Least-squares prediction of horizontal coordinate distortions in Canada |
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| Authors: | Gérard Lachapelle André Mainville |
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| Institution: | (1) Sheltech Canada, P.O. Box 100, T2P 2H5 Calgary, Alberta, Canada;(2) Geodetic Survey of Canada, 615, Booth Street, K1A 0E9 Ottawa, Ontario, Canada |
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| Abstract: | A least-squares prediction method is described to estimate horizontal coordinate distortions at lower order points of a network
using known coordinate differences (NAD27 coordinate distortions Δϕ′s and Δλ′s) at higher order points between NAD27 coordinates
and coordinates derived from a recent (MAY 76), relatively distortion free, adjustment of these points. Empirical autocovariance
functions of Δϕ and Δλ and crosscovariance function between Δϕ and Δλ are derived from some 5,250 data points and modelled
using series of exponential functions. Empirical mean square values of Δϕ and Δλ, which are a measure of the distortions in
NAD27 ϕ and λ, are 0.051 and 0.645 arcsecs2 respectively. The corresponding mean value of the product ΔϕΔλ, which is a measure of the correlation between Δϕ and Δλ,
is 0.056 arcsecs2. The accuracy obtainable for predicted Δϕ and Δλ at an arbitrary point (e.g., lower order station) is a function of the accuracy
and configuration of known Δϕ′s and Δλ′s in the surrounding area. Accuracies obtainable for various types of data configuration
are given. Under favorable conditions taking place in about 60% of cases, accuracies in terms of ms agreement with known values
of 0″.02 (0.6 m) and 0″.01 (0.2 m along parallel at latitude 50°) for the predicted latitude and longitude distortions are
obtainable. Finally, a comparison with a method based on the use of complex polynomials is made.
Presented at International Symposium on Geodetic Networks and Computations, Munich, August–September 1981. |
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