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The dynamics of quantum Fisher information (QFI) of the phase parameter in adriven two-state system is studied within the framework of non-Markoviandissipative process. The influences of memory effects, classical driving anddetunings on the parameter-estimation precision are demonstrated by exactlysolving the Hamiltonian under rotating-wave approximation. In sharp contrastwith the results obtained in the presence of Markovian dissipation, we findthat classical driving can drastically enhance the QFI, namely, the precisionof parameter estimation in the non-Markovian regime. Moreover, theparameter-estimation precision may even be preserved from the influence ofsurrounding non-Markovian dissipation with the assistance of classical driving.Remarkably, we reveal that the enhancement and preservation of QFI highlydepend on the combination of classical driving and non-Markovian effects.Finally, a phenomenological explanation of the underlying mechanism ispresented in detail via the quasimode theory

Classical-driving-enhanced parameter-estimation precision of a non-Markovian dissipative two-state system