SpiceGravityDynamics.compute_covariance_dynamics

giant.ufo.dynamics:

SpiceGravityDynamics.compute_covariance_dynamics(state, et_time, radial_distance_cb, position_sc_to_bodies, radial_distance_sc_to_bodies)[source]

This method computes the dynamics for the covariance matrix.

The dynamics for the covariance matrix is the product of the Jacobian matrix of the dynamics for the state with respect to the state and the current covariance matrix, plus the process noise matrix

\[\mathbf{\partial \mathbf{P}}{\partial t} = \mathbf{J}\mathbf{P} + \mathbf{P}\mathbf{J}^T + \mathbf{Q}\]

where \(\mathbf{P}\) is the covariance matrix, \(t\) is time,

\[\mathbf{J}=\frac{\partial \mathbf{f}(\mathbf{x})}{\partial\mathbf{x}}\]

with \(\mathbf{J}\) being the Jacobian matrix, \(\mathbf{f}(\mathbf{x})\) is the state dynamics function, and \(\mathbf{x}\) is the state vector.

Parameters:

  • state (ndarray) – The state vector at the current time

  • et_time (float) – The ephemeris time

  • radial_distance_cb (float) – The distance from the central body to the body we are estimating

  • position_sc_to_bodies (List[ndarray]) – The position from the spacecraft to the other bodies considered for gravity

  • radial_distance_sc_to_bodies (List[float]) – The distance from the spacecraft to the other bodies

Returns:

The covariance time derivative.

Return type:

ndarray