Sensors based on single spins can enable magnetic field detection with very
high sensitivity and spatial resolution. Previous work has concentrated on
sensing of a constant magnetic field or a periodic signal. Here, we instead
investigate the problem of estimating a field with non-periodic variation
described by a Wiener process. We propose and study, by numerical simulations,
an adaptive tracking protocol based on Bayesian estimation. The tracking
protocol updates the probability distribution for the magnetic field, based on
measurement outcomes, and adapts the choice of sensing time and phase in real
time. By taking the statistical properties of the signal into account, our
protocol strongly reduces the required measurement time. This leads to a
reduction of the error in the estimation of a time-varying signal by up to a
factor 4 compared to protocols that do not take this information into account.Comment: 10 pages, 6 figure
