On mutual information for observation-to-observation association

In this paper, we build on recent work to further investigate the use of mutual information to tackle the observation-to-observation association (OTOA) problem where we are given a set of observations at different time instances and wish to determine which of these observations were generated by the same RSO. The approach relies on using an appropriate initial orbit determination (IOD) method in addition to the notion of mutual information within an unscented transform framework. We assert that, because the underlying initial orbit determination algorithm is deterministic, we can introduce an approximate correction factor to the IOD methodology. The correction is a function represented by a constant bias for this work but can be expanded to other parametrizations. The application of this correction results in an order of magnitude improvement in performance for our mutual information data association technique over the previous results. The correction can be used in conjunction with other information theoretic discriminators for data association; however it was found in previous work that mutual information is the most precise discriminator. The information theoretic solution described in this paper can be adjusted to address the other (OTTA and TTTA) association problems, which will be the focus of future research. We will demonstrate the main result in simulation for LEO, MEO, GTO, and GEO orbit regimes to show general applicability.