Abstract
The determination of satellite orbital and attitude position and velocity from measurement of a single earth magnetic field (emf) vector without additional measurements, but using a state estimator, is a challenging problem. It is not obvious from first glance whether a solution exists at all – whether the problem is observable with the measurement of only a single emf vector, and an analysis is necessary. This paper performs this analysis for a simple linear system model. Almost circular low earth nearly polar orbits and a dipole emf model are considered. Although these are rather restrictive assumptions they nevertheless provide considerable insight. Both a purely algebraic situation as well as dynamic estimation are studied. It is shown that if the emf induction vector magnitude is used to estimate satellite orbit (position and velocity) and its three projections are used to estimate the attitude, that the situation is sufficiently observable for orbit and attitude determination using just magnetometer...
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