Observable quantities in satellite gradiometry: Fid-Bau Portal

Observable quantities in satellite gradiometry

Vermeer, Martin

Abstract Deriving the observables for satellite gravity gradiometry, several workers have identified the invariants under spatial rotation of the gravitation gradient tensor for obtaining quantities insensitive to the precise (unrecoverable) attitude of the satellite. Extending this work we show:Considering that an approximate (not precise) attitude recovery for these, three-axes-stabilised, satellites is to be expected, one can identifythree independent invariants instead of two.Besides studying gradient tensor invariants for one observation time, one should also study (as withGPS observables) first and seconddifferences between successive tensor component values in time. Bias and trend patterns in the measured tensor components caused by satellite rotation uncertainty, and by attitude uncertainty in some cross components, are shown to cancel. Information thus obtained is exclusively high-frequency, however. Observation equations for gradiometry are derived taking three satellite attitude angles into account. Various alternatives for the satellite’s nominalattitude law are discussed.