  Restriction varieties in the orthogonal Grassmannian are subvarieties of
$OG(k, n)$ defined by rank conditions given by a flag that is not necessarily
isotropic with respect to the relevant symmetric bilinear form. In particular,
Schubert varieties of Type B and D are examples of restriction varieties. In
this paper, we introduce a resolution of singularities for restriction
varieties in $OG(k, n)$, and give a description of their singular locus by
studying components of the exceptional locus of the resolution.
