  Quantum sensors based on single solid-state spins promise a unique
combination of sensitivity and spatial resolution. The key challenge in sensing
is to achieve minimum estimation uncertainty within a given time and with a
high dynamic range. Adaptive strategies have been proposed to achieve optimal
performance but their implementation in solid-state systems has been hindered
by the demanding experimental requirements. Here we realize adaptive d.c.
sensing by combining single-shot readout of an electron spin in diamond with
fast feedback. By adapting the spin readout basis in real time based on
previous outcomes we demonstrate a sensitivity in Ramsey interferometry
surpassing the standard measurement limit. Furthermore, we find by simulations
and experiments that adaptive protocols offer a distinctive advantage over the
best-known non-adaptive protocols when overhead and limited estimation time are
taken into account. Using an optimized adaptive protocol we achieve a magnetic
field sensitivity of $6.1 \pm 1.7$ nT *Hz$^{-1/2}$ over a wide range of 1.78
mT. These results open up a new class of experiments for solid-state sensors in
which real-time knowledge of the measurement history is exploited to obtain
optimal performance.
