  Localized spins in the solid state are attracting widespread attention as
highly sensitive quantum sensors with nanoscale spatial resolution and
fascinating applications. Recently, adaptive measurements were used to improve
the dynamic range for spin-based sensing of deterministic Hamiltonian
parameters. Here we explore a very different direction -- spin-based adaptive
sensing of random noises. First, we identify distinguishing features for the
sensing of magnetic noises compared with the estimation of deterministic
magnetic fields, such as the different dependences on the spin decoherence, the
different optimal measurement schemes, the absence of the modulo-2\pi phase
ambiguity, and the crucial role of adaptive measurement. Second, we perform
numerical simulations that demonstrate significant speed up of the
characterization of the spin decoherence time via adaptive measurements. This
paves the way towards adaptive noise sensing and coherence protection.
