Trevor Bennett, University of Colorado Boulder, Hanspeter Schaub, Professor, University of Colorado Boulder,
Keywords: Relative Motion Estimation, Relative Orbit Description, Space-Based Observations
Abstract:
There has been an increasing interest in space-based space situational awareness around satellite assets and the tracking of orbital debris. Of particular interest is the space-based tracking of objects near critical circular orbit regimes, for example near the Geostationary belt or the International Space Station. Relative orbit descriptions such as the Clohessy-Wiltshire equations describe the motion using time-varying Cartesian or curvilinear coordinates. Orbit element differences describe the unperturbed motion using constant variations of inertial orbit elements. With perturbations these only vary slowly, but can be challenging to estimate. Linearized Relative Orbit Elements (LROEs) employ invariants of the linearized relative motion, are thus constant for the unperturbed linear case, and share the benefit of the CW equations in that they directly related to space-based relative motion measurements. The variational LROE equations enable the relative orbit to be directly propagated including perturbation forces. Utilization of the invariant-inspired relative motion parameters exhibits exciting applications in relative motion sensing and control. Many methods of relative motion estimation involve the direct estimation of time-evolving position and velocity variables. Developed is an angles-only relative orbit Extended Kalman filter (EKF) navigation approach that directly estimates these nominally constant LROEs. The proposed variational equations and filtering scheme enables direct estimation of geometric parameters with clear geometric insight. Preliminary numerical simulation results demonstrate the relative orbit insight gained and speed of convergence. EKF implementations often exhibit significant sensitivity to initial conditions, however, initial results show that the LROE filter converges within fractions of an orbit with initialization errors that exceed 100 percent. The manuscript presents the invariants of motion, develops the variational equations for propagation, and demonstrates the effectiveness in an EKF approach. This approach is applied to space-based relative motion sensing to demonstrate the flexibility and benefit of LROE estimation. Several examples of drift-by, periodic orbits, and lead-follower estimation are generated.
Date of Conference: September 15-18, 2015
Track: Astrodynamics