On the satellite altimeter crossover problem

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Mean sea surface heights and residual radial orbit errors are estimated simultaneously in a single global crossover adjustment of multiple cycles of satellite altimetry data. The rank defect inherent in the estimation problem is explicitly identified and treated in various ways to give solutions that minimise (in norm) either orbit errors or mean sea surface heights. The rank defect gives rise to geographically correlated orbit error, consisting of those components of the orbit error or those components of the map of sea surface heights which fall within the nullspace of the estimation problem and which cannot be distinguished as orbit error or ocean signal. We show that, in the case of Topex/Poseidon data, the geographically correlated error consists largely of long-wavelength and long-period sea surface fluctuations, which in the past has often been assigned as orbit error.