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A short arc approach to the determination of the oceanic geoid from observations made by a satellite-borne radar altimeter entails the recovery of geoidal parameters simultaneously with the recovery of weakly constrained orbital state vectors defining a very large number (i.e., thousands) of independent, interlocking short arcs (arcs typically 1/6 to 1/8 revolution in length). Patterned characteristics of the normal equations make such a simultaneous solution possible, no matter how many sets of orbital parameters are to be recovered. Computer simulations demonstrate that the approach is strongly determinate and can reasonably be expected to produce an oceanic geoid having an rms accuracy approaching one meter from the reduction of GEOS C observations. The major advantage offered by the short arc approach is that it in no way depends on the establishment of a highly accurate reference orbit and thus places only minimal requirements on satellite tracking by external systems. An additional advantage is that observational residuals can be expected to be relatively uncompromised by orbital biases. (Modified author abstract).
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The computer program SAGG (Satellite Altimetry and Ground Gravity) has been used to determine the global geoid and the earth's gravity field, based on the combination of altimetric observations and gravity anomalies. A typical feature of SAGG is the simultaneous recovery of the orbit parameters and the spherical harmonic potential coefficients. The short arc adjustment mode makes these determinations possible without the requirement of highly precise reference orbits. In this mode, the state vector components are subject to adjustment and represent, in fact, a set of independent weighted parameters. Orbits good to approximately 20 m are adequate for precise reductions. Altimetric data processed by SAGG was gathered by the GEOS-3 satellite over adjacent portions of the Indian and South Pacific Oceans and a portion of the NORTH Atlantic; gravity anomaly data is represented by mean anomalies from over 2200 1 deg x 1 deg geographic blocks. The recovered geoid over most of the globe shows good agreement with gravimetric geoids. This is especially true of the areas covered by GEOS-3 when compared with the earlier reported results of the AFGL computer program SARRA (Short Arc Reduction of Radar Altimetry).