The Orbital Coherence Function: A Keplerian Pre-Filter for Ensemble Orbit Determination

We introduce the Orbital Coherence Function (OCF), a computationallyinexpensive pre-filter for reducing large ensembles of candidate orbits generatedby initial orbit determination (IOD) in planetary defense applications.The OCF exploits the three-way Keplerian identity K = G′/G = p/r =1 + e cos θ, where G′ ≡ ω2r3/M is the instantaneous gravitational coupling, toquantify the dynamical inconsistency of each candidate orbit relative to a nom-inal solution. Specifically, the OCF accumulates the squared difference betweenthe Keplerian index predicted by a candidate orbit and the index derived fromthe IOD nominal orbit across all available observation epochs.We demonstrate the method on a controlled synthetic benchmark: 500 candi-date orbits for asteroid 99942 Apophis over a 30-day arc, with the IOD nominalorbit taken as a perturbed Gauss solution. The true orbit ranks first in everytested configuration. Candidate reduction exceeds 95% under ideal (two-body,noiseless) conditions.