  Future in situ space plasma investigations will likely involve spatially
distributed observatories comprised of multiple spacecraft, beyond the four and
five spacecraft configurations currently in operation. Inferring the magnetic
field structure across the observatory, and not simply at the observation
points, is a necessary step towards characterizing fundamental plasma processes
using these unique multi-point, multi-scale data sets. We propose improvements
upon the classic first-order reconstruction method, as well as a second-order
method, utilizing magnetometer measurements from a realistic nine-spacecraft
observatory. The improved first-order method, which averages over select
ensembles of four spacecraft, reconstructs the magnetic field associated with
simple current sheets and numerical simulations of turbulence accurately over
larger volumes compared to second-order methods or first-order methods using a
single regular tetrahedron. Using this averaging method on data sets with fewer
than nine measurement points, the volume of accurate reconstruction compared to
a known magnetic vector field improves approximately linearly with the number
of measurement points.
