Thomas H. Meyer's Peer-reviewed ArticlesCopyright (c) 2019 University of Connecticut All rights reserved.
https://opencommons.uconn.edu/thmeyer_articles
Recent documents in Thomas H. Meyer's Peer-reviewed Articlesen-usSun, 25 Aug 2019 08:53:32 PDT3600Position Errors Caused by GPS Height of Instrument Blunders
https://opencommons.uconn.edu/thmeyer_articles/4
https://opencommons.uconn.edu/thmeyer_articles/4Mon, 18 Jul 2005 12:31:36 PDT
Height of instrument (HI) blunders in GPS measurements cause position errors. These errors can be pure vertical, pure horizontal, or a mixture of both. There are different error regimes depending on whether both the base and the rover both have HI blunders, if just the base has an HI blunder, or just the rover has an HI blunder. The resulting errors are on the order of 30 cm for receiver separations of 1000 km for an HI blunder of 2 m. Given the complicated nature of the errors, we believe it would be difficult, if not impossible, to detect such errors by visual inspection. This serves to underline the necessity to enter GPS HI's correctly.
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Thomas H. Meyer et al.What Does Height Really Mean? Part II: Physics and Gravity
https://opencommons.uconn.edu/thmeyer_articles/3
https://opencommons.uconn.edu/thmeyer_articles/3Fri, 13 May 2005 11:36:13 PDT
This is the second paper in a four-part series considering the fundamental question, “what does the word height really mean?” The first paper in this series explained that a change in National Geodetic Survey’s policy, coupled with the modern realities of GPS surveying, have essentially forced practicing surveyors to come to grips with the myriad of height definitions that previously were the sole concern of geodesists. The distinctions between local and equipotential ellipsoids were considered, along with an introduction to mean sea level. This paper brings these ideas forward by explaining mean sea level and, more importantly, the geoid. The discussion is grounded in physics from which gravitational force and potential energy will be considered, leading to a simple derivation of the shape of the Earth’s gravity field. This lays the foundation for a simplistic model of the geoid near Mt. Everest, which will be used to explain the undulations in the geoid across the entire Earth. The terms geoid, plumb line, potential, equipotential surface, geopotential number, and mean sea level will be explained, including a discussion of why mean sea level is not everywhere the same height; why it is not a level surface.
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Thomas H. Meyer et al.What Does Height Really Mean? Part I: Introduction
https://opencommons.uconn.edu/thmeyer_articles/2
https://opencommons.uconn.edu/thmeyer_articles/2Fri, 13 May 2005 11:32:07 PDT
This is the first paper in a four-part series considering the fundamental question, “what does the word height really mean?” National Geodetic Survey (NGS) is embarking on a height modernization program in which, in the future, it will not be necessary for NGS to create new or maintain old orthometric height benchmarks. In their stead, NGS will publish measured ellipsoid heights and computed Helmert orthometric heights for survey markers. Consequently, practicing surveyors will soon be confronted with coping with these changes and the differences between these types of height. Indeed, although “height’” is a commonly used word, an exact definition of it can be difficult to find. These articles will explore the various meanings of height as used in surveying and geodesy and present a precise definition that is based on the physics of gravitational potential, along with current best practices for using survey-grade GPS equipment for height measurement. Our goal is to review these basic concepts so that surveyors can avoid potential pitfalls that may be created by the new NGS height control era. The first paper reviews reference ellipsoids and mean sea level datums. The second paper reviews the physics of heights culminating in a simple development of the geoid and explains why mean sea level stations are not all at the same orthometric height. The third paper introduces geopotential numbers and dynamic heights, explains the correction needed to account for the non-parallelism of equipotential surfaces, and discusses how these corrections were used in NAVD 88. The fourth paper presents a review of current best practices for heights measured with GPS.
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Thomas H. Meyer et al.The Discontinuous Nature of Kriging Interpolation for Digital Terrain Modeling
https://opencommons.uconn.edu/thmeyer_articles/1
https://opencommons.uconn.edu/thmeyer_articles/1Fri, 13 May 2005 11:26:00 PDT
Kriging is a widely employed method for interpolating and estimating elevations from digital elevation data. Its place of prominence is due to its elegant theoretical foundation and its convenient practical implementation. From an interpolation point of view, kriging is equivalent to a thin-plate spline and is one species among the many in the genus of weighted inverse distance methods, albeit with attractive properties. However, from a statistical point of view, kriging is a best linear unbiased estimator and, consequently, has a place of distinction among all spatial estimators because any other linear estimator that performs as well as kriging (in the least squares sense) must be equivalent to kriging, assuming that the parameters of the semivariogram are known. Therefore, kriging is often held to be the gold standard of digital terrain model elevation estimation. However, I prove that, when used with local support, kriging creates discontinuous digital terrain models, which is to say, surfaces with “rips” and “tears” throughout them. This result is general; it is true for ordinary kriging, kriging with a trend, and other forms. A U.S. Geological Survey (USGS) digital elevation model was analyzed to characterize the distribution of the discontinuities. I show that the magnitude of the discontinuity does not depend on surface gradient but is strongly dependent on the size of the kriging neighborhood.
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Thomas H. Meyer