Treatment of Geodetic Leveling in the Integrated Geodesy Approach
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Date
1988-09
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Ohio State University. Division of Geodetic Science
Abstract
Integrated geodesy is a method which models a wide variety of surveying measurements in terms of geometric positions and the earth's geopotential. Using heterogeneous data, both geometric and gravimetric quantities are simultaneously estimated by a least-squares procedure. Heretofore, geodetic leveling differences have been reduced into pseudo-observables using assumed values of gravity. This study compares the errors in estimates of geometric and gravimetric quantities obtained from integrated geodesy least-squares adjustments of geodetic leveling differences, potential differences, or Helmert height differences. The error computation is based on a procedure used by Molodensky. An analytic model (a Molodensky mountain) composed of a point mass and the OSU86F geopotential, provides a priori values of geometric and gravimetric quantities, including gravity and level measurements on a mountain. Derived data, which correspond to the pseudo-observables, are formed from the analytic data set. Integrated adjustments are computed using models, and analytic and derived data consistent with a given observational scenario. The error is the difference between the estimates and the true values from the analytic model. I derive a new, integrated model for geodetic level differences based upon a normal plane construction. Results show the geodetic level difference and the potential difference models are comparable, and that the Helmert height difference model gives slightly worse performance. A model variant, geodetic level differences summed between benchmarks, was computationaly faster than the level difference model, but showed larger errors . The estimation error between these models was less than the measurement noise of leveling. Linearization about an ellipsoidal geopotential model, instead of a spherical harmonic expansion model, was found to be a greater error source than the choice of a model. Inclusion of ellipsoidal height differences (such as obtained from reduction of Global Positioning System signals) or addition of a grid of gravity data, improved both geometric and gravimetric estimates. New equations, expressed in terms of elliptic integrals, were derived for the covariance and cross-covariances of a point mass.