Single track orbit determination analysis for low Earth orbit with approximated J2 dynamics

In the domain of Space Situational Awareness (SSA), the challenges related to orbit determination and catalog correlation are notably pronounced, exacerbated by data scarcity. This study introduces an initial orbit determination methodology that relies on data obtained from a single surveillance radar, with the need for fast algorithms within an operational context serving as the main design driver. The result is a linearized least-squares fitting procedure incorporating an analytically formulated approximation of the dynamics under the $J_2$ perturbation, valid for short-term propagation. This algorithm utilizes all available observables, including range-rate, distinguishing it from other similar methods. A significant contribution of this paper is the enhancement of estimation quality by incorporating information about the object’s predicted orbital plane into the methodology, a method denoted as OPOD. The proposed methods are evaluated through a series of simulations against a classical range and angles fitting method (GTDS) to examine the effects of track length and measurement density on the quality of full state estimation, including the impact of using arcs that are too short. The OPOD methodology shows promising results throughout a wide range of scenarios.