Authors: Y. Kim; G. Vukovich
Addresses: Canadian Space Agency, Space Science and Technologies, St. Hubert, QC, J3Y 8Y9, Canada ' Lassonde School of Engineering, York University, Toronto, ON M3J 1P3, Canada
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 measurements. However, for nearly polar orbits, longitude and east velocity are difficult to estimate due to weak observability, and estimation convergence time can be lengthy with poor accuracy.
Keywords: satellite orbit estimation; satellite attitude estimation; magnetometer; Earth magnetic field; EMF induction vector magnitude; satellite navigation; low Earth orbit; linear system modelling; satellite velocity; satellite position; satellite orbits.
International Journal of Space Science and Engineering, 2014 Vol.2 No.3, pp.276 - 304
Received: 18 Mar 2014
Accepted: 26 May 2014
Published online: 04 Aug 2014 *