Optimal Orbit Determination

Optimal Orbit Determination (OOD) methods have the following characteristics:

Optimal Orbit Determination
Property Manifestation in OOD
Input Tracking measurements with tracking platform locations, an a priori state estimate (inclusive of orbit estimate, and an a priori state error covariance matrix
Output Optimal state estimates and realistic state error covariance matrices
A priori orbit estimate Required
A priori state error covariance matrix Required
Methods Filter Methods are forward-time recursive sequential machines consisting of a repeating pattern of:
  • filter time update of the state estimate - propagates the state estimate forward, and
  • filter measurement update of the state estimate - incorporates the next measurement
Smoother Methods are backward-time recursive sequential machines consisting of a repeating pattern of state estimate refinement using filter outputs and backwards transition.
Time transitions (for both methods) Dominated most significantly by numerical orbit propagators, OOD methods are characterized by optimality:
  • Fundamental Theorem of Estimation (Sherman's Theorem)
  • Completeness in the state estimate structure
  • Connection of all state estimate models and state estimate error models to appropriate force modeling physics and tracker performance
  • Connection of all measurement models and measurement error models to appropriate tracker hardware description and tracker performance
Sources The search for optimality was begun by Wiener, Kalman, Bucy and others. Wright seeks significant improvements for OD using optimal estimation theory.

Operationally, OOD enables real-time performance, autonomous measurement processing, minimum orbit error variance estimates, and real-time trajectory accuracy performance assessment.

ODTK 6.5