Lustrumboek "The 5th Element"
model for various instrumental errors, e.g. various misalignment errors, scaling
errors, and non-perfect drag and attitude control. The behaviour of the coupled
system of proof masses is modelled by a system of differential equations ("forward
step"). From the solution of the equations of motion and after adding read-out
errors linear accelerations, Euler accelerations, and gravity gradients as measured
are computed ("backward step"). The linear accelerations are due to non-
gravitational forces mainly atmospheric drag and solar radiation pressure. They
are fed into the drag free control system (DFC). Then, a pair of on thrusters
corrects for these disturbances such that the orbit is reconstituted. From the
measured Euler accelerations and the observations of a star camera any attitude
motion of the satellite can be computed. This information is fed into the attitude
control system (ACS), causing a set of cold-gas proportional thrusters to control
this attitude motion. However, DFC and ACS cause control forces and moments,
respectively, which in turn affect for instance the satellite orbit, the satellite dynamics,
and the gradiometer signal. They are fed into the gradiometer forward model,
which closes the loop ('closed-loop simulation').
^non-gravitational
Fcontrol
modelling
Figure 1 1GOCE end-to-end closed-loop simulator
The result of such a closed-loop simulation is a time series of output gravity
gradients. We compare them with the input gravity gradients, and from the error
powerspectral densities (error PSD's) is computed. Figure 12 shows as an example
th error PSD derived from a simulation with all known types of errors switched on.
For comparison, the mission requirements of 5 mE/ÖHz and 1 /f behaviour below
27 cpr (5 x 1 0"3 Hz) are also shown in this figure. In a second step we propagate
14