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.

翻译：数据在时间与空间上的测量在工程到物理等众多领域中至关重要。执行这些测量的设备必须极高精度以获得正确的系统诊断和准确预测，因此在使用前需要建立严格的校准程序来建模其误差。尽管误差的确定成分不构成主要建模挑战，但过去多年研究主要集中在提供能够解释和估计这些误差复杂随机成分的方法。这些努力已极大提升了测量设备的精度和不确定性量化，但迄今未考虑许多设备中存在的显著随机噪声：振动噪声。实际上，在滤除此噪声的物理成因后，残留的随机成分常会严重影响测量精度。该成分可能源于多种来源，包括测量设备内部机械结构，以及设备置于运动物体或车辆上时的移动。为从信号中消除这种干扰，本文提出针对此类特定噪声的建模框架，并改进广义小波矩量法来估计这些模型。我们给出了该方法应用于含振动噪声过程时的渐近性质，并通过仿真与案例研究展示了该方法的显著实践优势。