  We consider processes where an electroweak gauge boson ($W$ and $Z$) is
produced in the decays of a heavy fermion. The polarization state of the
produced gauge boson is given in terms of a vector polarization and a rank-2
tensor polarization. In the rest frame of the mother fermion, these are given
directly by the dynamical parameters of the underlying theory. In a frame where
the mother particle is moving, the polarization parameters of the gauge boson
are dependent additionally upon kinematical factors. We show that these
kinematical factors depend only on the magnitude of the velocity of the mother
particle and derive analytical expressions for them. We apply the results to
pair production of heavy fermions at the LHC with one of the fermions decaying
to a gauge boson ($W$, $Z$) and a light Standard Model fermion. We construct
estimators of laboratory frame values of polarization parameters of the
produced gauge boson. These estimators can be used to estimate the laboratory
frame values of polarization parameters of the produced gauge boson without a
detailed simulation of the entire process. We validate our expressions with
detailed Monte Carlo simulations in the context of beyond the Standard Model
scenarios which have a vector-like top partner. We also indicate how to include
finite width effects of the heavy fermion in some special cases.
