Relative position estimation using modulated magnetic field for close proximity formation flight

This paper presents a method to estimate relative position vectors between spacecraft equipped with magnetic coils and magnetic field sensors for close proximity operation. Filters can segregate a magnetic field with particular frequency if spacecraft drive their coils with this specific frequency. The proposed method utilizes the amplitude of the magnetic field with a particular frequency to estimate relative position vectors. The method consists of an initial position estimator and a sequential position estimator, which is an unscented Kalman filter. The initial position estimator provides a coarse estimate for the relative position vectors using the segregated magnetic field. Relation between the magnetic field and relative position vector is derived analytically in this article for the initial position estimator. The unscented Kalman filter refines the estimation accuracy by initializing the filter with the estimate by the initial position estimator. It is shown that a spacecraft can conduct relative position vector estimation using the magnetic field of a target spacecraft, provided that a few conditions clarified in the article are satisfied. Finally, the proposed estimators are evaluated numerically via simulations.