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Quantum metrology studies quantum strategies which enable us to outperformtheir classical counterparts. In this framework, the existence of perfectclassical reference frames is usually assumed. However, such ideal referenceframes might not always be available. The reference frames required inmetrology strategies can either degrade or become misaligned during theestimation process. We investigate how the imperfectness of reference framesleads to noise which in general affects the ultimate precision limits inmeasurement of physical parameters. Moreover, since quantum parameterestimation can be phrased as a quantum communication protocol between twoparties, our results provide deeper insight into quantum communicationprotocols with misaligned reference frames. Our framework allows for the studyof general noise on the efficiency of such schemes.

Quantum parameter estimation with imperfect reference frames