New Approach to Multiple Data Association for Initial Orbit Determination Using Optical Observations

The proposed approach aims to develop a new method of forming and processing of multiple hypotheses for initial orbit determination using optical observations. This method allows us to generalize the existing 2-dimensional flat constrained admissible region (CAR) to a unique 3-dimensional (3D) manifold of points corresponding to the pairs of observed right ascension and declination. Another advantage of this method is that unlike the existing methods of initial orbit determination using CAR, the range, range rate and angular rates are computed analytically using the angle observations, the location coordinates of the observation station, the semi-parameter and semi-major axis corresponding to the CAR. Unlike the existing 2D CAR, the 3D manifold does not include the pairs of range and range rate that do not correspond to the observed angles and computed range rat and angular rates. Given the the semi-parameter and semi-major axis, the proposed approach allows us to analytically compute the orientation angles as the Keplerian orbital elements, including the longitude of ascending node, inclination and argument of perigee. The resulting method represents a new and computationally efficient procedure for multiple data association processing through multiple hypotheses filter and allows for an uncertainty quantification.