  Let $(A,\sigma)$ be an Azumaya algebra with involution over a regular ring
$R$. We prove that the Gersten-Witt complex of $(A,\sigma)$ defined by Gille is
isomorphic to the Gersten-Witt complex of $(A,\sigma)$ defined by
Bayer-Fluckiger, Parimala and the author. Advantages of both constructions are
used to show that the Gersten-Witt complex is exact when $\dim R\leq 3$,
$\mathrm{ind}\, A\leq 2$ and $\sigma$ is orthogonal or symplectic. This means
that the Grothendieck-Serre conjecture holds for the group $R$-scheme of
$\sigma$-unitary elements in $A$ under the same hypotheses; $R$ is not required
to contain a field.
