Accounting for Vibration Noise in Stochastic Measurement Errors of Inertial Sensors

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, such as inertial sensors, need to be extremely precise to obtain correct system diagnostics and accurate predictions, consequently requiring a rigorous calibration procedure before being employed. 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. In this context, the Generalized Method of Wavelet Moments emerges as a computationally efficient estimator with appropriate statistical properties and with different advantages over existing methods such as those based on likelihood estimation and the Allan variance. However it has this far not accounted for a significant stochastic noise that arises for many of these devices: vibration noise. This component can originate from different sources, including the internal mechanics of the sensors as well as the movement of these devices when placed on moving objects. 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.