Probabilistic Initial Orbit Determination Using Gaussian Mixture Models

The most complete description of the state of a system at any time is given by knowledge of the probability density function, which describes the locus of possible states conditioned on any available measurement information. When employing optical data, the concept of the admissible region provides a physics-based region of the range/range-rate space that produces Earth-bound orbit solutions. This work develops a method that employs a probabilistic interpretation of the admissible region and approximates the admissible region by a Gaussian mixture to formulate an initial orbit determination solution. The Gaussian mixture representation of the probability density function is then forecast and updated with subsequent data to iteratively refine the region of uncertainty. Simulation results are presented using synthetic data over a range of orbits, in which it is shown that the new method is consistently able to initialize a probabilistic orbit solution and provide iterative refinement via follow-on tracking.