  The measurement of data over time and/or space is of utmost importance in a
wide range of domains from engineering to physics. Devices that perform these
measurements therefore need to be extremely precise to obtain correct system
diagnostics and accurate predictions, consequently requiring a rigorous
calibration procedure which models their errors before being employed. While
the deterministic components of these errors do not represent a major modelling
challenge, most of the research over the past years has focused on delivering
methods that can explain and estimate the complex stochastic components of
these errors. This effort has allowed to greatly improve the precision and
uncertainty quantification of measurement devices but has this far not
accounted for a significant stochastic noise that arises for many of these
devices: vibration noise. Indeed, having filtered out physical explanations for
this noise, a residual stochastic component often carries over which can
drastically affect measurement precision. This component can originate from
different sources, including the internal mechanics of the measurement devices
as well as the movement of these devices when placed on moving objects or
vehicles. To remove this disturbance from signals, this work puts forward a
modelling framework for this specific type of noise and adapts the Generalized
Method of Wavelet Moments to estimate these models. We deliver the asymptotic
properties of this method when applied to processes that include vibration
noise and show the considerable practical advantages of this approach in
simulation and applied case studies.
