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# Doppler satellite control

## Description

The application of the Transit Doppler satellite system to geodetic positioning, is investigated, using the operational ephemeris for satellite coordinates, and navigation-type receivers to track the satellites. A set of test data from eight stations in Atlantic Canada is analyzed. Four a priori decisions were to use the shortest possible integration interval (4.6 seconds); to use the technique of translocation to reduce the effect of ephemeris and refraction errors to allow the satellite trajectory to relax parallel to itself during the adjustment; and to process the data completely automatically. Transit mathematical models are related to the basic principles of electromagnetic metrology. The assumptions involved in Transit mathematical models are analyzed in detail. The least squares approximation, least squares spectral analysis and least squares estimation algorithms used here are related to the basic principles of Hilbert space optimization. The accuracy of the operational ephemeris is investigated by comparing it to the NWI, precise ephemeris; by comparison between stale and fresh ephemerides during injection passes; and Guier plane navigation. The operational ephemeris errors are found to be well represented by biases in the along track, radial, and cross track directions which have standard deviations (from pass to pass) of 26, 5 and 10 m respectively. The shape of the operational ephemeris is investigated by a comparison between Transit and Keplerian orbit elements; time series analysis of Transit variable orbit parameters; and least squares approximation of the Transit variable orbit parameters. The shape of each of the variable orbit parameters ∆E, ∆a, ɳ is well approximated by the base functions ɸ = {1, cos2nt, sin2nt, t} where n is the satellite mean motion and t is time. The measurement variances of three models of Transi navigation receiver are found to be 1.5, 4.0 and 10.0 counts [subscript 2] respectively for the ITT 5001, Marconi 722 and Magnavox 702. The internal consistency of multipass point positioning station coordinates is found to be 1.3 m. However this is found to be optimistic, since the orbit was held fixed for these computations. The internal consistency of adjusted network coordinates is less than one metre, but again this is found to be optimistic. The index of external consistency (rms value of ∆/σ [subscript ∆]) between independent point positioning solutions at one station are found to be 2.4 to 4.0 for point positioning when the orbit is fixed and 1.2 to 1.5 when the orbit is relaxed. The external consistency between two sets of point positioning solutions using data one year apart is 4.7, attributed principally to uncorrected pole motion effects. The external consistency between an adjusted Transit network and a terrestrial network is 1.6.