Distance between Keplerian orbits in the correlation of short arc radar tracks

Radar observations are used to track space objects in the Low Earth Orbit region. The observations consist of short arc tracks containing range and angular information. The association of two or more observed tracks of the same space object is in general necessary to calculate the orbit of the object with a better accuracy. In the radar case the availability of range and angle measurements allows the computation of an initial orbit from a single track. As a consequence, the association of tracks can be based on a direct comparison of the calculated initial orbits. In this work a new definition of distance between Keplerian orbits is proposed. The definition extends the existing formulation based on only five Keplerian orbital elements without the anomaly. The modified distance considers an additional term due to the anomaly. The obtained distance can be scaled as a function of the covariance of the orbital elements and can be expressed as Mahalanobis distance. Some application of the distance definition is shown and compared with results obtained using the orbital distance in curvilinear coordinates.