Orbit Error Transition Method

The OrbitErrorTransitionMethod attribute specifies the means of computing the transitive partials for the orbit error estimate including the 6x6 orbit state and any estimated force model parameters (such as the ballistic coefficient).

Available Options

The following options are available:

Orbit Error Transition Methods
Method Description
Variational Equations The force model variational equations are used during the computation of transitive partials. Note that many of the individual force models have settings controlling inclusion in the variational equations. This method is efficient and works well for both dense data and prediction.
Numerical

If numerical partials are selected, the orbit error transition is computed by forward differencing numerically integrated perturbations to the nonlinear trajectory. This method is comparatively slow, but is included for comparison purposes.

Note: This method is not supported when generating a predicted ephemeris using the Gauss-Jackson integrator. When using the Gauss-Jackson integrator, variational equations will always be used regardless of this setting.

Some Background

The orbit error transition matrix is an NxN matrix that maps a slight deviation in the position/velocity/force model parameters of the satellite to a deviation at a later time. This is part of the overall state error transition matrix, which includes all elements of the estimated state. The state error transition matrix is used in the propagation of the covariance matrix. The variational equations are the partial derivatives of the accelerations with respect to the satellite position, velocity and estimated force model parameters and are used to compute the time derivative of the orbit error transition matrix. In this case, the orbit error transition matrix is numerically integrated along with the satellite state during a time update. In the case where numerical partials are selected, ODTK actually propagates N additional trajectories (each with a small perturbation to one component of the position or velocity or an estimated force model parameter) and uses these to construct the orbit error transition matrix.

ODTK 6.5