvers. Such spacecraft is referred to as Lorentz spacecraft. Modeling the Earth’s magnetic field as a tilted magnetic dipole rotating with the Earth, this paper first presents the analytical expressions that characterize the orbital motion of Lorentz spacecraft with respect to inclined low Earth orbit. Using the information from line-of-sight observations and gyro measurements, coupled with the proposed dynamical model, both extended and unscented Kalman filter are designed to perform relative navigation for Lorentz spacecraft. Two scenarios are simulated to illustrate the accuracy of derived analytical solutions and the performance of proposed filters, respectively. Through comparison with previous work, the accuracy of relative motion model has proved to be greatly enhanced. Numerical simulation results also show that unscented Kalman filter presents more accurate relative state estimation for Lorentz spacecraft than extended Kalman filter.