Orbit determination for space-based near co-planar observations of space debris using Gooding's method and extended Kalman filtering

Abstract

This report examines the feasibility of determining an objects state from a set of space-based angles only observations taken in a near co-planar orbit. Initial range estimates are presumed to be accurate to within 0.5 km of the object’s true position. A modified Gooding method is used to perform the initial orbit determination and subsequent measurements are processed using an Extended Kalman Filter. The simulations are performed in MATLAB, with line of sight vectors generated from the orbits of a satellite and a piece of debris. The debris orbit is created by perturbing the orbital elements of an expected reference trajectory which is also used to define expected initial range estimates. The performance of the Gooding Method and the Extended Kalman Filter is evaluated using a set of 10 fixed perturbed orbits as well as a mass random assortment of randomly perturbed orbits. Three co-planar orbits are also assessed to examine the vulnerabilities of both methods in low relative motion scenarios. An approach scenario is examined to observe the effects of the rendezvous process on the performance of the filter. The Gooding method produces an initial state with an average position error of 0.055 km and standard deviation of 0.115 km for orbits that fall within the 0.5 km confidence criteria. Furthermore, the estimate provided by the Gooding Method to the Extended Kalman Filter are accurate enough to allow the EKF to reduce the overall state errors. The two methods were able to generate meaningful estimates for co-planar configurations, however the Gooding algorithm is much more sensitive to initial range errors whereas the EKF is more sensitive to the lack of relative motion. For this reason, the maneuver process increases the time it takes for the EKF to converge to the steady state error.