  The ubiquitous presence of shot noise sets a fundamental limit to the
measurement precision in classical metrology. Recent advances in quantum
devices and novel quantum algorithms utilizing interference effects are opening
new routes for overcoming the detrimental noise tyranny. However, further
progress is limited by the restricted capability of existing algorithms to
account for the decoherence pervading experimental implementations. Here,
adopting a systematic approach to the evaluation of effectiveness of
metrological procedures, we devise the Linear Ascending Metrological Algorithm
(LAMA), which offers a remarkable increase in precision in the demanding
situation where a decohering quantum system is used to measure a continuously
distributed variable. We introduce our protocol in the context of magnetic
field measurements, assuming superconducting transmon devices as sensors
operated in a qudit mode. Our findings demonstrate a quantum-metrological
procedure capable of mitigating detrimental dephasing and relaxation effects.
