  We experimentally investigate an optical frequency standard based on the
$^2S_{1/2} (F=0)\to {}^2F_{7/2} (F=3)$ electric octupole (\textit{E}3)
transition of a single trapped $^{171}$Yb$^+$ ion. For the spectroscopy of this
strongly forbidden transition, we utilize a Ramsey-type excitation scheme that
provides immunity to probe-induced frequency shifts. The cancellation of these
shifts is controlled by interleaved single-pulse Rabi spectroscopy which
reduces the related relative frequency uncertainty to $1.1\times 10^{-18}$. To
determine the frequency shift due to thermal radiation emitted by the ion's
environment, we measure the static scalar differential polarizability of the
\textit{E}3 transition as $0.888(16)\times 10^{-40}$ J m$^2$/V$^2$ and a
dynamic correction $\eta(300~\text{K})=-0.0015(7)$. This reduces the
uncertainty due to thermal radiation to $1.8\times 10^{-18}$. The residual
motion of the ion yields the largest contribution $(2.1\times 10^{-18})$ to the
total systematic relative uncertainty of the clock of $3.2\times 10^{-18}$.
