1 DEMONSTRATION OF THE DSST STATE TRANSITION MATRIX TIME-UPDATE PROPERTIES USING THE LINUX GTDS PROGRAM

The semi-analytical theory for the motion of a space object replaces the conventional equations of motion with two formulas: (1) equations of motion for the mean equinoctial elements, and (2) expressions for the short periodic motion in the equinoctial elements. Very complete force models have been developed for the mean element equations of motion and for the short periodic motion. There is also a semi-analytical theory for the partial derivatives of the perturbed motion. An interpolation strategy greatly assists in producing the mean elements, the osculating elements, the perturbed position and velocity, and the partial derivatives at the output request times. The semi-analytical satellite theory has been interfaced with a variety of batch least squares and Kalman Filter estimation processes. The current effort improves the software implementation of the semi-analytical theory for the partial derivatives so that (1) the mean element state transition matrix can be integrated backwards in time consistent with the interpolation architecture and (2) the epoch in a mean element orbit determination process can have an arbitrary location in a span of observation data. Both of these new capabilities support studies of the propagation of the state error covariance in the mean equinoctial elements. The paper describes the mathematical formulation and the software implementation in the Linux GTDS DSST program, and provides several test cases to illustrate the capabilities