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 Mat\'ern processes. The advantages of our method are also illustrated using real time series from GNSS stations located in the Eastern part of the USA.Comment: 30 pages, 11 figures, 3 table

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.Comment: 30 pages, 9 figure

On Performance Evaluation of Inertial Navigation Systems: The Case of Stochastic Calibration

In this work we address the problem of rigorously evaluating the performances of a inertial navigation system under design in presence of multiple alternative choices. We introduce a framework based on Monte-Carlo simulations in which a standard extended Kalman filter is coupled with realistic and user-configurable noise generation mechanisms and attempts to recover a reference trajectory from noisy measurements. The evaluation of several statistical metrics of the solution, aggregated over hundreds of realizations, gives a reasonable estimate of the expected performances of the system in real-world conditions and allow the user to operate the choice between alternative setups. To show the generality of our approach, we consider an example application to the problem of stochastic calibration. Two compet- ing stochastic modeling techniques, namely, the widely popular Allan variance linear regression, and the emerging generalised method of wavelet moments are rigorously compared in terms of the framework defined metrics and in multiple scenarios. We find that the latter provides substantial advantages and should be preferred, at least for certain classes of inertial sensors. Our framework allows to consider a wide range of problems related to the quantification of navigation system performances such as, for example, the robustness of an INS with respect to outliers or other modeling imperfections. While real world experiments are essential to assess to performance of new methods they tend to be costly and are typically unable to lead to a sufficient number of replicates to evaluate, for example, the correctness of estimated uncertainty. Therefore, our method can bridge the gap between these experiments and pure statistical consideration as done, for example, in the stochastic calibration literature</p

Airborne sensor fusion: Expected accuracy and behavior of a concurrent adjustment

Tightly-coupled sensor orientation, i.e. the simultaneous processing of temporal (GNSS and raw inertial) and spatial (image and lidar) constraints in a common adjustment, has demonstrated significant improvement in the quality of attitude determination with small inertial sensors. This is particularly beneficial in kinematic laser scanning on lightweight aerial platforms, such as drones, which employ direct sensor orientation for the spatial interpretation of laser vectors. In this study, previously reported preliminary results are extended to assess the gain in accuracy of sensor orientation through leveraging all available spatio-temporal constraints in a dynamic network i) with a commercial IMU for drones and ii) with simultaneous processing of raw-observations of several low-quality IMUs. Additionally, we evaluate the influence of different types of spatial constraints (image 2D and point-cloud 3D tie-points) and flight geometries (with and without a cross flight line). We present the newly implemented estimation of confidence levels and compare those with the observed residual errors. The empirical evidence demonstrates that the use of spatial constraints increases the attitude accuracy of the derived trajectory by a factor of 2–3, both for the commercial and low-quality IMUs, while at the same time reducing the dispersion of geo-referencing errors, resulting in a considerably more precise and self-coherent geo-referenced point-cloud. We further demonstrate that the use of image constraints (additionally to lidar constraints) stabilizes the in-flight lidar boresight estimation by a factor of 3–10, establishing the feasibility of such estimation even in the absence of special calibration patterns or calibration targets

UAV in the advent of the twenties: Where we stand and what is next

The use of Unmanned Aerial Vehicles (UAVs) has surged in the last two decades, making them popular instruments for a wide range of applications, and leading to a remarkable number of scientific contributions in geoscience, remote sensing and engineering. However, the development of best practices for high quality of UAV mapping are often overlooked representing a drawback for their wider adoption. UAV solutions then require an inter-disciplinary research, integrating different expertise and combining several hardware and software components on the same platform. Despite the high number of peer-reviewed papers on UAVs, little attention has been given to the interaction between research topics from different domains (such as robotics and computer vision) that impact the use of UAV in remote sensing. The aim of this paper is to (i) review best practices for the use of UAVs for remote sensing and mapping applications and (ii) report on current trends - including adjacent domains - for UAV use and discuss their future impact in photogrammetry and remote sensing. Hardware developments, navigation and acquisition strategies, and emerging solutions for data processing in innovative applications are considered in this analysis. As the number and the heterogeneity of debated topics are large, the paper is organized according to very specific questions considered most relevant by the authors.Peer reviewe