  Quantum magnetic field sensing is an important technology for material
science and biology. Although experimental imperfections affect the
sensitivity, repetitions of the measurements decrease the estimation
uncertainty by a square root of the total number of the measurements if there
are only statistical errors. However, it is difficult to precisely characterize
the coherence time of the system because it fluctuates in time in realistic
conditions, which induces systematic errors. In this case, due to residual bias
of the measured values, estimation uncertainty cannot be lowered than a finite
value even in the limit of the infinite number of measurements. On the basis of
the fact that the decoherence dynamics in the so-called Zeno regime are not
significant compared to other regimes, we propose a novel but very simple
protocol to use measurements in the Zeno regime for reducing systematic errors.
Our scheme allows the estimation uncertainty $\delta ^2 \omega$ to scale as
$L^{1/4}$ where $L$ denotes the number of the measurements even when we cannot
precisely characterize the coherence time.
