Christopher Roscoe, Applied Defense Solutions, Islam Hussein, Applied Defense Solutions, Matthew Wilkins, Applied Defense Solutions, Paul Schumacher, Jr., Air Force Research Laboratory,
Keywords: admissible region, angles-only, space surveillance, multiple hypothesis tracking, probabilistic
Abstract:
The admissible region, in the space surveillance field, is defined as the set of physically acceptable orbits (e.g., orbits with negative energies) consistent with one or more observations of a space object. Given additional constraints on orbital semimajor axis, eccentricity, etc., the admissible region can be constrained, resulting in the constrained admissible region (CAR). Based on known statistics of the measurement process, one can replace hard constraints with a probabilistic representation of the admissible region. This results in the probabilistic admissible region (PAR), which can be used for orbit initiation in Bayesian tracking and prioritization of tracks in a multiple hypothesis tracking framework.
The PAR concept was introduced by the authors at the 2014 AMOS conference. In that paper, a Monte Carlo approach was used to show how to construct the PAR in the range/range-rate space based on known statistics of the measurement, semimajor axis, and eccentricity. An expectation-maximization algorithm was proposed to convert the particle cloud into a Gaussian Mixture Model (GMM) representation of the PAR. This GMM can be used to initialize a Bayesian filter. The PAR was found to be significantly non-uniform, invalidating an assumption frequently made in CAR-based filtering approaches. Using the GMM or particle cloud representations of the PAR, orbits can be prioritized for propagation in a multiple hypothesis tracking (MHT) framework.
In this paper, the authors focus on expanding the PAR methodology to allow additional constraints, such as a constraint on perigee altitude, to be modeled in the PAR. This requires re-expressing the joint probability density function for the attributable vector as well as the (constrained) orbital parameters and range and range-rate. The final PAR is derived by accounting for any interdependencies between the parameters. Noting that the concepts presented are general and can be applied to any measurement scenario, the idea will be illustrated using a short-arc, angles-only observation scenario.
Date of Conference: September 15-18, 2015
Track: Poster