Associating optical measurements and estimating orbits of geocentric objects with a Genetic Algorithm: performance limitations.

Currently several thousands of objects are being tracked in the MEO and GEO regions through optical means. With the advent of improved sensors and a heightened interest in the problem of space debris, it is expected that the number of tracked objects will grow by an order of magnitude in the near future. This research aims to provide a method that can treat the correlation and orbit determination problems simultaneously, and is able to efficiently process large data sets with minimal manual intervention. This problem is also known as the Multiple Target Tracking (MTT) problem. The complexity of the MTT problem is defined by its dimension S. Current research tends to focus on the S = 2 MTT problem. The reason for this is that for S = 2 the problem has a P-complexity. However, with S = 2 the decision to associate a set of observations is based on the minimum amount of information, in ambiguous situations (e.g. satellite clusters) this will lead to incorrect associations. The S > 2 MTT problem is an NP-hard combinatorial optimization problem. In previous work an Elitist Genetic Algorithm (EGA) was proposed as a method to approximately solve this problem. It was shown that the EGA is able to find a good approximate solution with a polynomial time complexity. The EGA relies on solving the Lambert problem in order to perform the necessary orbit determinations. This means that the algorithm is restricted to orbits that are described by Keplerian motion. The work presented in this paper focuses on the impact that this restriction has on the algorithm performance.