arXiv subjects

Davide A. Cucci

Publications and source records attributed to Davide A. Cucci.

4 recordsLinked to original sources

arXiv2023

Accounting for Vibration Noise in Stochastic Measurement Errors

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.

stat.ME↗

arXiv2022

The Generalized Method of Wavelet Moments with Exogenous Inputs: a Fast Approach for the Analysis of GNSS Position Time Series

The Global Navigation Satellite System (GNSS) daily position time series are often described as the sum of stochastic processes and geophysical signals which allow studying global and local geodynamical effects such as plate tectonics, earthquakes, or ground water variations. In this work we propose to extend the Generalized Method of Wavelet Moments (GMWM) to estimate the parameters of linear models with correlated residuals. This statistical inferential framework is applied to GNSS daily position time series data to jointly estimate functional (geophysical) as well as stochastic noise models. Our method is called GMWMX, with X standing for eXogeneous variable: it is semi-parametric, computationally efficient and scalable. Unlike standard methods such as the widely used Maximum Likelihood Estimator (MLE), our methodology offers statistical guarantees, such as consistency and asymptotic normality, without relying on strong parametric assumptions. At the Gaussian model, our results show that the estimated parameters are similar to the ones obtained with the MLE. The computational performances of our approach has important practical implications. Indeed, the estimation of the parameters of large networks of thousands of GNSS stations quickly becomes computationally prohibitive. Compared to standard methods, the processing time of the GMWMX is over $1000$ times faster and allows the estimation of large scale problems within minutes on a standard computer. We validate the performances of our method via Monte-Carlo simulations by generating GNSS daily position time series with missing observations and we consider composite stochastic noise models including processes presenting long-range dependence such as power-law or Matérn processes. The advantages of our method are also illustrated using real time series from GNSS stations located in the Eastern part of the USA.

stat.ME↗

arXiv2021

Multi-Signal Approaches for Repeated Sampling Schemes in Inertial Sensor Calibration

Inertial sensor calibration plays a progressively important role in many areas of research among which navigation engineering. By performing this task accurately, it is possible to significantly increase general navigation performance by correctly filtering out the deterministic and stochastic measurement errors that characterize such devices. While different techniques are available to model and remove the deterministic errors, there has been considerable research over the past years with respect to modelling the stochastic errors which have complex structures. In order to do the latter, different replicates of these error signals are collected and a model is identified and estimated based on one of these replicates. While this procedure has allowed to improve navigation performance, it has not yet taken advantage of the information coming from all the other replicates collected on the same sensor. However, it has been observed that there is often a change of error behaviour between replicates which can also be explained by different (constant) external conditions under which each replicate was taken. Whatever the reason for the difference between replicates, it appears that the model structure remains the same between replicates but the parameter values vary. In this work we therefore consider and study the properties of different approaches that allow to combine the information from all replicates considering this phenomenon, confirming their validity both in simulation settings and also when applied to real inertial sensor error signals. By taking into account parameter variation between replicates, this work highlights how these approaches can improve the average navigation precision as well as obtain reliable estimates of the uncertainty of the navigation solution.

eess.SP↗

arXiv2021

Scale-wise Variance Minimization for Optimal Virtual Signals: An Approach for Redundant Gyroscopes

The increased use of low-cost gyroscopes within inertial sensors for navigation purposes, among others, has brought to the development of a considerable amount of research in improving their measurement precision. Aside from developing methods that allow to model and account for the deterministic and stochastic components that contribute to the measurement errors of these devices, an approach that has been put forward in recent years is to make use of arrays of such sensors in order to combine their measurements thereby reducing the impact of individual sensor noise. Nevertheless combining these measurements is not straightforward given the complex stochastic nature of these errors and, although some solutions have been suggested, these are limited to certain specific settings which do not allow to achieve solutions in more general and common circumstances. Hence, in this work we put forward a non-parametric method that makes use of the wavelet cross-covariance at different scales to combine the measurements coming from an array of gyroscopes in order to deliver an optimal measurement signal without needing any assumption on the processes underlying the individual error signals. We also study an appropriate non-parametric approach for the estimation of the asymptotic covariance matrix of the wavelet cross-covariance estimator which has important applications beyond the scope of this work. The theoretical properties of the proposed approach are studied and are supported by simulations and real applications, indicating that this method represents an appropriate and general tool for the construction of optimal virtual signals that are particularly relevant for arrays of gyroscopes. Moreover, our results can support the creation of optimal signals for other types of inertial sensors other than gyroscopes as well as for redundant measurements in other domains other than navigation.

stat.AP↗