(Georgia Institute of Technology, 2023-08)
Henry, Sébastien; Christian, John A.
This work explores the problem of initial orbit determination (IOD) using relative
position measurements between a pair of spacecraft in Keplerian orbits. We first
show that the solution to this problem is not unique, even under certain classes of
perturbations. We propose an algorithm to retrieve the inertial state of both orbiting
spacecraft using the relative acceleration and Lambert's problem. Various
options are compared to estimate the relative acceleration from a set of relative position
measurements. Simulation results suggest that the proposed IOD algorithm
is suitable for onboard navigation filter (re)initialization, and can thus improve
constellation and formation-flying mission autonomy.
(Georgia Institute of Technology, 2022-10)
Henry, Sébastien; Christian, John A.
Optical measurements are a key part of
modern interplanetary navigation. The statistically optimal
Linear Optimal Sine Triangulation (LOST) algorithm
is applied to the context of celestial navigation. In
addition to optimal triangulation methods, celestial navigation
requires the consideration or target ephemeris errors,
light aberration, and light time-of-flight. In most
cases, only light aberration and light time-of-flight change
the expected direction of the measured line-of-sight (LOS).
These effects are found to be non-negligible at typical observer
velocities (for light aberration) and planet velocities
(for light time-of-flight). The effects of the position uncertainty
of planets are only important when the observer
is close to them. The LOST framework provides a mechanism
to conveniently consider all of these effects.