  The inconsistency between experiments in the measurements of the local
Universe expansion rate, the Hubble constant, suggests unknown systematics in
the existing experiments or new physics. Gravitational-wave standard sirens, a
method to independently provide direct measurements of the Hubble constant,
have the potential to address this tension. Before that, it is critical to
ensure there is no substantial systematics in the standard siren method. A
significant systematic has been identified when the viewing angle of the
gravitational-wave sources, the compact binary coalescences, is inferred
inaccurately from electromagnetic observations of the sources. Such systematic
has led to more than 10% discrepancy in the standard siren Hubble constant
measurements with the observations of binary neutron star merger, GW170817. In
this Letter, we develop a new formalism to infer and mitigate this systematic.
We demonstrate that the systematic uncertainty of the Hubble constant
measurements can be reduced to smaller than their statistical uncertainty with
5, 10, and 20 binary neutron star merger observations. We show that our
formalism successfully reduces the systematics even if the shape of the biased
viewing angle distribution does not follow precisely the model we choose. Our
formalism ensures unbiased standard siren Hubble constant measurements when the
binary viewing angles are inferred from electromagnetic observations.
