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Global Navigation Satellite Systems (GNSS), such as GPS, have become an efficient, reliable and standard tool for a wide range of applications. However, when processing GNSS data, the stochastic model characterising the precision of observations and the correlations between them is usually simplified and incomplete, leading to overly optimistic accuracy estimates. This work extends the stochastic model using signal-to-noise ratio (SNR) measurements and time series analysis of observation residuals. The proposed SNR-based observation weighting model significantly improves the results of GPS data analysis, while the temporal correlation of GPS observation noise can be efficiently described by means of autoregressive moving average (ARMA) processes. Furthermore, this work includes an up-to-date overview of the GNSS error effects and a comprehensive description of various mathematical methods.
This proceedings book discusses state-of-the-art research on uncertainty quantification in mechanical engineering, including statistical data concerning the entries and parameters of a system to produce statistical data on the outputs of the system. It is based on papers presented at Uncertainties 2020, a workshop organized on behalf of the Scientific Committee on Uncertainty in Mechanics (Mécanique et Incertain) of the AFM (French Society of Mechanical Sciences), the Scientific Committee on Stochastic Modeling and Uncertainty Quantification of the ABCM (Brazilian Society of Mechanical Sciences) and the SBMAC (Brazilian Society of Applied Mathematics).
In geodesy and geoinformation science, as well as in many other technical disciplines, it is often not possible to directly determine the desired target quantities. Therefore, the unknown parameters must be linked with the measured values by a mathematical model which consists of the functional and the stochastic models. The functional model describes the geometrical–physical relationship between the measurements and the unknown parameters. This relationship is sufficiently well known for most applications. With regard to the stochastic model, two problem domains of fundamental importance arise: 1. How can stochastic models be set up as realistically as possible for the various geodetic observation methods and sensor systems? 2. How can the stochastic information be adequately considered in appropriate least squares adjustment models? Further questions include the interpretation of the stochastic properties of the computed target values with regard to precision and reliability and the use of the results for the detection of outliers in the input data (measurements). In this Special Issue, current research results on these general questions are presented in ten peer-reviewed articles. The basic findings can be applied to all technical scientific fields where measurements are used for the determination of parameters to describe geometric or physical phenomena.
This book constitutes the refereed proceedings of the 22nd International Conference on Analytical and Stochastic Modelling Techniques and Applications, ASMTA 2015, held in Albena, Bulgaria, in May 2015. The 15 full papers presented in this book were carefully reviewed and selected from numerous submissions. The papers discuss the latest developments in analytical, numerical and simulation algorithms for stochastic systems, including Markov processes, queueing networks, stochastic Petri nets, process algebras, game theory, etc.
Kinematic Systems in Geodesy, Surveying, and Remote Sensing provides a state-of-the-art discussion on the use of the Global Positioning System (GPS) in combination with Inertial Navigation Systems (INS) for detailed sensing of the Earth's surface. Divided into two parts, the book first discusses GPS/INS with respect to theory and modelling, equipment trends, estimation methods and quality control, algorithms, and software trends. It then describes the applications of these kinematic systems to positioning and navigation, modelling and measurement of gravity, gravity gradiometry, and altitude. This collection of 63 presentations documents the symposium of the same name held in Banff, Alberta, September 1990. It is the sixth volume of the International Association of Geodesy Symposia series published by Springer-Verlag New York.
An in-depth description of the theory and mathematical models behind the application of the global positioning system in geodesy and geodynamics. The contributions by leading experts in the field ensure a continuous flow of ideas and developments. The mathematical models for GPS measurements are developed in the first half of the book, and these are followed by GPS solutions for geodetic applications on local, regional and global scales.
IAG Symposium, Cairns, Australia, 22-26 August, 2005
Traditional methods for handling spatial data are encumbered by the assumption of separate origins for horizontal and vertical measurements. Modern measurement systems operate in a 3-D spatial environment. The 3-D Global Spatial Data Model: Foundation of the Spatial Data Infrastructure offers a new model for handling digital spatial data, the global spatial data model or GSDM. The GSDM preserves the integrity of three-dimensional spatial data while also providing additional benefits such as simpler equations, worldwide standardization, and the ability to track spatial data accuracy with greater specificity and convenience. This groundbreaking spatial model incorporates both a functional model and a stochastic model to connect the physical world to the ECEF rectangular system. Combining horizontal and vertical data into a single, three-dimensional database, this authoritative monograph provides a logical development of theoretical concepts and practical tools that can be used to handle spatial data more efficiently. The book clearly describes procedures that can be used to handle both ECEF and flat-Earth rectangular components in the context of a rigorous global environment.