Space-Based Orbit Determination Using Passive Optical Measurements in LEO

The increasing number of artificial objects placed in Low Earth Orbit (LEO) has created the need for improvement in the present Space Surveillance and Tracking (STT) systems, which perform Orbit Determination (OD) to estimate their trajectories. Special interest has been developed on passive optical Space-Based Space Surveillance (SBSS), since the proximity to the targets and the non-dependence to atmospheric effects, offer advantages in terms of the measurement quality and the variety of detectable objects. In this work, a passive optical SBSS satellite with a field of view (FOV) of 4° X 4° is simulated. Focusing on Low Earth Orbit (LEO), the Starlink mega constellation is used as a test sample. A Sun-Synchronous Orbit (SSO), 100 km below the targets, is found to be the optimal orbit for their observation. The Gaussian Initial Orbit Determination (IOD) method is implemented, confirming its accuracy when dealing with purely Keplerian orbits, but showing its weakness by being highly sensitive to perturbations and measurement errors. A Weighted Least Squares (WLS) fit using a batch processor, is sought as an alternative. Considering orbits generated by a zonal geopotential with terms up to J6, fitting a J2 model to data perturbed by noise at the typical measurement error levels, produced estimation errors of the order on 10 km in position. The inclusion of additional observations, either following the initial set or after half an orbit, reduces the errors to a safer 5 km level. The uncertainty of the estimations is propagated with the covariance matrix, finding that a minimum of 9 measurements is required for a confident interception of the target by the observer's FOV after half an orbit, to produce a follow-up measurement.