On odd unitary Steinberg group

Let $R$ be a ring with pseudo-involution, $\mathfrak{L}$ be an odd form parameter, $\mathrm{U}(2n,R,\mathfrak{L})$ be an odd hyperbolic unitary group, $\mathrm{E}\mathrm{U}(2n,R,\mathfrak{L})$ be it elementary subgroup and $\mathrm{S}\mathrm{t}\mathrm{U}(2n,R,\mathfrak{L})$ be an odd unitary Steinberg group. We compute the Schur multipliers of $\mathrm{S}\mathrm{t}\mathrm{U}(2n,R,\mathfrak{L})$ and $\mathrm{E}\mathrm{U}(R,\mathfrak{L})$.