  Quantum metrology with entangled resources aims to achieve sensitivity beyond
the standard quantum limit by harnessing quantum effects even in the presence
of environmental noise. So far, sensitivity has been mainly discussed from the
viewpoint of reducing statistical errors under the assumption of perfect
knowledge of a noise model. However, we cannot always obtain complete
information about a noise model due to coherence time fluctuations, which are
frequently observed in experiments. Such unknown fluctuating noise leads to
systematic errors and nullifies the quantum advantages. Here, we propose an
error-mitigated quantum metrology that can filter out unknown fluctuating noise
with the aid of purification-based quantum error mitigation. We demonstrate
that our protocol mitigates systematic errors and recovers superclassical
scaling in a practical situation with time-inhomogeneous bias-inducing noise.
Our results reveal the usefulness of purification-based error mitigation for
unknown fluctuating noise, thus paving the way not only for practical quantum
metrology but also for quantum computation affected by such noise.
