  We propose a state estimation scheme for spins, using a modified setup of the
Stern-Gerlach experiment, in which a beam of neutral spin-1/2 point particles
interacts with a quadrupolar magnetic field. The proposed linear inversion
estimation procedure, based on a quadrant intensity detector, requires a
suitable initial spatial state of the beam. The statistical characterization of
the estimator of the initial spin state allows us not only to associate an
error to the estimated parameters, but also to define a measure for comparing
estimation procedures corresponding to different Stern-Gerlach setups.
