  The magnetic diagnostics subsystem of the LISA Technology Package (LTP) on
board the LISA PathFinder (LPF) spacecraft includes a set of four tri-axial
fluxgate magnetometers, intended to measure with high precision the magnetic
field at their respective positions. However, their readouts do not provide a
direct measurement of the magnetic field at the positions of the test masses,
and hence an interpolation method must be designed and implemented to obtain
the values of the magnetic field at these positions. However, such
interpolation process faces serious difficulties. Indeed, the size of the
interpolation region is excessive for a linear interpolation to be reliable
while, on the other hand, the number of magnetometer channels does not provide
sufficient data to go beyond the linear approximation. We describe an
alternative method to address this issue, by means of neural network
algorithms. The key point in this approach is the ability of neural networks to
learn from suitable training data representing the behavior of the magnetic
field. Despite the relatively large distance between the test masses and the
magnetometers, and the insufficient number of data channels, we find that our
artificial neural network algorithm is able to reduce the estimation errors of
the field and gradient down to levels below 10%, a quite satisfactory result.
Learning efficiency can be best improved by making use of data obtained in
on-ground measurements prior to mission launch in all relevant satellite
locations and in real operation conditions. Reliable information on that
appears to be essential for a meaningful assessment of magnetic noise in the
LTP.
