  Coalescing binary black holes emit anisotropic gravitational radiation. This
causes a net emission of linear momentum that produces a gradual acceleration
of the source. As a result, the final remnant black hole acquires a
characteristic velocity known as recoil velocity or gravitational kick. The
symmetries of gravitational wave emission are reflected in the interactions of
the gravitational wave modes emitted by the binary. In this work we make use of
the rich information encoded in the higher-order modes of the gravitational
wave emission to infer the component of the kick along the line-of-sight (or
\textit{radial kick}). We do this by performing parameter inference on
simulated signals given by numerical relativity waveforms for non-spinning
binaries using numerical relativity templates of aligned-spin (non-precessing)
binary black holes. We find that for suitable sources, namely those with mass
ratio $q\geq 2$ and total mass $M \sim 100M_\odot$, and for modest radial kicks
of $120km/s$, the $90\%$ credible intervals of our posterior probability
distributions can exclude a zero kick at a signal-to-noise ratio of $15$; using
a single Advanced LIGO detector working at its early sensitivity. The
measurement of a non-zero radial kick component would provide the first
observational signature of net transport of linear momentum by gravitational
waves away from their source.
